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If (x – 3)(x + 2) = (x – 2)(x + 3), then x =

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Senior Manager
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Joined: 02 Jan 2017
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Location: Canada
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If (x – 3)(x + 2) = (x – 2)(x + 3), then x =  [#permalink]

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New post 03 Mar 2017, 06:09
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

96% (00:48) correct 4% (00:31) wrong based on 82 sessions

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If (x – 3)(x + 2) = (x – 2)(x + 3), then x =

(A) –3

(B) –2

(C) 0

(D) 2

(E) 3
CEO
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Joined: 12 Sep 2015
Posts: 2884
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Re: If (x – 3)(x + 2) = (x – 2)(x + 3), then x =  [#permalink]

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New post 03 Mar 2017, 07:33
Top Contributor
vikasp99 wrote:
If (x – 3)(x + 2) = (x – 2)(x + 3), then x =

(A) –3

(B) –2

(C) 0

(D) 2

(E) 3


Great question!
I love that we can eliminate 4 answer choices by inspection.

For example, if x = 3 (answer choice E), then we can see that we get: (3 – 3)(3 + 2) = (3 – 2)(3 + 3)
Simplify (in head) to get: (ZERO)(non-zero #) = (non-zero #)(non-zero #)
This equation cannot hold true. So ELIMINATE E

Using the same logic we can also ELIMINATE A, B and D, which leaves us with C, the correct answer.
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Re: If (x – 3)(x + 2) = (x – 2)(x + 3), then x =  [#permalink]

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New post 03 Mar 2017, 08:55
Top Contributor
vikasp99 wrote:
If (x – 3)(x + 2) = (x – 2)(x + 3), then x =

(A) –3

(B) –2

(C) 0

(D) 2

(E) 3


The LONGER approach is to EXPAND and SOLVE

Given: (x – 3)(x + 2) = (x – 2)(x + 3)
Expand and simplify: x² - x - 6 = x² + x - 6
Add 6 to both sides to get: x² - x = x² + x
Subtract x² from both sides to get: -x = x
Add x to both sides: 0 = 2x
Solve: x = 0

Answer: C

Cheers,
Brent
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Re: If (x – 3)(x + 2) = (x – 2)(x + 3), then x =  [#permalink]

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New post 03 Mar 2017, 10:57
vikasp99 wrote:
If (x – 3)(x + 2) = (x – 2)(x + 3), then x =

(A) –3

(B) –2

(C) 0

(D) 2

(E) 3


\((x – 3)(x + 2) = (x – 2)(x + 3)\)

Test using the options, both side must have the same result, check using options ( The quickest possible way ) , answer must be (C)

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Re: If (x – 3)(x + 2) = (x – 2)(x + 3), then x = &nbs [#permalink] 03 Mar 2017, 10:57
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