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Advanced Numerical Reasoning Test 2
Solutions Booklet
Instructions
This numerical reasoning test comprises 30 questions, and you will have 30 minutes in
which to correctly answer as many as you can. Calculators are NOT permitted for this test,
and it is recommended you have some rough paper to work on.
This test comprises two sub-tests:
Subtest 1: Comparison of Quantities (Questions 1-15)
This test requires you to make a comparison between two quantities, A and B. For some of
the exercises, additional information is given which should also be used in your determination
of quantity.
Subtest 2: Sufficiency of Information (Questions 16-30)
This test consists of exercises in which you are given a question and two statements, labelled
(A) and (B), which give certain information. You are asked to decide whether the information
given in the two statements is sufficient to answer the question, either separately or in
combination.
Try to find a time and place where you will not be interrupted during the test. The test will
begin on the next page.
AssessmentDay
Practice Aptitude TestsA B
30% 1/3
Q1 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Express 1/3 as a percentage, and compare to 30%.
1/3 = 0.3333 = 33.33%
30% < 33.33%
Thus, the correct answer is (B) Quantity B is greater than Quantity A.
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The revenue generated from selling 55 units of The gross profit generated from selling 60
product A units of product B
Note: Product A is sold for £50. Product B is sold for £75. Both product A and B cost £30 to make.
Q2 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate the revenue generated from selling 55 units of product A by multiplying £50 by 55.
£50 x 55 = £2,750
Step 2 – Calculate the profit generated from selling 60 units of product B by calculating the revenue
generated, and subtracting the production cost of product B. Next, we compare A and B.
£75 x 60 = £4,500
£4,500 – (60 x £30) = £2,700
£2,750 > £2,700
Thus, the correct answer is (A) Quantity A is greater than Quantity B.
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5 x 9 x 3 35 + 45 + 51
Q3 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate the sum in A.
5 x 9 x 3 = 135
Step 2 – Calculate the sum in B and compare to A.
35 + 45 + 51 = 131
135 > 131
Thus, the correct answer is (A) Quantity A is greater than Quantity B.
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The gross profit of company A The net profit of company B
Note: Company A generates 11.3 million in revenue with 8.5 million in costs. Company B generates
15.8 million in revenue with 12.4 million in costs.
Q4 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – We are not provided with sufficient information to calculate the net profit, only the gross
profit.
Thus, the correct answer is (D) Insufficient information is given to make the comparison.
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16% of 527 0.095 x 876
Q5 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate 16% of 527.
527 x 0.16 = 84.32
Step 2 – Calculate 0.095 x 876 and compare to A.
0.095 x 876 = 83.22
84.32 < 83.22
Thus, the correct answer is (A) Quantity A is greater than Quantity B.
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An absolute majority of votes across 2.3 million A simple majority of votes across 4.8 million
voters voters
Q6 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Although an absolute majority must be over 50%, a simple majority does not. Therefore, it is
not possible to speculate as to the size of B.
Thus, the correct answer is (D) Insufficient information is given to make the comparison.
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One third, of one fourth, of one sixth One half, of one eighth of one fifth
Q7 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate one third, of one fourth, of one sixth
0.333 x 0.25 x 0.167 = 0.014
Step 2 – Calculate one half of one eighth of one fifth. Then, compare with A.
0.5 x 0.125 x 0.20 = 0.013
0.014 > 0.013
Thus, the correct answer is (A) Quantity A is greater than Quantity B.
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40 % of 8 sales averaging £2.80 per sale
30% of 5 sales averaging £5.85 per sale
Q8 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate 30% of 5 sales averaging £5.85 per sale.
0.3 x 5 x £5.85 = £8.78
Step 2 – Calculate 40 % of 8 sales averaging £2.80 per sale and compare to A.
0.4 x 8 x 2.8 = £8.96
£8.78 < £8.96
Thus, the correct answer is (B) Quantity B is greater than Quantity A.
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(8 + Y) / X (3 + X) / (7 – Y)
Note: 5 < X < Y
Q9 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Depending on the size of Y, either A or B could be the larger number. As a result, we cannot
accurately deduce whether A or B is larger.
Thus, the correct answer is (D) Insufficient information is given to make the comparison.
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The GDP per capita of country A The GDP per capita of country B
Note: County A has a GDP of 267 billion, and a population of 25 million. Country B has a GDP per
capita of £10,680.
Q10 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate the GDP per capita of country A by dividing the GDP by the population. Compare
this number to the GDP of country B (£10,680).
287,000,000,000 / 25,000,000 = £10,680
£10,680 = £10,680
Thus, the correct answer is (C) Quantities A and B are equal.
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Out of 150 throws, the estimated number of
Out of 50 throws, the estimated number of odd
2s landed on.
numbers landed on.
Note: The die is 6 sided and fair.
Q11 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate the estimated number of odd numbers landed on out of 50 throws.
50 / 2 = 25
Step 2 – Calculate the estimated number of 2s landed on out of 150 throws, then compare against A.
150 / 6 = 25
25 = 25
Thus, the correct answer is (C) Quantities A and B are equal.
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The estimated number of poisonous mushrooms The estimated number of poisonous
among 50 red mushrooms and 24 green mushrooms among 30 green mushrooms and
mushrooms 32 blue mushrooms.
Note: 22% of red mushrooms are poisonous. A third of green mushrooms are poisonous. Seven out
of 20 blue mushrooms are poisonous.
Q12 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate the estimated number of poisonous mushrooms among 50 red mushrooms and 24
green mushrooms.
(50 x 0.22) + (24 x 0.334) = 19
Step 2 – Calculate the estimated number of poisonous mushrooms among 30 green mushrooms and
32 blue mushrooms. Then, compare with A.
(30 x 0.334) + (32 x 0.35) = 21.22
19 < 21.22
Thus, the correct answer is (B) Quantity B is greater than Quantity A.
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The speed of a car moving at 1.2 miles per
The speed of a train moving at 75 miles an hour
minute
Q13 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Convert the speed of the car to miles per minute, and compare against B.
75 / 60 = 1.25 miles per minute
1.25miles per minute > 1.2miles per minute
Thus, the correct answer is (A) Quantity A greater than Quantity B.
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The probability of selecting a yellow ball at The probability of selecting a green ball at
random random
Note: A bag contains fewer than 25 balls. 5 blue balls, 3 red balls, 8 green balls and the remainder
are yellow balls.
Q14 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – The question states that “fewer” than 25 balls are in the bag, and that the remainder are
yellow (i.e. anywhere between 1 and 8 yellow balls). Because we cannot deduce the number of yellow
balls, we cannot answer the question.
Thus, the correct answer is (D) Insufficient information is given to make the comparison.
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200%
The percentage increase from £150 to £450
Q15 Which value is greater A or B?
(A) Quantity A is greater than Quantity B.
(B) Quantity B is greater than Quantity A.
(C) Quantities A and B are equal.
(D) Insufficient information is given to make the comparison.
Step 1 – Calculate the size of the percentage increase from £150 to £450 and compare this to 200%.
450 – 150 = 300
300 / 150 = 2 = 200%
200% = 200%
Thus, the correct answer is (C) Quantities A and B are equal.
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One ounce of silver is worth £11.75 at week 1
Frank’s silver was worth £12,763 on week 3
and £24.21 by week 4.
Note: Frank invests in silver in week 1. By Week 2, his investment has increased by 3% in value. On
week 3, his investment drops by 1.3% from the previous week. On week 4, the value of his
investment doubles from the week 2 value.
Q16 How much is Frank’s silver worth on week 4?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the
question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Knowing the value of the silver in week 3 allows us to work backwards. We reverse the
decrease in this figure by 1.3%, and then double it to obtain the value in week 4.
£12,763 / 0.987 = £12,931.10436
£12,931.10436 * 2 = £25,862.21
Step 2 – Knowing the value of silver by the ounce does not help us answer the question, as we do not
know how many ounces of silver Frank owns.
Thus, the correct answer is(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient
to answer the question.
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Half of employees contribute 3% of their The average employee earns £2,218 per
monthly wages to their pension fund. month
Note: 46 employees are paying into a pension fund. Half of the employees contribute the same
amount each month.
Q17 How much does the average employee contribute in £?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – We are told that half of employees contribute 3% of their monthly wages to their pension
fund. This is not enough to calculate the average employee contribution.
Thus, the correct answer is (E) Statements 1 and 2 together are NOT sufficient to answer the
question asked.
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The shares have increased in value by £2,115 The shares have accrued £134 worth of
every year since the shares were purchased 3 dividends every year since the shares were
years ago. purchased.
Q18 How much gross income would have been made on the shares if they were
to be sold now?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Knowing how much the shares have increased in value helps us calculate the answer to the
question. We multiply the number of years since the investment by the total increase in value per
year.
£2,115 x 3 = £6,345
Step 2 – Knowing the dividends accrued per year also helps us answer the question, but only in
conjunction with the information in B. We then combine the numbers from and A and B to answer the
question.
£134 x 3 = £402
£402 + £6,345 = £6,747
Thus, the correct answer is (C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the
question, but NEITHER statement ALONE is sufficient.
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Michele and Janice’s combined income exceeds Michelle earns £5,000 per year more than
Albert’s. Janice.
Note: Albert earns double what Janice earns.
Q19 Who earns the most out of these three?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – It is not possible to determine how much any of these people earn. All we know for certain is
that Michelle earns more than Janice, and that Albert earns more than Janice. We cannot tell whether
Michele earns more than Albert or vice versa. (For example, if Janice earns £5,000 per year, Michelle
and Albert will earn the same amount of money).
Thus, the correct answer is(E) Statements 1 and 2 together are NOT sufficient to answer the question
asked.
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The cargo ship makes 4 journeys to city A from The cargo ship delivers £25,000,000 worth of
city B, and is 75% full for each journey. cargo each trip, with each tonne of cargo
valued at £30,303.03
Note: A cargo ship can transport a maximum of 275 tonnes of cargo at any given time.
Q20 What is the total combined value of the cargo transported across all four
trips?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Knowing that the cargo ship makes 4 journeys means we can later calculate the total value
of four trips.
Step 2 – Knowing the value of the cargo, and the value of cargo per tonne allows us to calculate the
value of four trips.
4 x £25,000,000 = £100,000,000
Thus, the correct answer is (C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the
question, but NEITHER statement ALONE is sufficient.
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At the beginning of 2013, company A had 5,460 The number of employees at company A
employees and 187 employees left company A increased by 7% by the end of 2013
during 2013.
Q21 What was the net change (%) in company A’s number of employees at the
end of 2013?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the
question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Knowing how many employees have left the company does not tell us the net change in the
number of employees. Without knowing how many employees joined, we cannot answer the question
with A.
Step 2 – If the number of employees at company A increases by 7%, that means that a net increase
of 7% occurred by the end of 2013.
Thus, the correct answer is (B) Statement 2 ALONE is sufficient, but statement 1 alone is not
sufficient to answer the question.
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A maximum of 130 bushels of corn can be Corn is currently valued at £2.12 per bushel.
grown per acre per year.
Q22 How much profit can be generated by selling the maximum amount of corn
that can be grown from 17 acres of farm land in 1 year?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – The question asks for profit, not revenue. Because we are not given the associates costs of
growing and selling corn, we cannot calculate the answer.
Thus, the correct answer is (E) Statements 1 and 2 together are NOT sufficient to answer the
question asked.
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A visitor has a 1/5 chance of making a purchase The average purchase on the website is
valued at £5.82
Note: The website received 32,827 visitors this month.
Q23 How much revenue would be generated per visitor?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Knowing that a visitor has a 1/5 chance of making a purchase, that the average purchase
equals £5.82 and that the website receives 32,826 visitors per month allows us to calculate the
amount of revenue generated per visitor.
0.2 x 5.82 x 32,827 = £38,210.632
Thus, the correct answer is(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the
question, but NEITHER statement ALONE is sufficient.
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Denise and her partner’s combined monthly Denise pays £850 per month in rent. This
expenses equal £3,124, which is paid for accounts for an absolute majority of her
equally between the two of them. This monthly outgoings.
constitutes all of their expenses.
Note: Denise earns £2,478 per month after tax.
Q24 How much money will Denise have at the end of the month?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the
question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Knowing that Denise the combined monthly expenses equal £3,124 and are equally divided
between them means that she spends £1,562 per month. We then subtract this from her earnings and
we have the answer to the question.
£2,478 - £1,562 = £916
Step 2 – Knowing that her rent accounts for an absolute majority of her outgoings won’t help us
answer the question, and enough information is found in A to answer the question.
Thus, the correct answer is (A) Statement 1 ALONE is sufficient, but statement 2 alone is not
sufficient to answer the question.
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Charities account for 18% of research
Government funding accounted for 32% of all
funding, and private corporations provided
research funding. Government funding is the
£850,000 this year. There are only three
second largest source of funds for research.
sources of funding.
Q25 How much funding did the research department receive this year?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Using both A and B, we can deduce that government funding and charities account for 50%
of all research funding, and therefore private companies must account for the other 50%. Since
£850,000 accounts for 50% of funding, doubling this figure reveals the answer.
£850,000 x 2 = £1,700,000
Thus, the correct answer is (C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the
question, but NEITHER statement ALONE is sufficient.
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Product A costs £51 to produce. Product A has a gross profit margin of 20%.
Note: A gross profit of £12.75 is made on every sale of product A.
Q26 How much is product A sold for?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – If product A costs £51 to produce, and it is sold at a gross profit of 12.75, it must therefore
cost £63.75.
Step 2 – To calculate the price of product A we can divide the gross profit margin by the gross profit,
identifying the original price.
12.75 / 0.2 = £63.75
Thus, the correct answer is (D) EACH statement ALONE is sufficient to answer the question asked.
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Two thirds of all emails are legitimate emails On average, 24 emails are received per day
from the contact list.12.5% of all emails received during the week. On average, 11 emails are
are advertisements. 15% of emails are received per day during the weekend.
legitimate emails from senders not listed on the
contact list. The remainder are phishing emails.
Q27 What is the probability that any given email will be a phishing email?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the
question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – If two thirds (66.67%) of emails are legitimate emails from the contact list, 12.5% are
advertisements and 15% are legitimate emails not from the contact list,5.83% of emails must be
phishing emails.
Step 2 – The number of emails received is not required to calculate the probability of a particular
email being a particular email. The question asks for the probability that an email will be a phishing
email, not the number of phishing emails.
Thus, the correct answer is (A) Statement 1 ALONE is sufficient, but statement 2 alone is not
sufficient to answer the question.
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The investor purchased £5,671.00 worth of An ounce of platinum and an ounce of silver
platinum and £1,215.21 worth of silver. cost £782.03 and £10.68, respectively, at the
time of purchase.
Note: An investor purchases gold, silver and platinum at a ratio of 4:3:7 in (£).
Q28 How much gold did the investor purchase in ounces?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – We cannot deduce how much was spent on the ounces of gold which were purchased by
the investor, as we do not know the price of gold per ounce. The ratio of 4:3:7 only refers to the prices
paid of silver, gold and platinum, purchased in relation to each other, and has no bearing to the
weight/quantity of these metals.
Thus, the correct answer is (E) Statements 1 and 2 together are NOT sufficient to answer the
question asked.
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The odds of rolling a 6 are doubled and the On the last 7 rolls, the number 4 came up 5
odds of rolling a 2 are zero. times.
Q29 What are the odds of rolling a 5 on a 6 sided die?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the
question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Because the odds of rolling a 6 are doubled, and the die will never roll a 2, the odds of rolling
a 5 will be the same as it would be on a fair die, a 1 in 6 chance.
1/6 = 16.67%
Step 2 – Knowing the numbers that previously came up does not help us calculate the answer as it
has no bearing on future throws.
Thus, the correct answer is (A) Statement 1 ALONE is sufficient, but statement 2 alone is not
sufficient to answer the question.
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Customer services staff spend on average 3.4 Customer service staff talk to between 25-45
hours per day handling phone calls from customers per day on the phone.
customers.
Q30 How much time is spent on the phone on average with each customer?
(A) Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question.
(B) Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question.
(C) BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements 1 and 2 together are NOT sufficient to answer the question asked.
Step 1 – Without knowing the exact number of customers which staff talk to per day, we cannot
accurately calculate the amount of time spent on the phone to customers on average.
Thus, the correct answer is (E) Statements 1 and 2 together are NOT sufficient to answer the
question asked.
-- End of Test --
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