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
OA:B
Source:GMATPrep
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If the integers a and n are greater
This topic has expert replies
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
8! = 8*7*6*5*4*3*2 = (2³)(7)(2*3)(5)(2²)(3)(2) = (2�)(3)(5)(7).NandishSS 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
Since the product above is a multiple of a^n, we get:
(2�)(3)(5)(7) = (a^n)(k), where k is a positive integer.
Statement 1:
It's possible that a=2, n=6 and k=2*3*5*7, with the result that the following values in red are equal:
(2�)(3)(5)(7) = (2�)(2)(3)(5)(7)
It's possible that a=4, n=3 and k=2*3*5*7, with the result that the following values in blue are equal:
(2�)(3)(5)(7) = (4³)(2)(3)(5)(7).
Since a can be different values, INSUFFICIENT.
Statement 2:
(2�)(3)(5)(7) = (a�)(k).
The equation above is valid only if a=2 and k=2*3*5*7, as follows:
(2�)(3)(5)(7) = (2�)(2)(3)(5)(7).
Thus, a=2.
SUFFICIENT.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
For the red colored part, how did it strike to you that you have to split it?Statement 1:
It's possible that a=2, n=6 and k=2*3*5*7, with the result that the following values in red are equal:
(2�)(3)(5)(7) = (2�)(2)(3)(5)(7)
It's possible that a=4, n=3 and k=2*3*5*7, with the result that the following values in blue are equal:
(2�)(3)(5)(7) = (4³)(2)(3)(5)(7).
Since a can be different values, INSUFFICIENT.
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Follow the portions in red and blue.sampatr wrote:For the red colored part, how did it strike to you that you have to split it?Statement 1:
It's possible that a=2, n=6 and k=2*3*5*7, with the result that the following values in red are equal:
(2�)(3)(5)(7) = (2�)(2)(3)(5)(7)
It's possible that a=4, n=3 and k=2*3*5*7, with the result that the following values in blue are equal:
(2�)(3)(5)(7) = (4³)(2)(3)(5)(7).
Since a can be different values, INSUFFICIENT.
Statement 1: a^n = 64
(2�)(3)(5)(7) = (a^n)(k).
(64*2)(3)(5)(7) = (a^n)(k).
Thus:
64 = a^n.
2*3*5*7 = k.
Statement 2: n=6
(2�)(3)(5)(7) = (a�)(k).
(2�*2)(3)(5)(7) = (a�)(k).
Thus:
2� = a�.
2*3*5*7 = k.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We are given that integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, thus:NandishSS 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
8!/a^n = integer
Recall that 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = (2^7) x (3^2) x 5 x 7.
We must determine the value of a.
Statement One Alone:
a^n = 64
There are multiple possible values of a. For instance, a = 2 and n = 6 (since 2^6 = 64) or a = 4 and n = 3 (since 4^3 = 64). Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
n = 6
Since n = 6, we know the following:
8!/a^6 = integer
The only factor in the prime factorization of 8! that has a power greater than 6 is 2^7; thus, the only possible value of a that will allow for 8!/a^6 to be an integer is 2.
Answer:B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
