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# When a positive integer p is divided by 3, what is the remainder? 1) W

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Math Revolution GMAT Instructor
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When a positive integer p is divided by 3, what is the remainder? 1) W [#permalink]

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20 Sep 2017, 00:48
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[GMAT math practice question]

When a positive integer p is divided by 3, what is the remainder?

1) When p^2 is divided by 3, the remainder is 1
2) When p is divided by 2, the remainder is 1
[Reveal] Spoiler: OA

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When a positive integer p is divided by 3, what is the remainder? 1) W [#permalink]

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20 Sep 2017, 06:27
MathRevolution wrote:
[GMAT math practice question]

When a positive integer p is divided by 3, what is the remainder?

1) When p^2 is divided by 3, the remainder is 1
2) When p is divided by 2, the remainder is 1

Statement 1: if $$p^2=25$$ when divided by 3 leaves 1 as a remainder, but $$p=5$$ when divided by 3 leaves a remainder 2.

Now if $$p^2=49$$ when divided by 3 leaves 1 as remainder, but $$p=7$$ when divided by 3 leaves a remainder 1.

So we get two remainders for different values of $$p^2$$. Hence Insufficient

Statement 2: This implies that $$p$$ is ODD. but Odd number when divided by 3 can leave 1 & 2 as remainders. Hence Insufficient

Combining 1 & 2. both the statements are not sufficient to lead to the value of p and as is clear from the illustrations there can be two different remainders. Hence insufficient

Option E

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Math Revolution GMAT Instructor
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Re: When a positive integer p is divided by 3, what is the remainder? 1) W [#permalink]

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24 Sep 2017, 19:20
=>

Condition 1) & 2)
The remainder of p = 5 is 2, when it is divided by 3.
The remainder of p = 7 is 2, when it is divided by 1.

Ans: E
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Re: When a positive integer p is divided by 3, what is the remainder? 1) W   [#permalink] 24 Sep 2017, 19:20
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