BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

GMAT PREP Ques - Need expert advice

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 447
Joined: Sun Apr 22, 2012 7:13 am
Thanked: 46 times
Followed by:13 members
GMAT Score:700

by hemant_rajput » Sun May 19, 2013 11:13 pm
Manpreet Singh 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


Is the integer n odd?
(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n

Please don't post multiple question in one post. It won't help others to make proper use of the solution or idea posted in your post.

Now lets take your questions.

1.

Product of 1st +ve integers will be 1*2*3*4*5*6*7*8 = 2^7 * 3^2 * 5 * 7.
This is a multiple of a^n, where a,n > 1

a. 2^6 = 64 or 4^2 = 64. hence not sufficient.

b only 2 is the possible value of a as it can only be raised to 6.


Answer is B.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 447
Joined: Sun Apr 22, 2012 7:13 am
Thanked: 46 times
Followed by:13 members
GMAT Score:700

by hemant_rajput » Sun May 19, 2013 11:14 pm
2.
n = odd ?

a. 3 is odd while 6 is even. hence not sufficient.
b. 2n has double the factor as n has.
lets say n is odd and of form a^p * b^q * c^r where a,b and c are all odd prime integer and p,q and r are just +ve number.
so no. of factor of n will (p+1)*(q+1)*(r+1) which will be odd.
so 2n will be of form 2 * a^p * b^q * c^r and have total factor of
(1 + 1)* (p+1)*(q+1)*(r+1).
but if n is even then this statement won't stand.

Hence b is sufficient.

Answer is B.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
Top
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Wed Apr 17, 2013 7:46 am
Thanked: 2 times

by [email protected] » Tue May 21, 2013 1:02 am
Manpreet Singh 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


Is the integer n odd?
(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n
Here is my two cents for the second question.
Statement 1: clearly insufficient becasue n can be 3, 12, 6, 15 etc
statement 2: If n is an odd number than 2n has twice the number of factors than that of n.

For Eg n=3 has two factors 1 and 3.
2n= 6 has four factors 1,2,3 and 6.

Thus B alone is sufficient.
Top
Post new topic Post Reply
• Page 1 of 1