OG Is 5^(X+2)/25 < 1?

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Wed Aug 23, 2017 9:21 pm

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Is 5^(x+2)/25 < 1?

(1) 5^x < 1
(2) x < 0

D

Source: Beat The GMAT — Data Sufficiency | Wed Aug 23, 2017 9:21 pm

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by [email protected] » Thu Aug 24, 2017 6:03 pm

Hi AbeNeedsAnswers,

We're asked if [5^(X+2)]/25 is less than 1. This is a YES/NO question. With certain DS prompts, it can sometimes help to do a bit of set-up work before you work on the two Facts.

Here, we know that 5^2 = 25, so if X=0, then we'd have 25/25 = 1. So the issue here really comes down to whether X is less than or equal to 0. If it IS less than or equal to 0, then the answer to the question will be YES. If X is > 0 though, then the answer will be NO.

1) 5^X < 1

Since 5^0 = 1, with this Fact we know that X MUST be less than 0... so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) X < 0

From our set-up work, we know that this leads to an ALWAYS YES answer.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue May 29, 2018 5:19 pm

AbeNeedsAnswers wrote:Is 5^(x+2)/25 < 1?

(1) 5^x < 1
(2) x < 0

We can simplify the inequality:

5^(x+2)/25 < 1

(5^x * 5^2)/25 < 1

5^x < 1

Thus the question becomes: Is 5^x < 1?

Statement One Alone:

5^x < 1

Since we are given 5^x < 1, so statement one is sufficient to answer the question.

Statement Two Alone:

x < 0

If x < 0, then 5^x < 5^0. That is, 5^x < 1. Statement two is also sufficient to answer the question.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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