GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If x is the product of the positive integers from 1 to 8, in
[#permalink]
11 Aug 2020, 09:34
11 Aug 2020, 09:34
Expert Reply
1
Bookmarks
00:00
Question Stats:
77% (01:09) correct
22% (01:31) wrong based on 22 sessions
Hide Show timer Statistics
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that \(x = 2^i * 3^k * 5^m * 7^p\), then \(i + k + m + p =\)
A. 4
B. 7
C. 8
D. 11
E. 12
A. 4
B. 7
C. 8
D. 11
E. 12
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x is the product of the positive integers from 1 to 8, in
[#permalink]
11 Aug 2020, 09:43
11 Aug 2020, 09:43
1
Carcass wrote:
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that \(x = 2^i * 3^k * 5^m * 7^p\), then \(i + k + m + p =\)
A. 4
B. 7
C. 8
D. 11
E. 12
A. 4
B. 7
C. 8
D. 11
E. 12
GIVEN: x = (8)(7)(6)(5)(4)(3)(2)(1)
Let's find the prime factorization of x by rewriting each value as the product of primes.
We get: x = (2)(2)(2)(7)(2)(3)(5)(2)(2)(3)(2)
Rearrange to get: x = (2)(2)(2)(2)(2)(2)(2)(3)(3)(5)(7)
Rewrite as powers to get: \(x = (2^7)(3^2)(5^1)(7^1)\)
We're told that \(x = (2^i)(3^k)(5^m)(7^p)\)
This means: i = 7, k = 2, m = 1 and p = 1
So, i + k + m + p = 7 + 2 + 1 + 1 = 11
Answer: D
Cheers,
Brent
gmatclubot
Re: If x is the product of the positive integers from 1 to 8, in [#permalink]
11 Aug 2020, 09:43
Moderators:
