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

Re: If the integers a and n are greater than 1 and the product [#permalink]
14 May 2012, 01:48

Expert's post

kashishh wrote:

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 th [#permalink]
21 Jan 2013, 22:36

This one is a fun question (a good practice of our understanding of factors)!

Analyze the given first before delving into the statements. 8*6*7*5*4*3*2*1 = a^n * R

Statement (1): a^n = 64 8*6*7*5*4*3*2*1 = 64 * R

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]
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