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• ### The winning strategy for a high GRE score

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# M70-02

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Math Expert
Joined: 02 Sep 2009
Posts: 52108

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03 Sep 2018, 00:56
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Difficulty:

45% (medium)

Question Stats:

67% (01:25) correct 33% (01:44) wrong based on 6 sessions

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If x is a positive integer that is less than 20, what is x?

(1) $$x + 7$$ divided by 5 has a remainder of 1.

(2) $$x$$ divided by 4 has a remainder of 2.

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Math Expert
Joined: 02 Sep 2009
Posts: 52108

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03 Sep 2018, 00:56
Official Solution:

We’ll go for PRECISE because all the information we need is in the question.

(1) If $$x$$ is a positive integer under 20, $$x + 7$$ must be a positive integer under 27. The integers in this range that have a remainder of 1 when divided by 5 are those that are larger by 1 than a multiple of 5: these are the numbers 1, 6, 11, 16, 21, and 26 – meaning that x can be 4, 9, 14 or 19. But which one? (A) and (D) are eliminated.

(2) The numbers under 20 that have a remainder of 2 when divided by 4 are larger by 2 than a multiple of 4: 2, 6, 10, 14, and 18, so we don’t have a definite result. (B) is eliminated. Combining (1) and (2) leaves only 14 as a possible answer. Enough! (E) is eliminated.

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Joined: 10 Oct 2018
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Location: India
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03 Dec 2018, 06:04
Why 14?
Re: M70-02 &nbs [#permalink] 03 Dec 2018, 06:04
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# M70-02

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