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# Find the number of factors of the number p

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Find the number of factors of the number p [#permalink]
souvik101990 wrote:

GST Week 2 Day 5 e-GMAT Question 5

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Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as $$x^{2}$$, $$y^{3}$$ or $$z^{6}$$ where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.

Statement 1: There are many number <=100 which have odd factors. Examples: 2^2, 2^4, 2^6, etc..In these examples the factors will be 3, 5, and 7 respectively. Hence, this can't give us an answer. Thus, INSUFFICIENT.

Statement 2: Lets take number 64 because if we take any other number raised to power 6 it will be >100. 64 can be written as 2^6, 4^3, and 8^2. Even in this case we have different number of factors i.e. 7, 4, and 3. Thus also INSUFFICIENT.

Taking Statement 1 and 2 together: Statement 1 says p must have odd factors, hence we can only take 2^6 and 8^2. But even among these 2 we have different number of factors, i.e. 7 and 3.

So, even after combining 2 statements we cant solve it. Hence E
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Re: Find the number of factors of the number p [#permalink]
with first condition we can conclude that p can be only the square number under 100 so that will square of the number between 1 to 9
and for the second condition we can se only 1 and 64 are the number that satisfy the requirement.

Hence alone these statement cannot go and even if we take 1 and 64 two choice left hence insufficient data to conclude
Re: Find the number of factors of the number p [#permalink]
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