X is a multiple of 5, X=a^2 *b, a and b are integers. Which of the following must be the multiple of 125?
1) a.b
2) a.b^2
3) a^2.b^2
4) a^3.b^3
5) 2.a.b
1) a.b
2) a.b^2
3) a^2.b^2
4) a^3.b^3
5) 2.a.b
NK
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
Multiple of 5 and 125. x=a^2*b?
Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Location: Milpitas, CA
- Thanked: 1854 times
- GMAT Score:770
If X is a multiple of 5, then either a^2 or b or both are multiples of 5.
Let us solve by example.
Now, 80 = 4^2 * 5. So let a = 4, b = 5, X = 80.
So, 80 is a multiple of 5.
Now ab = 20 is not a multiple of 125.
a *b^2 = 4 * 5^2 = 100 is not a multiple of 125.
a^2 * b^2 = 4^2 * 5^2 = 400 is not a multiple of 125.
a^3 * b^3 = 4^3 * 5^3 = 64 * 125, which is a multiple of 125.
2ab is 2*4*5 = 40 which is not a multiple of 125.
The correct answer is hence 4).
Let us solve by example.
Now, 80 = 4^2 * 5. So let a = 4, b = 5, X = 80.
So, 80 is a multiple of 5.
Now ab = 20 is not a multiple of 125.
a *b^2 = 4 * 5^2 = 100 is not a multiple of 125.
a^2 * b^2 = 4^2 * 5^2 = 400 is not a multiple of 125.
a^3 * b^3 = 4^3 * 5^3 = 64 * 125, which is a multiple of 125.
2ab is 2*4*5 = 40 which is not a multiple of 125.
The correct answer is hence 4).
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
I took a different approach. Since X is a multiple of 5, so we can conclude that either a or b or both (since a & b are integers, a can't take the value of 5^1/2 in which case a^2 would be a multiple of 5) is a multiple of 5. In case of a^2, assuming that 5 appears in the list of factors of 'a' at least once we can can make sure that its divisible by 125, i.e. 5^3, by multiplying it by simply another 'a'. So it becomes a^3 and its certain to be divisible by 125.
Similarly in case of b, assuming that 5 appears in the list of factors of 'b' at least once, we can multiply it by b^2 to increase the no of '5' factors to 3.
So a^3*b^3 is the answer. I hope I am clear.
Similarly in case of b, assuming that 5 appears in the list of factors of 'b' at least once, we can multiply it by b^2 to increase the no of '5' factors to 3.
So a^3*b^3 is the answer. I hope I am clear.
