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 - The Beat The GMAT Forum

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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue Sep 22, 2020 7:25 am

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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

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Source: Beat The GMAT — Problem Solving | Tue Sep 22, 2020 7:25 am

swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Tue Sep 22, 2020 11:35 am

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

by Scott@TargetTestPrep » Fri Sep 25, 2020 1:24 pm

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]

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