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If a and b are positive integers such that a/b = 82.024, which of the following can be the value of b?

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Re: If a and b are positive integers such that a/b = 82.024, which of the following can be the value of b?

by Brent@GMATPrepNow » Thu May 18, 2023 5:46 am
BTGmoderatorDC wrote: ↑
Wed May 17, 2023 5:56 pm
 If a and b are positive integers such that a/b = 82.024, which of the following can be the value of b?

(A) 100
(B) 150
(C) 200
(D) 250
(E) 550


OA D

Source: Veritas Prep
Notice that we can rewrite 82.024 as 82 + 24/1000
So, 82.024 = 82 + 24/1000
Simplify to get: 82.024 = 82 + 3/125
Rewritten as an ENTIRE fraction, we get: 82.024 = [(82)(125) + 3]/125

a/b = [(82)(125) + 3]/125, so b COULD equal 125.
When we check the answer choices, we don't see 125.
That's okay, because we can rewrite [(82)(125) + 3]/125 as an EQUIVALENT fraction, just like we can rewrite 3/7 as 6/14 or 9/21 or 12/28 etc.

Likewise, if we rewrite [(82)(125) + 3]/125 as an EQUIVALENT fraction, the denominator (b) can be ANY MULTIPLE of 125
Checking the answer choices, only 250 is a multiple of 125

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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