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Re: If the integers a and n are greater than 1 and the product [#permalink]

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14 May 2012, 01:41

Bunuel wrote:

subhajeet wrote:

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6

Can anyone help me with this question. How is B the correct answer.

Prime factorization would be the best way to attack such kind of questions.

Given: \(a^n*k=8!=2^7*3^2*5*7\). Q: \(a=?\)

(1) \(a^n=64=2^6=4^3=8^2\), so \(a\) can be 2, 4, or 8. Not sufficient.

(2) \(n=6\) --> the only integer (more than 1), which is the factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient.

Answer: B.

Dear Bunuel, OA is B but why B? Kindly tell the source from where you get all these number properties/Prime no. properties? If its your Brain then only the explaination for the above will do ! All DS are on Number Properties and i am doing silly mistakes. i opted 'C' Thanx

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6

Can anyone help me with this question. How is B the correct answer.

Prime factorization would be the best way to attack such kind of questions.

Given: \(a^n*k=8!=2^7*3^2*5*7\). Q: \(a=?\)

(1) \(a^n=64=2^6=4^3=8^2\), so \(a\) can be 2, 4, or 8. Not sufficient.

(2) \(n=6\) --> the only integer (more than 1), which is the factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient.

Answer: B.

Dear Bunuel, OA is B but why B? Kindly tell the source from where you get all these number properties/Prime no. properties? If its your Brain then only the explaination for the above will do ! All DS are on Number Properties and i am doing silly mistakes. i opted 'C' Thanx

64 could be 2^6 or 8^2. In 8!, it contains at least 6 factors of 2. In 8!, it also contains 2 factors of 8. Thus, a could be 2 or 8. Thus, INSUFFICIENT.

Statement (2): n = 6 Let us analyze 8! = 8*7*6*5*4*3*2*1. How many prime factors have at least 6 factors in 8!. Let us start with a = 2. YES! Let us then try a=3. NO!

We are certain that 2 has the most number of factors in 8! and it has at least 6. SUFFICIENT. a = 2

Re: If the integers a and n are greater than 1 and the product [#permalink]

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22 Jan 2013, 12:22

product of the first 8 integers is: (2^8)(3^2)(5)(7)

Statement 1: a^n = 64. this means a could equal 2,4, or 8 because we don't know what n is. Not sufficient. Statement 2: if n = 6 the only possible value for a is 2 as the product of the first 8 integers does not include any other number raised to the 6th power. Sufficient

If the integers a and n are greater than 1 and the product of the first 8 positive integers of all real numbers is a multiple of a^n, what is the value of a?

If the integers a and n are greater than 1 and the product of the first 8 positive integers of all real numbers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6

The question is correct as it is. The first 8 positive integers are 1, 2, 3, 4, 5, 6, 7, and 8. What does "of all real numbers" has to do here? Also, notice that this is an official question from GMAT Prep, so it's as correct as it gets.
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Re: If the integers a and n are greater than 1 and the product [#permalink]

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27 Oct 2017, 09:05

When the question asked for the first 8 positive numbers, it was clearly describing a set. However, it wasn't clear to me what set they were describing. I spent time wondering if they were describing a set of "a" multiple, "n" multiples, or "a^n" multiples. There are many other GMAT questions were the wording is extremely specific but for this question you had to assume that we were looking at all real numbers, which is not always the case for other GMAT questions. So to me this is a very poorly worded question. You are very good at GMAT questions so you may have been able to recognize the question pattern right away, but for someone who is unable to make assumptions based on the question maker's mind, this question was not solvable. And the fact that this is a GMATPrep question does not make it infallible, in fact I have done other GMATPrep questions where even you yourself have stated that they made a mistake

When the question asked for the first 8 positive numbers, it was clearly describing a set. However, it wasn't clear to me what set they were describing. I spent time wondering if they were describing a set of "a" multiple, "n" multiples, or "a^n" multiples. There are many other GMAT questions were the wording is extremely specific but for this question you had to assume that we were looking at all real numbers, which is not always the case for other GMAT questions. So to me this is a very poorly worded question. You are very good at GMAT questions so you may have been able to recognize the question pattern right away, but for someone who is unable to make assumptions based on the question maker's mind, this question was not solvable. And the fact that this is a GMATPrep question does not make it infallible, in fact I have done other GMATPrep questions where even you yourself have stated that they made a mistake

Sorry but this does not make sense.

"The product of the first 8 positive integers" cannot possible mean anything but 1*2*3*4*5*6*7*8.
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