Here's a nice discussion about this question: https://www.beatthegmat.com/veritas-quan ... 79772.html
Cheers,
Brent
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Exponents-problem
Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
-
MartyMurray
- Legendary Member
- Posts: 2135
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- GMAT Score:800
If a and b are integers, then (ab)� = (all of the prime factors of a and b)�.lucas211 wrote:If a and b are integers and (ab)� = 96y, y could be
(a) 5
(b) 9
(c) 27
(d) 81
(e) 125
So the prime factors in 96y have to all be raised to the fifth power.
96 = 3 x 32 = 3 x 2�.
2 is raised to the fifth power, but 3 is not. So y must include in its prime factors at least 3�.
3� = 81. Seeing that, you can immediately choose answer choice D.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Location: Palo Alto, CA
- Thanked: 2867 times
- GMAT Score:800
Hi lucas211,
This question is essentially about prime-factorization - the idea that any positive integer greater than 1 is either prime or the product of a bunch of primes.
Here, we're told that (AB)^5 = 96Y, and that A and B are integers, which means...
(AB)(AB)(AB)(AB)(AB) = 96Y
We can rewrite this as....
(A^5)(B^5) = (2^5)(3)(Y)
We're asked for what Y COULD equal. This means that Y could be MORE than one value...so we should start by looking for the smallest value that Y could equal.
Notice how 2^5 could "account for" either A or B, so we need to make sure that the "Y", when combined with the "3" that's already there, could account for the other variable....
If Y = 3^4, then 96Y would = (2^5)(3^5), which gives us two integers raised to the 5th power.
Y COULD = 3^4 = 81
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question is essentially about prime-factorization - the idea that any positive integer greater than 1 is either prime or the product of a bunch of primes.
Here, we're told that (AB)^5 = 96Y, and that A and B are integers, which means...
(AB)(AB)(AB)(AB)(AB) = 96Y
We can rewrite this as....
(A^5)(B^5) = (2^5)(3)(Y)
We're asked for what Y COULD equal. This means that Y could be MORE than one value...so we should start by looking for the smallest value that Y could equal.
Notice how 2^5 could "account for" either A or B, so we need to make sure that the "Y", when combined with the "3" that's already there, could account for the other variable....
If Y = 3^4, then 96Y would = (2^5)(3^5), which gives us two integers raised to the 5th power.
Y COULD = 3^4 = 81
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
