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Of the numbers q, r, s, and t, which is greatest?

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by BTGModeratorVI » Wed Feb 26, 2020 4:15 pm

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Answers

A

B

C

D

E

Stats

Difficulty—

Of the numbers q, r, s, and t, which is greatest?

(1) The average (arithmetic mean) of q and r is s.
(2) The sum of q and r is t.

Answer: E
Source: Official Guide
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Source: — Data Sufficiency |

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Re: Of the numbers q, r, s, and t, which is greatest?

by Jay@ManhattanReview » Thu Feb 27, 2020 9:40 pm
BTGModeratorVI wrote: ↑
Wed Feb 26, 2020 4:15 pm
 Of the numbers q, r, s, and t, which is greatest?

(1) The average (arithmetic mean) of q and r is s.
(2) The sum of q and r is t.

Answer: E
Source: Official Guide
Statement 1 is insufficient as we do not have any information about t, whereas Statement 2 is insufficient as we do not have any information about s.

(1) and (2) together

Case 1: Say q, r, s, and t are all positive.

From (1), we conclude that s is not the greatest and from (2), we conclude that q and r are not the greatest; thus, t is the greatest. The answer is t.

Case 2: Say q, r, s, and t are all negative.

From (1), we conclude that s is not the greatest and from (2), we conclude that t is the smallest; thus, q or r is the greatest. No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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Re: Of the numbers q, r, s, and t, which is greatest?

by Brent@GMATPrepNow » Fri Feb 28, 2020 9:32 am
BTGModeratorVI wrote: ↑
Wed Feb 26, 2020 4:15 pm
 Of the numbers q, r, s, and t, which is greatest?

(1) The average (arithmetic mean) of q and r is s.
(2) The sum of q and r is t.

Answer: E
Source: Official Guide
Target question: Of the numbers q, r, s, and t, which is greatest?

Statement 1: The average (arithmetic mean) of q and r is s
No information is given about t
Statement 1 is NOT SUFFICIENT

Statement 2: The sum of q and r is t.
No information is given about s
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that (q + r)/2 = s
Multiply both sides by 2 to get: q + r = 2s

Statement 2 tells us that q + r = t

There are several values of q, r, s and t that satisfy BOTH statements. Here are two:
Case a: q = -1, r = 1, s = 0 and t = 0. In this case, the answer to the target question is r is the greatest value
Case b: q = 1, r = -1, s = 0 and t = 0. In this case, the answer to the target question is q is the greatest value
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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