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# 25% of (1/4)% of x

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GRE Instructor
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25% of (1/4)% of x [#permalink]  11 May 2017, 08:38
Expert's post
00:00

Question Stats:

57% (01:02) correct 42% (01:10) wrong based on 99 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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GRE Instructor
Joined: 10 Apr 2015
Posts: 3869
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Kudos [?]: 4628 [0], given: 70

Re: 25% of (1/4)% of x [#permalink]  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
[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

[Reveal] Spoiler:
B

Cheers,
Brent
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Re: 25% of (1/4)% of x [#permalink]  24 Jul 2018, 19:04
2
KUDOS
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]  25 Jul 2018, 01:35
1
KUDOS
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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Manager
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Re: 25% of (1/4)% of x [#permalink]  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.
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Re: 25% of (1/4)% of x [#permalink]  04 Aug 2020, 07:48
msawicka wrote:
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?

It said (1/4)% which means one by forth per cent = 1/4 divided by 100 = 0.25/100
therefore,
= (100 * 0.25/100) * 0.25
= 0.0625
Re: 25% of (1/4)% of x   [#permalink] 04 Aug 2020, 07:48
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# 25% of (1/4)% of x

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