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Find the number of factors of the number p

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GMATBusters
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Re: Find the number of factors of the number p [#permalink] Find the number of factors of the number p   03 May 2018, 18:10
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Hii

Initially there was a typo (x^12) in the question.
It was revised to x^2 later.

Now, the question and OA are correct.

2) x, y, z given can be equal unless explicitly mentioned that they are distinct.

Try the question again, taking x^2.
Tag me if u dont get the right answer now.

jayantk94 wrote:
I feel if the terms are given as x, y and z , they are bound to be distinct terms.
This leads us to the fact that P != 1 , and P= 2 , can be the only solution.
IMO B is the correct choice here.

P.S. : I see some folks have used x^12 , while I see x^2 in the question. Can anyone clarify?
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rajneetsingh29
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Re: Find the number of factors of the number p [#permalink] Find the number of factors of the number p   05 May 2018, 18:51
If we assume that x,y and z could be the same number then as per statement (2) numbers could be 1 or 2, as explained by the expert, then after considering statement (1) where no is having odd no of factors then 1 is the no that satisfied the both the condition so the answer should be C
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amanvermagmat
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Re: Find the number of factors of the number p [#permalink] Find the number of factors of the number p   07 May 2018, 08:33
rajneetsingh29 wrote:
If we assume that x,y and z could be the same number then as per statement (2) numbers could be 1 or 2, as explained by the expert, then after considering statement (1) where no is having odd no of factors then 1 is the no that satisfied the both the condition so the answer should be C


Hello

The number 'p' can actually be either '1' or '64', NOT 1 or 2.

If p=1, then p can be written as 1^2 or 1^3 or 1^6.
If p=64, then p can be written as 8^2 or 4^3 or 2^6.

Both 1 and 64 have odd number of factors (1 has 1 factor and 64 has 7 factors). Hence answer is E
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bunny12345
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Find the number of factors of the number p [#permalink] Find the number of factors of the number p   07 May 2018, 09:23
souvik101990 wrote:

GST Week 2 Day 5 e-GMAT Question 5


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details



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.


Answer is Option E.

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] Find the number of factors of the number p   25 Sep 2019, 00:02
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
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Re: Find the number of factors of the number p [#permalink]
25 Sep 2019, 00:02
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