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25% of (1/4)% of x

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25% of (1/4)% of x [#permalink] New post 11 May 2017, 08:38
Expert's post
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Question Stats:

58% (01:07) correct 41% (01:24) wrong based on 31 sessions
x > 0

Quantity A
Quantity B
25% of (1/4)% of x
1/16 of 10% of x


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Kudos [?]: 1110 [0], given: 7

Re: 25% of (1/4)% of x [#permalink] New post 12 May 2017, 05:59
Expert's post
GreenlightTestPrep wrote:
x > 0

Quantity A
Quantity B
25% of (1/4)% of x
1/16 of 10% of x




Let's work exclusively with fractions

Note:
25% = 25/100 = 1/4
(1/4)% = (1/4)/100 = 1/400
10% = 1/10

So, we get:
Quantity A: (1/4)(1/400)(x)
Quantity B: (1/16)(1/10)(x)

Simplify:
Quantity A: x/1600
Quantity B: x/160

Since the denominator of 160 is LESS THAN the denominator of 1600, x/160 must be greater than x/1600
Answer:
[Reveal] Spoiler:
B


However, if you're not 100% convinced, we can keep going:
Take:
Quantity A: x/1600
Quantity B: x/160

Multiply both quantities by 1600 to get:
Quantity A: x
Quantity B: 10x

Divide both quantities by x to get:
Quantity A: 1
Quantity B: 10

Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
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Re: 25% of (1/4)% of x [#permalink] New post 24 Jul 2018, 19:04
I tried this problem by picking numbers and used 100 for x since it is easy to work with:

Quantity A: 1/4% of 100 is 25
25% of 25 is 6.25

Quantity B: 10% of 100 is 10
1/16 of 10 is .625

This makes A bigger?
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Re: 25% of (1/4)% of x [#permalink] New post 25 Jul 2018, 01:35
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Expert's post
I think you would like to recheck your calculation for quantity A

\((\frac{1}{4})\%\) of 100 is \(\frac{1}{400}\times 100 = 0.25\)
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Re: 25% of (1/4)% of x [#permalink] New post 05 Aug 2018, 14:40
First thing I did was pick a number. x=10
A: 1/4=0.25. So 1/4%= 0.25/100. Therefore: 10*0.25*25/100*100 I just clubbed the whole thing. When you simplify it = 1/160
B: 1/16th of 10*10/100. When you simplify it = 1/16

There are lot of ways to do this I guess. I do not think there is any particular time-saving method. Just figure out what you understand better and what works for you best. I work better by picking numbers while others could do it just using the variable.
Re: 25% of (1/4)% of x   [#permalink] 05 Aug 2018, 14:40
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