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If a and b are positive integers such that a/b = 82.024

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by BTGModeratorVI » Wed Mar 25, 2020 6:30 am

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E

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Difficulty—

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

Answer: D
Source: Veritas Prep
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Re: If a and b are positive integers such that a/b = 82.024

by swerve » Wed Mar 25, 2020 12:34 pm
BTGModeratorVI wrote: ↑
Wed Mar 25, 2020 6:30 am
 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

Answer: D
Source: Veritas Prep
\(b\) must be the factor of \(1000\) because \(82.024 = 82,024/1000\), \(a\) must be integer
\(\Rightarrow\) I crossed out: B, E

If \(b = 100 \Rightarrow a=8202.4\): not integer: OUT
If \(b = 200 \Rightarrow a\) is not integer because \(82,024\) is not divisible by \(5\)
If \(b = 250 \Rightarrow a=20506\): integer: OK

Therefore, D
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Re: If a and b are positive integers such that a/b = 82.024

by Brent@GMATPrepNow » Wed Mar 25, 2020 2:38 pm
BTGModeratorVI wrote: ↑
Wed Mar 25, 2020 6:30 am
 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

Answer: 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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Re: If a and b are positive integers such that a/b = 82.024

by Scott@TargetTestPrep » Fri Mar 27, 2020 6:09 am
BTGModeratorVI wrote: ↑
Wed Mar 25, 2020 6:30 am
 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

Answer: D
Source: Veritas Prep
We can create the equation:

a/b = 82 + 24/1000

a/b = 82 + 6/250

Thus:

r/b = 6/250

Therefore, b can be 250.

Answer: D

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