p, q, and r are different prime numbers. What is the value o

This topic has expert replies
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

p, q, and r are different prime numbers. What is the value of q?

1) (pq)^2=36
2) (qr)^2= 225

User avatar
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

by GMATGuruNY » Tue Mar 26, 2019 2:26 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Max@Math Revolution wrote:[GMAT math practice question]

p, q, and r are different prime numbers. What is the value of q?

1) (pq)^2=36
2) (qr)^2= 225
Statement 1:
(pq)² = 36
pq = 6
Case 1: p=2 and q=3
Case 2: p=3 and q=2
Since q can be different values, INSUFFICIENT.

Statement 2:
(qr)² = 225
qr = 15
Case 1: q=3 and r=5
Case 2: q=5 and r=3
Since q can be different values, INSUFFICIENT.

Statements combined:
Only one case satisfies pq = 6 and qr = 15:
p=2, q=3 and r=5
Thus, q=3.
SUFFICIENT.

The correct answer is C.
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

User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Thu Mar 28, 2019 12:33 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (p, q and r) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Since p^2q^2=2^23^2 and q^2r^2 = 3^25^2, we have p = 2, q = 3 and r = 5.
Conditions 1) & 2) are sufficient, when applied together.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since p^2q^2=2^23^2, we must have p = 2, q = 3 or p = 3, q = 2.
Condition 1) is not sufficient since it does not yield a unique solution.

Condition 2)
Since q^2r^2=3^25^2, we have q = 3, r = 5 or q = 5, r = 3.
Condition 2) is not sufficient since it does not yield a unique solution.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with "3 variables", or "4 variables and 1 equation", or "5 variables and 2 equations", conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.