For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a val

This topic has expert replies
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a value of \(x?\)

A. -4
B. -3
C. 2
D. 3
E. 6

Answer: A

Source: Veritas Prep

Legendary Member
Posts: 2218
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members
VJesus12 wrote:
Tue Sep 22, 2020 7:25 am
For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a value of \(x?\)

A. -4
B. -3
C. 2
D. 3
E. 6

Answer: A

Source: Veritas Prep
Given \(a\%b = (a + b)(a - b)\) and \(5\% x = 9\), we have

\(5\% x = (5+x) \cdot (5-x) = 25 - x^2\)

So, \(25 -x^2 = 9 \Longrightarrow x^2 = 16 \Longrightarrow x = \pm 4\)

Therefore, the correct answer is A

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
VJesus12 wrote:
Tue Sep 22, 2020 7:25 am
For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a value of \(x?\)

A. -4
B. -3
C. 2
D. 3
E. 6

Answer: A

Solution:

Translating 5%x = 9 into a regular equation, we have:

(5 + x)(5 - x) = 9

25 - x^2 = 9

16 = x^2

x = 4 or -4

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage