文档内容
Numerical Drills
第一组 14题
1.What is the average of 520，540and 560?
A. 550 B. 530 C. 540 D. 540.5
答案解析：C
There is no need to use the average formula to solNve this problem.Notice how
the dfrence between both 560 and 520 and 540 are the same.
560-540=+20
520-540= -20
Remember.The average is the value which cancels out the dfrences between the
items in the set and the average telf.+20 and -20 cancel each other out (20-20=0)
Thus,you can detemine tatthe average is 540 without using the average fomula.
If you were to use the formula, you would calculate:
Average =(sum of tems)/(number of tems)= (520+540+560)3 = 1620/3= 540
2.Ruth eared a score of 80 on her history exam and a score of 65 on her maths
exam.What is the average test score?
A. 85 B. 72.5 C. 70 D. 77
答案解析：B
Ruth eamed 2 grades:80 and 65.
In order to calculate the average of the two grades, sum up the grades and divide by 2 ：
(80+65)2=145/72=72.5.
3.Calculate the average of the following numbers:3,8,12,21,and 26.
A. 14.5 B. 14 C. 13 D. 12
答案解析：B
The lomua to cacuale an average is.
Awerage = sum of tems/ number of lemns = (3+8+12+21+26)/5= 70/5= 14
4.What is the average of 2,586,000;147,000;36 ,000; and 31,978,000?
A. 8,686,750 B. 6,949,400 C. 34,747,000 D. 11,582,333
答案解析：A
(2,586,000+147,000+36 ,000+31,978,000)/4=8,686,750
5.In2013,the average number of biths aCross the globe was 1.169.000 per month.
What was the total number of biths that year?
A. 930.750 B. 93.075 C. 1.028,000 D. 1.402,800
答案解析：C
Based on the basic average formula, fomulale the flowing equation.
Average no.ofirts per month=no.of birts per yer/no.of moths per year
Thus, no.ofbiths per year= average no ofirtis per month"no of months per year.Now,pace the fgures povided in he question nto this fomua.
Annual no.ofbrts = 1.09.0020134.028000
Aaster solto woud be 10 rond 1.169,00010.0.000 and mutly by 12toget 100000
Since 1.1.1000 geater tan 10.0000 the core answer must be geater than 132 00
and only one answer choice flss that rquirement.
6.Which of the following groups has an average of 42 ?
A. 1 52 67 23 B. 73 52 18 25 C. 12 80 21 90 D. 92 51 53 22
答案解析：B
Aaeagesthe suainoumberss dineheberofterees Snoneneowathee nuroriemeinin
engnpip4andthe aeage defis 42 henthe usumnsemoeortopros
b42=168
Theoaly ansner that mees hisenis"(B)
7.The temperature on Monday was (-6)℃ , Tuesday was 2℃ and Wednesday was
7℃.What was the average temperature Over the three days?
A. 1℃ B. (-1)℃ C. 0℃ D. (-2)℃
答案解析：A
In order to calculate the average,sum up the temperatures over the three days,and then
divide by
3 days to arrive at the average temperature per day.Note that the temperature below
zero is addressed as a negative number：
(-6+2+7)/3=1℃
8.The average age of the 20 kids in class is 9 years.What is the sum of their ages?
A. 180 B. 181 C. 182 D. Cannot say
答案解析：A
The formula to calculate an average is:
Average =(sum of items)/ (number of items)
The question provides you with the average and the number of items.
To isolate their sum, multiply each side of the formula by the number of items:
(Sum of items) = average " (number of items)=920=180
9.The temperature On Monday Was (-6)℃,on Tuesday itwas2℃, and towards the
weend the temperature cimbdupto 10℃.What was the average tmperature over
the we?
A. 2℃ B. 1℃ C. 6℃ D. Cannot say
答案解析：D
The question requires you to calculate the average temperature over 7 days (a week) while
providing data for only two days.Thus, the average temperature per day over 7 days cannot be
calculated as you do not know the actual temperature for every day.
10.Loren worked 6 hours on Monday.7 hours on Tuesday.4 hours on Wednesday,and5
hours on Friday.She was about to turn in her attendance card at work when sherealised she forgot to log her working hours for Thursday.Loren knows that her average
working hours per day this week was 6.How many hours did she work on Thursday?
A. 6 B. 8 C. 5 D. 7
答案解析：B
This problem can be solved in 2 ways:
1.Use the average to calculate the total number of hours Loren worked this week:6
hours per day on average multiplied by 5 working days=30 hours.Then deduct the has
logged to arrive at the missing hours she worked on Thursday:30-(6+7+4+5)=8 hours.
2.Eliminate distractors by trying to understand whether the number of hours Loren
worked on Thursday was greater or less than the average.Since the average always seeks
to represent the "middie" of a set of numbers,We can use the average as an"anchor
and categorise Loren's working hours according to the average:on Monday Loren worded
the same number of hours as the average.On Tuesday she worked (+1) more than the
average. On Wednesday she worked (-2) hours less than the average and on Friday she
worked (-1) hours less than the average. In order for the average to stay"centred",
Loren's working hours on Thursday should be greater than the averageby2(+2)
Thus,the correct answer is 6+2=8.
11. Three photo albums an average of 23 per album 12in one,24 in the second and33 in the
third
How many photos will each album have on average if we add another 6 to the second album?
A. 25 B. 21 C. 22 D. 23
答案解析：A
There are2 ways to solve this problem:
1.Elimination
Take a look at the answer options.,Answers (B)(C) and(D) are either lower than,or identical to
the old average.
Since the number of photos in the second album increased (24+6=30)the average will increase
as well. Answer(A) is the only one which is higher than23,and is,therefore,the correct answer.
2.Average calculation
Calculate the sum of the new set of numbers,and then divide by the number of items.
In this particular case, however you can use a much shorter calculation the difference
between the new number of photos and old number of photos is 6.Divide this by the
number of items to learn how much the average will increase:
(Difference between sums of items)/ (number of items)=6/3=2
The average will increase by2.Thus,the new average will be:23+2=25
12.BG Toy’s head of marketing asked his assistant to hand him a report covering the
company's sales during the past3 weeks.The assistant who was still missing the data
from the last 2 days,decided to hand in an inbial report without
These days,stating that the company’s average daily revenue during that period was 0.85
million pounds Once the assistant was informed that the revenues in the last 2 days
were 0.7million pounds and 1 million pounds, he immediately updated his report toinclude this new informaion What happened to the average daly revenue updated
report?
答案解析：C
First of all it is important to understand why the answer is not cannot say." Although you are not
provided:
with data concerning the daily revenues of the days included in the report, you do know their
average
daily revenue Knowing the average of a group of values is sufficient for determining how an
addition of one or more values to the group tan influence its average Nor.determine how this
addition can influence the average in our casein order to do so, you need to calculate the
difference between each of the 2 values and the average
The difference between 0.7 and0.85=0.7-0.85=0.15
The difference between 1.and 0.85=1-0.85=0.15
As the dailv revenues in these 2 days are egually different from the average daily revenue,
including them in the report would not influence the average
An alternative method is to calculate the average of these two days :
(0.7+1)/2=0.85
Since it is identical to the previous average,It would not influence the result
13.Randy bought three products at the grocery store.1 kg of tomatoes for 3,a loaf of
bread for 2,and eggs for1.50
What will happen to the average price of all three products if,at the cash register,Randy
is informed that here is a 25%discount on the price of bread?
A. It will increase by0.50
B. It will decrease by0.16
C. It will stay the same
D. It will increase by 0.25
答案解析：B
You can solve this question in two ways.
1.Calculate the previous average:(3 +2+1.5)/3=2.16 and the new average:
(3+1.5+1.5)/3=200.Then,deduct the previous average from the new average to arrive
at-0.16 to mark a decrease of 0.16 in the average price.
2.Eliminate distractors by trying to understand whether the average increased,decreased, or
stayed the same.since the average always seeks to represent the "middie" of a set of numbers, if
one number should decrease, then the average will decrease as well.Thus,the only correct
answer is (B).Moreover,you can calculate the exact decrease in the average by calculating
the change in bread price.25%of 2 equals 0.50.The actual decrease in price,divided by 3
products,equals a change of 0.16.
14.Grace owns four vehicles which can travel at varying speeds:16 km/hr and 26 km/hr.If
Grace bought 2 more vehicles one which can travel at a speed of 13 km/hr and
another which can travel at 25 km/hr,what would be the difference between the average
speed of Grace’s vehicles before and after her purchase?
A. 0 B. 1 C. 2 D. 3答案解析：A
Calculate the average speed of the first four vehicles, and compare it to the new average speed
(which includes the 2 new vehicles).
Start with the first four.
Average = (sum of items) / (number of items)=(11+16+23+26)/4=76/4=19
Before you carry on to calculate the second average,take a look at the figures you have.The
average of the first four vehicles is 19 km/hr.The new vehicles travel at 13 and 25
km/hr.The size of the difference
between 19 and 13 is equal to that of the difference between 19 and 25.
19-13=+6
19-25=-6
When you add 2 numbers, one greater and one less than the average, but both equally distant
from it, the average remains the same because their distances from the average cancel
each other out +6-6=0.
Therefore, there is no need to calculate the new average to know that the difference between
the new one and the old one is zero.
材料2
第二组 15题
1. What is the value of 1000 THB in Japanese YEN in 2011?
A. 261.27 B. 26.127 C. 2612.7 D. 382.74 E. 3827.4
答案解析：C
1THB=2.6127JPY
Therefore,1000*2.6127=2612.7
2.How many S can be purchased for 770 USD in 2011?
A. 2639 B. 263.9 C. 88.935 D. 1155 E. 26.39
答案解析：A
We must first find out how much 1 USD is worth in ILS by using information from the THBexchange rate table.In order to do this,we divide ILs by USD.
According to the table，ILS to USD:
0.1155/o.0337=3.427
Hence,each 1 USD is worth 3.427 ILS.
770*3.427=2638.71～2639
3.How many more BRL would have been purchased for 5000 THB in 2012 compared to
2011?
A. 52.1 B. 5.21 C. 0.0521 D. 0.521 E. Cannot say
答案解析：D
0.20%=0.002.
once we recognise there is a o.002 positive change in THB's value，we should only look for this
change's worth:
5000*0.0521*(0.002)=0.521 BRL
which is a shortcut way of doing:
(After)-(Before):
Since the exchange rate was changed by o.2% or 0.002,the old exchange rate should be
multiplied by 100.02% or 1.002 to receive the new exchange rate:
(5000 THB*0.0521 BRL*1.002)-(50O0 THB*0.0521 BRL)=0.521 BRL
4.Approximately how many USD can be purchased for 2550 CHF at the end of 2012?
A. 3187 B. 250,952 C. 3230 D. 3209 E. 2231
答案解析：A
The table lists exchange rates from THB to other currencies.Since we do not know the exchange
rate from CHF to USD, we will have to calculate it ourselves.
First, we need to calculate the exchange rates to CHF and USD in 2012,using the percentage
changes in the right column:
THB to CHF in 2012: -0.14% = -o.0014,hence 0.027*(1-0.0014) = 0.02696
THB to USD in 2012:0.07% = 0.0007,hence (0.0337*1.0007)= 0.03372
Now we need to find the exchange rate from CHF to USD,so we can calculate how many USD can
be purchased for 2550 CHF:
1CHF is worth (THB to USD/THB to CHF)=
(0.03372/0.02696)=1.25 USD
Therefore, with 255O CHF, one can purchase:
2550*1.25 = 3187.5 USD
5.What is the exchange rate of Brazilian Real (BRL) to THB in 2011?
A. 0.1919 B. 19.19 C. 1.919 D. 0.01919 E. 191.9
答案解析：B
1 THB=0.0521 BRL and 1 BRL=1/0.0521=19.19 THB6.What is the value of 1000 JPY in EUR?
A. 9 B. 900 C. 1261 D. 126,101 E. 9000
答案解析：A
1PY=0.009EUR
Multiply both by 1000 :
1000JPY=9EUR
7. How many GBP can be purchased for 7500 CAD?
A. 11,772 B. 4776 C. 477.6 D. 8720 E. 6369
答案解析：B
7500 CAD"0.6369=4776.75 GBP.
This means you can buy 4776 GBP with 7500 CAD since you don't quite have enough CAD to buy
4777 GBP.
8.GBP equals to a.s.6azlotych. hat is the value of 3250 Zlotych in CAD?
A. 458 B. 4580 C. 1100 D. 1130 E. 719
答案解析：D
Convert 3250 Zlotych to GBP: 3250/4.5164=719.6 GBP
Convert GBP to CAD: 719.6*1.5701=1129.8 CAD
Thus,the correct answer is 1130.
9. In percentages, how much more USD will one get when exchanging 1,223,500jpY compared
to exchanging o750 EUR?
A. 13.3% B. 88.3% C. 117.7% D. 35.5% E. 90.2%
答案解析：A
First convert Euros to USD:
975O EUR"1.4401=14,040.975 USD.
Then convert JPY to USD:
1,223,500 JPY*0.013=15,9o5.5 USD.
Now calculate according to the percentage change formula:
[(New value/Previous value)-1]*100
(15,905.5/14,040.975)-1 = 0.133 *100% = 13.3%
10.Approximately,how many GBP can be purchased for 1500 CAD if the value of CAD
compared to GBP drops by 2.79%?
A. 890 B. 793 C. 930 D. 990 E. 893
答案解析：C
According to the table: 1CAD=0.6369 GBPA drop of 2.7% means that there is 97.3% remaining,which,when translated to decimals is equal
to 0.973.
Thus: 0.6369*0.973=0.6197
Therefore:
1500*0.6197=930.
11.Approximately how many Jamaican Dollar (MD) can be purchased for 8oo GBP in year
1?
A. 111,180 B. 112,987 C. 122,298 D. 122,299 E. 111,181
答案解析：A
800 GBP*138.9751=111,180.08
12.How many more/less Turkish Lira (TRY) could have been purchased for 3240 GPB in
year 1
compared to year2？
A. 1167 TRY more B. 1066.7 TRY more C. 1322.2 TRY less
D. 1166 TRY less E. 1322.2 TRY more
答案解析：D
Year 2 -3240*3.11 = 10,076.4.
Year 1 -3240*2.7499 = 8909.676.
1o,076.4-8909.676 = 1166.724 less in year 1.
Tip:This calculation can be significantly simplified to save us some valuable time.If we put it all in
one line - (32403.11- 3240""2.7499)- we can see that 3240 is a common factor in both
terms.Thus,we can use factorisation to simplify the calculation:
(3.11-2.7499)-3240 = 1166.724
In other words,we may measure the difference between both exchange rates first (3.11-
2.7499),and then multiply by 3240.
13.which of the following arguments is not true?
1. USD has appreciated
2. ARS exchange rate had the smallest relative change
3. In year 10SD is the second strongest currency in the table
4. ARS exchange rate has depreciated by 0.62%%
A. only 1 is not true
B. only 2 is not true
C. only 3 is not trueD. only 4 is not true
E. More than 1 argument is not true
答案解析：D
1 is correct.If the exchange rate goes down,the meaning is that the currency has
appreciated(became stronger).The same reason indicates that 3 is also correct,since its
exchange rate is the second to lowest.2 is also correct.The relative change of the ARS exchange
rate was (1-6.9873/7.0307 = 0.0062)，which is the smallest relative change compared to all other
differences between year 2 and year 1.However,this change indicates that the currency has
appreciated (stronger compared to the Pound Sterling) rather than depreciated.Therefore,only
option 4 is incorrect.
14. hat was the exchange rate of Turkish Lira(TRY)to GBP in year1?
A. 0.0036 B. 0.3736 C. 0.3636 D. 0.03636 E. 0.4
答案解析：C
1GBP=2.7499 TRY.
Therefore 1 TRY=1/2.7499=0.3636 GBP
15.What is the percentage change of the EUR exchange rate between Year l and Year 2?
A. 0.106% increase B. 0.0106% increase C. 1.06% decrease
D. 10.6% decrease E. None of the above
答案解析：C
In order to find the percentage change,we must place the data in the percentage change
formula:
Percentage change = (New value-Original value)/original value or: (new value/original value -
1)*100
Thus:
Percentage change between year 1 and year 2 = (exchange rate in year 2 -exchange rate in year
1)/ exchange rate in year i = (1.129-1.1411)/1.1411=-0.0106 = 0.0106 decrease
材料3
第三组 2题
1.Given that one megabyte equals 1024 kilobytes, what is the increase in average file
size (in kilobytes) in June compared to May.if the absolute increase in average file size
seen between April and May continues?
A. 167.5 B. 172.2 C. 186.1 D. 190 E. 194.6答案解析：E
In April the average file size was 3.06 megabytes,while in May it was 3.25 megabytes.This is a
0.19 megabyte difference.
since the same amount of growth occurs in the following month,.we need only calculate the
equivalent size in kilobyte.
we know that 1 megabyte is 1024 times greater than 1 kilobyte.
0.19*1024=194.56 kilobytes
2. Given that one megabyte equals 1024 kilobytes,what is the size difference between an
average file downloaded in February to an average file downloaded in May,in thousands of bits?
A. 1,258.291 B. 1,356,999 C. 1288.8 D. 1,288,800 E. Cannot say
答案解析：A
we need to calculate the difference between average files size in February and May.
The important thing to remember here Is to pay attention to the unit conversions:
Average size in February. 3.4 megabytes.
Average size in May.3.25 megabytes.
(a) The difference in megabytes (MB):
3.4-3.25=0.15MB
(b) Convert to kilobytes
The question states that 1 MB = 1024 kilobytes.Therefore,0.15MB is equal to:
0.15*1024= 153.6 kilobytes.
(c)Convert to bits:
According to the table,1 kilobyte = 8192 bits.Therefore，153.6 kilobytes equal to:
153.6*8192= 1.258.291 bits.
Now, divide by a thousand to get 1258.291 thousands of bits
第四组 16题
1.In 2011 Michael spent 56/71 of his salary on Gadgets.In 2012 Michael spent 64/81 of
his salary on gadgets.In which year did Michael spend more money on gadgets?Assume
Michael’s salary remains the same
A. 2011 B. 2012 C. No difference between the years
答案解析：B
This question requires us to convert from fraction to percentage.This can be
done by using the following formula:
fraction*100=%
2011： *100 = 78.8% 2012： *100 = 79.0%
Please note that although the difference is slight,it is still there.
2.Janet bought a packet of Smarties in the supermarket for 2.Lucy bought the same
packet of smarties in the kiosk for 2.40.Lucy paid_______more than Janet.
A. 25% B. 20% C. 15% D. 10%
答案解析：BThis question requires us to convert from fraction to percentage.This can be done by using the
following formula :
fraction * 100 = %
Note that this question also requires us to convert percentage to decimals.In order to do
so,divide the percentage value by 100.
=20%
Another way to approach this question is to simply calculate:
0.4/2 = 0.2
The nominator equals the difference between the amount of money Lucy spent compared to
Janet: 2.4-2 =0.4
The denominator represents our 100%，which is the 2 Janet paid.
3. Nick returned from the market with a bag full of 40 fruits and vegetables: 4 tomatoes,10
onions,16 blueberries and the rest were cucumbers.
What is the percentage of tomatoes out of all the fruits and vegetables?
A. 4% B. 40% C. 10% D. 1%
答案解析：C
This kind of question requires an understanding of the relation between a given percentage and
the proportion it represents (and vice versa)，This relation is represented by the following
formula:
( )*100=%
In this case:
*100= 10 %
4.The veterinarian informed the zoo manager that 20% of the Rhinoceros developed a
rash over
night. If there are 1350 rhinoceros in the zoo,and they were all healthy the previous
day, how
many of them have a rash?
A. 135 B. 270 C. 675 D. Cannot say
答案解析：B
This question requires us to find a portion out of a whole.we can isolate this variable out of the
formula:
*Total=Value
In this case:
1350*(20/100)=270
Solving tip: This question can easily be solved using the "10% method".
According to this method: 10% of 1350 are 135,135+135=270.
5.The veterinarian informed the zoo manager that 20% of the rhinoceros developed a
rash overnight. If there are 1350 rhinoceros in the zoo,how many of them are healthy?
* Assume that all rhinoceros are either healthy on suffer from a rash, and prior to that
night had all been healthy.
A. 135 B. 270 C. 1050 D. 1080 E. Cannot say
答案解析：D
This question requires us to find a portion out of a whole.We can isolate this variable out of the
formula:
Value =( )*total
In this case:
1-{1350* }=1080 or 1350* =1080 or 1350*0.8=1080
6. 8 professors in Cambridge University object to the latest test policies published.They
represents 2% of all professors teaching in the university.How many professors teach in the
university?
A. 100 B. 200 C. 400 D. 500 E.Insufficient data
答案解析：C
Total= *100
In this case:
*100=400 or =400
Solving tip: The relation between a percent and 100% is similar to the relation between a value
and its total: 2%*50=100% therefore 8*50=400
7. 30% of students in the local college are active in animal rights organizations and 10%
of animal
rights activists are political activists as well.How many students are both animal rights
activists and political activists if there are 1,200 students studying in this college?
A. 36 B. 30 C. 300 D. 120
答案解析：A
This kind of question requires an understanding of the relation between a given percentage and
the proportion it represents (and vice versa).This relation is represented by the following
formula:
( )*100=%
Specifically,this question requires us to find a portion out of a whole.We can isolate this variable
out of the formula:
Value =( )*total
Since we are asked to find a proportion out of a proportion of a whole in this question, we will
need to calculate in two steps:
step 1(total of students active in animal rights organizations):(30/100)*360=36
we can also calculate this in one step:
1200* * =36 or 1200*0.3*0.1=36
Alternative explanation: we may also calculate the total percentage of students active in both
animal rights and political organizations out of the total sum of students:
* =3%
Now we can use the formula for finding the value out of the total:
1200* =36
8.The price of a book before a 25% discount is 10.What is the price of the book after
the discount?
A. 2.5 B. 7.5 C. 6.25 D. 8.5
答案解析：B
A useful formula for this sort of question is:
New value = original value + — value of increase or decre
Note: The plus or minus sign is determined by the action preformed(increase/decrease).
In addition-
(value of increase or decrease)= original value *
In this case:
10-(10* )=7.5
An alternative approach: The new value after a decrease of 25% is 75% original value. In other
words,the new value equals:
*original price
In this case:
10* =7.5
9.The price of an Ipod Nano has gone up to 260, which is 130% of the original
price.What was the original price of the Ipod Nano?
A. 60 B. 210 C. 130 D. 200
答案解析：D
This is an increase/decrease question.In this type of question we are asked to either find the
new value of an item after an increase/decrease in price or find the original value，given the new
value of the item.A useful formula for this sort of questions is:
New value = original value +- ( Original value * )
In this question we are required to isolate the variable of the original price:Original value = *100
In this case:
*100=200
Note: you can use decimals in this formula,thus eliminating the need to multiply by 10o (you can
see an example of this in question 10)
10.The price of an electric guitar decreased by 20%last year due to lack of demand.This year there
was an additional 25% decrease in price due to the economy crisis.What was the guitar's price
at the beginning of last year, if this year the price is 150?
A. 250 B. 272.2 C. 100 D. 234.3
答案解析：A
This is a continuous increase/decrease question. In this type of questions we are asked to either
find the new value of an item after a continuous increase/decrease in price or find the original
value,given the new value of the item.
In this question we are asked to find the original value，given the new value:
original value=
Since there are 2 consecutive decreases in price,we will calculate each of them
separately,starting with the given price this year and going backwards:
step 1(finding original price before second decrease):
=200
step 2 (finding original price before first decrease):
=250
It is also possible to calculate this question in one step:
x* 0.8* 0.75= 150 >x = 250
*The x represents the original price we are looking for,80/100 =0.8
represents what is left after the 20% discount,75/100 = 0.75 represents what is left after the
additional 25% discount.
11.The value of an apartment in East London was estimated at 350,000 prior to a
30%increase in
price, which was shortly followed by a 30% decrease in price.What is the price of a
London
apartment today?
A. 350,000 B. 318,500 C. 358,500 D. 360,000
答案解析：B
This is a continuous increase/decrease question.In this type of question we are asked to either
find the new value of an item after a continuous increase/decrea price or to find the original
value,given the new value of the item.
In this question we are asked to find the new value，given the original one:New value = original value + - ( Original value * ）
since there are 2 consecutive changes,an increase followed by a decrease,we calculate each of
them separately:
step 1(increase):
350,000+350,000* =455,000 or 350,000* =455,000
step 2(decrease):
455,000-455,000* =318,500 or 455,000* =318,500
Solving tip: we can assume that the price of the apartment would be less that 350,000 since the
percent of increase and decrease is the same.However，the decrease is applied on a higher
value (after a 30%increase in price),therefore t
decrease in price is bigger than the increase in price, leading to a lower cost of :
London apartment than before.
Note: If a certain amount is increased and then decreased by the same percent or
decreased and then increased by the same percentage,the final amount would smaller
than the original amount.
12.Danny got a raise.His monthly salary was 6,300 and now it is 6725.What was Danny's
salary percent change?
A. 0.674% B. 0.06% C. 6.3% D. 6.74%
答案解析：D
This is a percentage change question.A useful formula for this sort of questions is:
% change = *100
In this case:
*100=6.74%
13.In what years was there a percentage change greater than 34% in Leeds? (in respect
to the previous year）
A. 2007,2008,2010,2012 B. 2008,2009,2011 C. 2009,2010,2012 D. 2007,2009,2010,2011
答案解析：C
This is a percentage change question. while some of us may use estimations to solve thisquestion,we will focus on practicing the use of the relevant formula:
% change = *100
For example, in 2008:
*100= *100=33.33%
Following the same calculation for the remaining years:
2009:62.5%
2010:61.54% (decrease)
2011:20%
2012:66.66% (decrease)
Note that a percentage change is an absolute value,i.e.65% will be the same as-65%，since we
are only interested in the size of the change and not its direction.Should the question ask about
a percentage increase or percentage decrease,the sign (direction) will be of importance.
14.What is the percentage change between the profits made in 200s and the profits
made in 2010?
profit=incomes-expenses
A. 2.13% B. 5.45% C. 3.83% D. 2.17%
答案解析：A
First, we need to figure out the profits made in 2005 and 2010:
2005: 5.5 - 0.8 =4.7
2o10: 5.2 -0.6 =4.6
Now we need to calculate the percentage change according to the following formula:
(new value - old value)/old value
(4.6-4.7)/4.7 =-0.02127=2.13% decrease.
15.Danny's savings accumulated an interest of 2.5% a year.Assuming that interests are
reinvested at the same rate, how much money does Danny have after 5 years, if at the
beginning he had 250?
A. 282.8 B. 280 C. 281.25 D. 285.5
答案解析：A
Interest questions are a specific case of continuous increase/decrease question:
interest is a continues increase of a constant value，Since all the increases are we can calculate
interest questions in one simple step:
original value * (interest)
250*(1.025) =282.852Instead of using this formula in s steps:
New value - original value + - ( Original value - )
Note that 1.025= 102.5/100
1. 250*1.025 =256.25
2. 256.25*1.025=262.65
3. 262.65* 1.025=269.2
4. 269.2*1.025= 275.9
5. 275.9*1.025=282.8
16.The price of a diamond ring was reduced by 80% then went up by 200%.What was
the
percentage change in the diamond ring's price?
A. 60% decrease B. 20% increase C. 40% decrease D. 120% increase
答案解析：C
This is a complex percentage change question,since we have no values to work with.In situations
such as this one, it is easiest to use 100 as the whole: Let's say the original price of the diamond
ring was 100.
After the first change,the new price is 20% of the original，thus:
20%*100=0.2*100= 20.
The second change is an addition of 200% which is :
200%"20= 40.Thus,the final price is : 20 +40 =60
Since we used 100 at the beginning, it is now easy to calculate the total change:
Initial price: 100.Final price: 60.
Change: (100-60)/100 = 40/100 = 40%decrease.
第五组 18题
1.What is the approximate ratio of 9 to 56?
A. 1:5 B. 1:6 C. 1:7 D. 1:8
答案解析：B
We need to find which of the options displays the same ratio as 9:56.
As the left side of all of the options is 1,we can simply divide both sides of9:56 by 9, thus arriving
at the ratio of 1:6.2
Since we are asked to find the approximate ratio, we need to choose the option that is the closest
to the actual result.
6.2is closer to 6 than it is to 7.Thus, the approximate ratio is 1:6.
2.For every one boy in the class there are three girls.
What is the ratio of girls to boys?
A. 1:3 B.3:1 C.1:4 D.4:1
答案解析：B
The order of words in the sentence is very important for every one boy there are 3 girls,thus the
ratio of boys to girls is 1:3.
However,for every three girls there is one boy .thus the ratio of girls to boys is 3:1.3.There are 363 blue stones for every 121 green stones in the box.what is the ratio of
blue to green stones?
A. 121:363 B. 3:1 C. 3:2 D. 1:3
答案解析：B
The ratio we need to find is of blue to green,or blue:green.Thus,the ratio is:33121
Cancel down by 121:
33121=3.1
Note that distracter A is incorrect for2 reasons:
a)It presents the opposite ratio(green to blue instead of blue to green).
b)Ratios should always be reduced to the lowest possible terns,whereas in this case the numbers
are left as they are.
4.There are 4/7 as many yellow jelly beans in the jar as there are red jelly beans.
what is the ratio of yellow jelly beans to red jelly beans in the jar?
A. 3:7 B. 4:3 C. 7:4 D. 4:7
答案解析：D
To say that there are 47 as many yellow jelly beans as there are red jelly beans means that for
every single red jelly bean there is 4/7 yellow jelly bean
Thus,the ratio of yellow to red is 47.1
By muitiplying both sides by 7,we arrive at the ratio of 47.
Note you reed to pay careful attention to the order of the words in the sentence
The ratio of X to Y is displayed as XY.That is why the correct answer is 4.7and not 74.
5.Mike owns a collection of toy cars.3/8 of the cars are green and the rest are pink
What is the ratio of green to pink cars?
A. 3:5 B. 3:8 C. 5:8 D. 8:5
答案解析：A
3/8 of the total number of cars are green.This means that out of a set of 8 cars in total,3 are
green.Since the cars are either green or pink,the ramaining 5 cars are pink Thus,the ratio of
green to pink cars is:3:5
6.A pet shop has0.75 as many dogs as cats.What is the ratio of cats to dogs in the
shop?
A. 1:1.25 B. 3:2 C. 3:4 D. 4:3
答案解析：D
This question provides the ratio of dogs to cats as a decimal To make things easier,
the first thing we need to do is to convert it into a fraction:
0.75=3/4.
There are 34 as many dogs,which means that for every 3 dogs,there are 4cats.
we need to find the ratio of cats to dogs,or cats.dogs.
Thus:Cats:dogs = 4:37.A dance group consists of 22 dancers.The ratio of men to women in the group is 5:6.
How many of the dancers are women?
A. 6 B. 8 C. 10 D. 12
答案解析：D
If there are 5 men for every 6 women,1means that there are 5+6=11 dancers in total in each"set"
of dancers.
It follows that5/11 of the dancers are men,and 6/11 of the dancers are women To find out how
many dancers are women,we need to multiply the number of dancers by 6/11:
22*(6/11)=(22/11)6=2*6=12
8.Lesley bought 36 apples in the market.20 apples were red and the remaining apples
were green.What is the ratio of green to red apples?
A. 16:36 B. 16:5 C. 4:5 D. 20:16
答案解析：C
There are a number of stages to calculate the answer to this question
First, we need to find out how many green apples were bought by Lesley.36-20=16.
Next we need to find the ratio of green to red apples:16:20.This is not the final answer,
however,as we are able to reduce this ratio by a common denominator of 4.
Thus, the correct answer is:4:5.
9.Peter and Paul are roommates.
Each of them pays the rent,according to their room's size.
Peter's room is twice as big as Paul’s.
How much rent does Peter pay, if the total rent is 1200?
A. 600 B. 800 C. 400 D. 500
答案解析：B
The correct answer is 800.
The ratio of Peter’s room size to Paul's room size is2:1.According to the data,the same ratio
applies to rent payment Peter pays twice as much as Paul.We can represent this using an
equation.2X+X=1200
Peter pays 2XPaul pays X and together the payment equals 1200(total sum of rent)
If we develop this equation we get 3X= 120→X=400
This means, that Paul pays 400 and Peter pays 800.
10.kairen keeps blue and red marbles in her pocket in a ratio of 4 to 9.What is the
ratio of red marbles to the total number of marbles in her pocket?
A. 4:13 B. 9:4 C. 4:9 D. 9:13
答案解析：D
The correct answer is:9:13.
The ratio of blue to red marbles is:4:9.
The total number of marbles is:4+9=13
Thus,the ratio of red marbles to the total number of marbles in the set is 9:13
Please note that is does not necessanly mean that Kairen has only 13 marbles in her pocket
she might have more than 13,as long as it is a multiple of this number (ie.26,39,52....)11.The ratio of smokers to non-smokers in the population is 3:17.
what is the ratio of smokers to the entire population?
A. 0.14:0.17 B. 0.17:1 C. 0.15:1 D. 0.85:1
答案解析：C
The population is composed of smokers and non-smokers.Based on the information provided in
the question,we can say that for every 20 people, 3 are smokers and 17 are non-smokers.Thus,
the ratio of smokers to the entire population is 3.20.
Unfortunately, this is not one of the answer choices.We therefore need to figure out which of
the options displays the same ratio as320.
Based on rough estimation,we can eliminate options A and D as they present a ratio close to 1:1,
while we are looking for a ratio of about 1.7.
Since both remaining options present a ratio of x to 1, it is best to divide both sides of the ratio
by 20,
thus arriving at the following x to 1 ratio-0.15:1.
12.At the "Run for Fun”marathon, the ratio of local runners to foreign runners is 1:17.
What is possibly the total number of runners in the marathon?
A. 19 B. 55 C. 72 D. 38
答案解析：C
Since We know that the ratio is 1.17, the total number of runners must be in ratio units of
17+1=18.
Therefore,the total number of runners must be divisible by 18 without a remainder, which
disqualifies all answers but 72
13.Liz wishes to bake bread.
According to the recipe, she needs to have
(amongst other ingredients) 2/3 cups of water and 1 1/2cups of flour.
Unfortunately, she only has one cup of flour.
How many cups of water would she need to use?
A. 2/3 cup B. 4/9 cup C. 1/3 cup D. 1/6 cup
答案解析：B
1 1/2 equals 3/2(since 1=2/2,and 2/2 + 1/2=3/2).thus the ratio of water to flour is 2/3.3/2.
Since we want to know how many cups of water Liz needs to use if she only has one cup of flour
fie what the ratio of water to 1 cup of flour is).we can dyide both sides by3/2
Flour : (3/2)/(3/2)=1
Water:(2/3)/(3/2)=(2/3)*(2/3)=(2*2)/(3*3)= 4/9
Thus.the ratio of water to flour is 4/9.1,meaning that for every cup of flour,Liz needs to use 4/9
cup of water.
14.The waiters divide the daily tips among themselves according to the length of their
shifts.
Andrew made 80 after working a shift twice as long as Mary.
How much did Anna make, if her shift lasted three times the length of Mary's shift?A. 100 B. 90 C. 110 D. 120
答案解析：D
We know from the question that the tip payment is based on the length of the waiter's shift and
we know how much Andrew made relative to Mary.The question asks us to find Anna's tip
payment, which is also relative to Mary's.Therefore,we first need to find Mary's earnings,which
are equal to half as much as Andrew's:80/2=40.Since Anna worked three times as much as
Mary,all we have to do is multiply Mary’s earnings by three:40*3=120.
Thus,we found that Anna made 120.
15.Milly and Bill's parents left an inheritance of 5000.
According to the parents' will,Milly will inherit twice as much as Bill.
The parents also stipulated that 40% of the original sum is to be transferred to their
favorite animal charity.
How much money will Bill inherit?
A. 2000 B. 3000 C. 1000 D. 2200
答案解析：C
The correct answer is 1000.
40%of the original sum of E5000 goes to a charity.This means that only 60% oft
he money will be divided between Bill and Milly. 5000*0.6= 3000.
The money will then be divided in a ratio of 12in favor of Milly. if we divide 3000 by three,
we see that Bill will receive 1000.
16.Due to customers' complaints, the director of a department store has decided to
increase the number of cashiers by 37.5%.
How many cashiers would work at the store after the change in workforce,if prior to
the change 104 people worked at the store and the ratio of cashiers to other staff
members was2.11?
A. 22 B. 26 C. 121 D. 11
答案解析：A
first me need to find out how many cashiers worked at the store before the change in work
foce.We know that at that time,for every 13(2+11)staff members 2were cashiers.In other
words,2/13 of the total number of employees were cashiers.Thus,the number of cashiers
was (2/13)104=16.
Now, we need to calculate the new number of cashiers atera37.5% increase.
16*(1+0.375)=16*1.375=22
17.In a group of 40 biology and chemistry students, for every 3 students who study
biology, there are 2 who study chemistry.
Last week two new students joined the biology department.
What is the new ratio of biology to chemistry students?
A. 5:2 B. 13:8 C. 2:5 D. 3:4
答案解析：B
The most common mistake in solving this type of question is to add1 2 biology students to the
existing 3 biology students to get (2+3)=5 biology students for every 2 chemistry students.Thiscalculation is incorrect because it disregards the change in the total number or students.
we need o do the following
(a)Find the number of biology and chemistry students BEFORE the new students joined the
faculty
(b)calculate the new number of biology students
(c)Find the new ratio.
(a)Before
If there were 3 biology students for every 2 chemistry students. it means that there were 3+2=5
items in the 'set" Thus:
3/5 of the students were biology students
3/5*40= 24 biology students
2/5 of the students were chemistry students
2/5*40=16 chemistry students
(b)After
tow there are 42 students in total, with 2 more biology students.
24+2= 26 biology students
(c)New ratio
Biology chemistry= 26:16
Cancel down by 2
13:8
18.There are 100 books in the library, divided into four categories.
The ratio of books is as follows: 3 science fiction books to every 2 history books
and 4 history books to every 3 comic books.The remaining books are art books.
How many art books are there in the library, if we know that it holds 9 comic books?
A. 61 B. 59 C. 39 D. 70
答案解析：A
The number of comic books is 9 and the ratio of history books to comic books is 4/3,This means
that there are 4l3 history books for every comic book.
To find out how many history books we have,We must multiply the number of comic books by
the ratio 4/3,
So the number of history books would be 9*(4/3)=12
Sine we know the ratio of science fiction books to history books is 32
We need to multiply the number of history books by the ratio 32to ascertain the number of
science fiction.12*(3/2)=18.
The question asks us to find how many art books there are n the library.This is the only category
left un-calculated,
So we can find this number by subtracting the other categories from the total number of books,
which is 100
100-9-12-18=61.
Thus, there are 61art books in the library.
第六组 13题
1.8 children attend "sunshine" kindergarten with an average age of 3.55 children attend "Rainbow" kindergarten with an average age of 5.
What is approximately the average age in both kindergartens?
A. 4.25 B. 4.5 C. 3.75 D. 4
答案解析：D
Since we have two kindergartens with a different number of children, one with 8 children and the
other only with 5,we must calculate a weighted average. In order to do that we multiply the
average age of each kindergarten by the number of children attending that kindergarten:
Sunshine":8 children " 3.5(average age)=28.
Rainbow: 5 children " 5 (average age)=25.
low we sum up the results and divide by the total number of children
attending both kindergartens to arrive at the correct answer.(28+25)/(8+5)=53/13=4.07≈4
2.A nursing home is holding a trivia toumament.Residents
have so far divided into three groups of different sizes and varying ages.
croup A: 3 people with the average age of 77.
Group B:.4 people with the average age of 86
Group C.5 people with the average age of92
What is the average age cf all the participants?
A. 85 B. 85.25 C. 86.25 D. 86
答案解析：C
We have three groups of people.Each group consists of a different number of people.For this
reason the contribution of each group to the overall average age is different and relative to its
size.This is a weighted average。
The formula to calculate a weighted average is:
weighted average =(value1"weight1 + value2'weight2 + value3*weight3) / (total value of
weights)
(77""3+854+92"5)/(3+4+5)=1035/12=85.25
3.Concert tickets are offered at15 for 20% of the seats,and 13 for the remainder of
seats.
The concert was sold out.
What is the average price paid for a ticket?
A. 13.4 B. 6.7 C. 13.5 D. 14
答案解析：A
20% of the tickets are sold for15 per ticket, and (100%-20%=)80% are sold for 13
per tcket15and13 are our two values,and 20% and 8O0%are their respective weights.
The formula to calculate a weighted average is:
Weighted average =(Value1"weight1 + value2"weight2)/ (total value of weights’
/=(15102+1310.8)/(02+0.8)=13.41=13.4
4.what is the average weight of 20 "Pink Lady apples each weighing 70 grams and 12
"Granny Smith" apples each weighing 100 grams?
A. 85 B. 81.25 C. 84.8 D. 79.75答案解析：B
Since we have two apple "groups" of different sizes,one with 20 apples and the other only with
12,we must calculate a weighted average. In order to do that we multiply each weight
category by the number of apples in that category.20 (PinkLadies770(grams) and
12("Granny Smiths")100 (grams).
The We sum up the results and divide by the total number of apples to arrive at the
correct answer (20*70+12*100)32=81.25.
Please note that you could use different 'weights”instead of the number of the apples
in each category (20& 12)
You could also use the weights 5 and 3 respectively as they represent the same ratio
between the
number of"Pink Lades" to "Granny Smiths".
5.The average score in Class A is 30,the average score in Class B is 40 and the average
score in Class C and D is 20.
Class C and D each have twice as many students as Class A and B.
The average score of the entire grade [Classe5 A-D] is.
A.Less than Class A's average score
B. More than Class A's average score
C. Equal to Class A's average score
D. lmpossible to say
答案解析：A
We can solve this question in two different ways
a) Using an equation based on the formula for calculating an average: (301+40"1+202+202)6=25
b) Understanding the true meaning of an average.an average always seeks to represent the
"middle" of a set of numbers.
Here is our set of numbers (arranged in order):
20(class C).20(class D),30(class A).40(Class B).
We can already see that there are 2 items in the set that are smaller than 30 (which is the
average grade of class A) and only 1 item larger.Therefore, the average for all the classes
combined,will necessarily be less than that of class A
Also,we must not forget that classes C and D are twice as big as the other classes.In weighted
average calculations,this means that they are "heavier than the other values, and that the
weighted average is "drawn" to them
Taking all this information into account. it is pretty safe to estimate that the weighted average is
smaller than 30.
6.A secretary typed 5 pages between9AM and 10AM,4 pages per hour between
10AM and 2PM and 2 pages per hour between 3PM and 5PM.
During her lunch break (2-3PM) the secretary did not type any pages.
what is the average typing rate of the secretary for the entire working day (break
included)?
A. 3.25 pages per hour
B. 3.125 pages per hourC. 4pages per hour
D. 3.5 pages per hour
答案解析：B
The Secretary's typing rate is distributed across the working day as followed:
9-10AM (1 hour) :5 pages per hour
10AM-2PM(4hours):4 pages per hour
2-3PM(1 hour):0 pages per hour
3-5PM(2 hour):2 pages per hour.
We can use the hours to assign a weight to the different typing rates ac1oss the day and
calculated a weighted average.
Average typing rate =[(type rate 1*weight 1)+(type rate 2*weight2)+(type rate 3*weight 3)+(type
rate 4*weight 4)]/ sum of weights =[(5*1)+(4*4)+(0*1)+(2*2)]/(1+4+1+2)=3.125 pages per hour
7.The average height of the girls in Miss.H's class is 3.9 feet and the average height of
the boys is 4.05 feet.
What is the average height of the students in Miss. H’s class if there are7/9 as many
boys in the class as there are girls?
A. 3.966 feet
B. 3.975 feet
C. 3.984 feet
D. Cannot say
答案解析：A
At first glance, We may think the correct answer should be “cannot say”, as we are only
provided with the ratio of girls to boy but not with the actual number of girls and
boys.However,Since we are asked to
calculate the weighted average,knowing the average height of each group girl/boys) and the
weight assigned to it(i.e.the number of student in that group) is sufficient
As the ratio of boys to girls is 79,We can assign the boys a weight of 7, and the girls a weight of9.
Now, we only need to place the data into the weighed average formula
Weighted average height=[(average height of girls'appropriate weight)+(average height of
boys’appropriate weight)]/ sum
Of weights = [(3.9*9)+(4.05*7)]/(9+7)=3.966
8.At the Eleanor Rigty Community College, a student will fail their first year f they
receive an average of less than 65.
Maths and Science classes are worth 70% of the final grade while Social Science courses
are worth 30% of the final grade.
Louse took fur classes in her first year.and received a grade of in her final Mathematics
test
10 in her Physics class,8o in Chemistry and 3l in Sociology (physics,Chemistry and math
are both considered science)
Did Louise pass her first year?
A. Yes B. No C. Cannot Say
答案解析：AThis question can be solved without any calculations as long as you understand one of the main
concepts of the weighted average:
the heavier the weight, the closer the weighted average will be to the value assigned to it.
At the weight of 70% we have the following grades:90,100 and 80(average of 90).
At the weight of 30% we have the following grade: 30.
If we calculated a "regular" average we would come to the conclusion that Louise faled her first
year,as the average of 90 and 30 is 60.However, since 70% is a much heavier weight than 30% the
weighted average is "puled”" away from 60 (the regular average), higher towards the grade of 90
(the value of the heavier weight).
in order to know the exact value of the weighted average we will have to calculate it, but we can
intuitively say that Louise probably dd not fail her first year since the value of 90 has a greater
'weight.
Here is the calculation:(90*0.7+30*0.3)/1= 72(this is the final grade).
9.It takes Robin 3 minutes to answer each of the first 5 questions in the first section
of the test, and 10 minutes to answer each question in the second section.
On average,it takes her 6.5 minutes to answer each question.
How many questions are there in the second section of the test?
A. 4 B. 5 C. 6 D. 7
答案解析：B
It takes Robin a different amount of time to answer different questions in the test in other
words,we can say that when calculating her average speed,each amount of time carries a
different weight in the calculation, so to speak, according to the appropriate number of
questions.This is a weighted average.
The formula to calculate a weighted average is:
Weighted average =(Value1*weight1+ value2*weight2)/ (total value of weights)
"5 questions in 3 minutes" provides the first value and its weight
"10 minutes per question" provides the second value.
"6.5 minutes on average" provides the weighted average.
We need to find the missing weight of the second value.Let's place all the figures we have in the
formula
6.5=(3*5+10*weight)/(5+weight)
Replace "weight" with "X” if you find this more comfortable, and solve for X：
6.5=(15+10X)/5+X
Multiply by (5+X):
6.5*(5+X)=15+10X
32.5+6.5X=15+10X
32.5-15=10X-6.5X
17.5=3.5X
X=5
10.Curt is a professional athlete.
On an average he burns 300 calories per hour.
A training day includes: running for 1 hour,bicycling for 4 hours and swimming for 2hours.
Curt knows he burns so0 calories per hour running and 400 calories per hour swimming.
How many calories does curt burn per hour on his bicycle?
A. 175 B. 225 C. 1800 D. 450
答案解析：A
In this question we are given a weighted average- the average of calories but on a day of
training.Given this information,we are asked to calculate how many calories are burnt during an
hour of cycling.In weighted average ferns we are asked to find the value of cycling.
Here is what we know.
Weighted average 300 cal
Running value is 60Ocal, weight is 1 (hour).
Swimming value is 400 cal, weight is 2 (hours)
Cycling value is unknown; weight is 4(hours).
We can simply place all the information in the weighted average
formula and find the missing value.(600*1+400*2+missing value*4)/7=300
600*1+400*2+missing value*4=30*7
400+4’missing value=2100
4’missing value =700
missing value =175
11.Class grades are calculated in the following way. the mid-term quiz is worth 20% of
the final grade, homework
assignments are worth 10%,class participation is worth 10% and the final exam is worth
60%
How much did Mar get on his mid-term quiz,if his final grade is 90),
and we know that he got g0 on his final exam and full credit for class participation and
homework assignments?
Note that100 is the highest mark possible and equals full credit.
A. 90 B. 100 C. 80 D. 95
答案解析：C
Since we know Mark's final grade,as well as his other grades apart from the quiz we can
place the data in the weighted average formula, with the unknown quiz grade marked as x
First, let's assign the appropriate weight for each grade:
Quiz:x→02
Homework:100→0.1
Class:100→0.1
Exam:90→0.6
This set is then divided by the sum of all weights,which is 1:
(0.2*X+0.1*100+0,1*100+0,6*90)/1=90
As Mark's final weighted grade is 90.the above set eguals 90.Since dividing
by 1 leaves the figure as it is,there is no need to factor this in to our calculation:
0.2*x+0.1*100+0,1*100+0.6*90=90
0.2*x=90-10-10-54
0.2*X=16X=80
Therefore, we can see that Mark's exam grade was 80.
12.The requirement to a certain University is a weighted grade of 85.
The grade is based on a high-school final average grade,which is worth 80% of the weighted
grade and an admission test,which is worth 20% of the weighted grade.
What is the minimal score that Margaret is required to get in her admission test in order to be
accepted, if her high-school final average grade is 90?
A. 90 B. 80 C. 50 D. 65
答案解析：D
Let Margaret’s unknown admission test grade be x
Now,since we have all the other variables -the remaining grades which make up the weighted
grade and the weighted grade it self - all we have to do It’s place the data into the weighted
average formula.
First.we assign each grade with its relative weight as fractions
0.2*X+0.8*90
Then.we divide this set by 1.which is the sum of the weights assigned tn the grades
There is no need for further calculations to factor this in, as dividing by 1 leaves the numbers as
they are.
This set equals 85, which is the weighted grade Margaret must receive.
Therefore.we arrive at the following equation:
0.2*x+0.8*90=85
In order to make the calculation easier by not using fractions,we can muitiply by 10:
2*X+8*90=850
2*X=850-720
2*X=130
X=65
The minimal store Margaret mus receive on her admission test is 65.
13.What is a company’s average profit per unit if the distribution of the number of
units sold per product(as % of all sales) is as
follows:ProdutA-10%,Produc1B-30%,ProductC-25%, and Product D-35% and the profits from
seling one unit of products A-D is 9,12,10 and 22 respectively?
A. 15.45 B. 14 C. 14.7 D. 18.1
答案解析：C
When calculating the company's average profit per unit,we need to take into account two factors:
the different products' profit per unit and the number (or more precisely, the %) of units sold per
product in other words,we need to calculate the weighted average of profit per unit,
with the profits per unit serving as the values and the % of all sales serving as the weights.
Profits per units and sales numbers (in %) are explicitly provided in the question
Thus,we can calculate the company's average profit per unit=
[(profit from A*weight of A)+(profit from B*weight of B)+(profit from C*weight of C)+(profit from
D*weight of D)]/sum of weights
=[(9*0.1)+(12*0.3)+(10*0.25)+(22*0.35)]/(0.1+03+0.25+0.35)=14.7/1=14.7
