If is n is multiple of 5, and n=p^2*q where p and q are prime, which of the following must be a multiple of 25?
A. p^2
B. q^2
C. pq
D. p^2*q^2
E. p^3*q
OA D
Source: GMAT Prep
If is n is multiple of 5, and n=p^2*q where p and q are prim
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- 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
Try to prove that four of the answer choices DO NOT have to be a multiple of 25.BTGmoderatorDC wrote:If is n is multiple of 5, and n=p^2*q where p and q are prime, which of the following must be a multiple of 25?
A. p^2
B. q^2
C. pq
D. p^2*q^2
E. p^3*q
The correct answer will be the remaining answer choice.
In order for n to be a multiple of 5, either p and/or q must be a multiple of 5.
Since the goal is to prove that four of the answer choices do NOT have to be a multiple of 25, start with the SMALLEST POSSIBLE COMBINATIONS.
Case 1: Let p=2 and q=5, so that n = 2²(5) = 20.
A) p² = 2² = 4. Not a multiple of 25. Eliminate A.
B) q² = 5² = 25. 25 is a multiple of 25. Hold onto B.
C) pq = 2*5 = 10. Not a multiple of 25. Eliminate C.
D) p²q² = 2²(5²) = 100. 25 is a multiple of 25. Hold onto D.
E) p³q = (2³)5 = 40. Not a multiple of 25. Eliminate E.
Case 2: Let p=5 and q=2, so that n = (5²)2 = 50.
B) q² = 2² = 4. Not a multiple of 25. Eliminate B.
The correct answer is D.
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
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's test some values that satisfy the given conditions (n is multiple of 5, and n = p²q, where p and q are prime numbers)BTGmoderatorDC wrote:If is n is multiple of 5, and n=p^2*q where p and q are prime, which of the following must be a multiple of 25?
A. p^2
B. q^2
C. pq
D. p^2*q^2
E. p^3*q
OA D
Source: GMAT Prep
How about: p = 2 and q = 5.
In this case, n = (2²)(5) = 20, and 20 is a multiple of 5, which satisfies the given condition.
Now plug p = 2 and q = 5 into the answer choices...
A) 2² = 4. This is NOT a multiple of 25. ELIMINATE
B) 5² = 25. This IS a multiple of 25. KEEP
C) (2)(5) = 10. This is NOT a multiple of 25. ELIMINATE
D) (2²)(5²) = 100. This IS a multiple of 25. KEEP
E) (2³)(5) = 40. This is NOT a multiple of 25. ELIMINATE
So, the correct answer is either B or D.
Let's try a new set of values.
How about: p = 5 and q = 2.
In this case, n = (5²)(2) = 20, and 20 is a multiple of 5, which satisfies the given condition.
Now plug p = 5 and q = 2 into the REMAINING answer choices...
B) 2² = 4. This is NOT a multiple of 25. ELIMINATE
NOTE: At this point, we can safely conclude that the correct answer is D.
But let's try D for "fun"...
D) (5²)(2²) = 100. This IS a multiple of 25.
Answer: D
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
A common phrase that is used on the GMAT is the word must. In this question, we are asked which of the following must be a multiple of 25. This means that one of our answer choices will always be a multiple of 25, no matter what. It is our job to determine which one, based on the given information.BTGmoderatorDC wrote:If is n is multiple of 5, and n=p^2*q where p and q are prime, which of the following must be a multiple of 25?
A. p^2
B. q^2
C. pq
D. p^2*q^2
E. p^3*q
OA D
Source: GMAT Prep
We are given that n is a multiple of 5, n = (p^2)q, and that p and q are prime numbers.
Because n is a multiple of 5, a prime number, we know that either p or q is 5. Let's now analyze each answer choice to determine which one MUST (in all cases) be a multiple of 25.
A) p^2
If p = 3, then p^2 = 9 is not a multiple of 25. Answer choice A is not correct.
B) q^2
If q = 3, then q^2 = 9 is not a multiple of 25. Answer choice B is not correct.
C) pq
If p = 5 and q = 3 (or vice versa), pq = 15 is not a multiple of 25. Answer choice C is not correct.
D) (p^2)(q^2)
Regardless of which values we select for p and q, since we know that either p or q is 5, (p^2)(q^2) will always be a multiple of 25. If this is too difficult to see, let's use numbers.
If p = 5 and q = 3, (p^2)(q^2) = (25)(9) is a multiple of 25.
If p = 3 and q = 5, (p^2)(q^2) = (9)(25) is also a multiple of 25.
Answer choice D is correct.
For practice, let's analyze answer choice E.
E) (p^3)q
If p = 3 and q = 5, then (p^3)q = 135 is not a multiple of 25. Answer choice E is not correct.
Answer: D
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