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If 75 reduced by x percent is 54, what is the value of x ?

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by BTGmoderatorDC » Mon Mar 14, 2022 1:40 am
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If 75 reduced by x percent is 54, what is the value of x ?

(A) 9
(B) 28
(C) 36
(D) 45
(E) 72


OA B

Source: Manhattan Prep
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Re: If 75 reduced by x percent is 54, what is the value of x ?

by Brent@GMATPrepNow » Mon Mar 14, 2022 6:21 am
BTGmoderatorDC wrote: ↑
Mon Mar 14, 2022 1:40 am
 If 75 reduced by x percent is 54, what is the value of x ?

(A) 9
(B) 28
(C) 36
(D) 45
(E) 72


OA B

Source: Manhattan Prep
75 - 54 = 21.
So, 75 is reduced by 21, which means we want to find the percentage that's equivalent to 21/75

STRATEGY: Before actually performing the long division involved with dividing 21 by 75, we should check the answer choices (always check the answers choices before beginning any calculations).
When we do so, we see that they are reasonably spread apart, so we can likely apply a little bit of number sense.

I know that 25/75 = 1/3 = 33 1/3%.
Since 21 is a little bit less than 25, we can conclude that 21/75 must be a little bit less than 33 1/3%

Answer: B
Brent Hanneson - Creator of GMATPrepNow.com
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