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M21-14

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Bunuel
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M21-14 [#permalink] New post  16 Sep 2014, 01:10
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66% (01:47) correct 34% (02:02) wrong based on 161 sessions
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What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2
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Bunuel
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Re M21-14 [#permalink] New post  16 Sep 2014, 01:10
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Official Solution:

What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2


We should find such \(x\) that satisfies the following equation: \(x=\frac{1}{x}+\frac{1}{x}*\frac{224}{100}\);

\(x=\frac{1}{x}*3.24\);

\(x^2=3.24\);

\(x=1.8\) (given that \(x\) is a positive number, \(x=-1.8\) is not valid).


Answer: D
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safaria25
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Re: M21-14 [#permalink] New post  03 Oct 2014, 11:47
Bunuel wrote:
Official Solution:

What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2


We should find such \(x\) that satisfy the following equation: \(x=\frac{1}{x}+\frac{1}{x}*\frac{224}{100}\);

\(x=\frac{1}{x}*3.24\);

\(x^2=3.24\);

\(x=1.8\) (since give that \(x\) is a positive number).


Answer: D


Hi Bunuel,

Can you please explain how you got the 3.24 in the 2nd equation?

Thank you
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Bunuel
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Re: M21-14 [#permalink] New post  03 Oct 2014, 11:50
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safaria25 wrote:
Bunuel wrote:
Official Solution:

What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2


We should find such \(x\) that satisfy the following equation: \(x=\frac{1}{x}+\frac{1}{x}*\frac{224}{100}\);

\(x=\frac{1}{x}*3.24\);

\(x^2=3.24\);

\(x=1.8\) (since give that \(x\) is a positive number).


Answer: D


Hi Bunuel,

Can you please explain how you got the 3.24 in the 2nd equation?

Thank you


\(x=\frac{1}{x}+\frac{1}{x}*\frac{224}{100}\);

\(x=\frac{1}{x}(1+\frac{224}{100}\);

\(x=\frac{1}{x}*3.24\).

Hope it's clear.
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buddyisraelgmat
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Re: M21-14 [#permalink] New post  11 Mar 2015, 21:26
Bunuel wrote:
Official Solution:

What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2


We should find such \(x\) that satisfy the following equation: \(x=\frac{1}{x}+\frac{1}{x}*\frac{224}{100}\);

\(x=\frac{1}{x}*3.24\);

\(x^2=3.24\);

\(x=1.8\) (since give that \(x\) is a positive number).


Answer: D



Brilliant way to solve this question !!!

I was manually backsolving by plugging in nos - Took ~ 3 Mins :(
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Re: M21-14 [#permalink] New post  11 Jul 2015, 05:59
Hello Bunnel,

Shouldn't be equation be written as

X = 1/X + X*224/100

Actually it is stated that "What positive number is 224 percent greater than its reciprocal

The point is, it is stated that 224% greater than its reciprocal but why we are taking 224% of reciprocal itself????

Looking for your response!

Please help.
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Bunuel
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Re: M21-14 [#permalink] New post  11 Jul 2015, 08:49
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vikasbansal227 wrote:
Hello Bunnel,

Shouldn't be equation be written as

X = 1/X + X*224/100

Actually it is stated that "What positive number is 224 percent greater than its reciprocal

The point is, it is stated that 224% greater than its reciprocal but why we are taking 224% of reciprocal itself????

Looking for your response!

Please help.


1.8 is 224% greater than 1/1.8: https://www.wolframalpha.com/input/?i=1. ... an+1%2F1.8
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Re: M21-14 [#permalink] New post  02 Aug 2016, 08:02
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according to the question (x-1/x)/(1/x) = 224/100. simplifying further we get x^2-1=224/100.
this implies x=1.8
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KillerGMAT
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Re: M21-14 [#permalink] New post  04 Jan 2018, 19:32
Can someone explain why 224% greater is 3.24? I always thought 100% is twice, 200% is 4 times, so if 224%=~225% then it should be 4.5 times.
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Re: M21-14 [#permalink] New post  04 Jan 2018, 20:32
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KillerGMAT wrote:
Can someone explain why 224% greater is 3.24? I always thought 100% is twice, 200% is 4 times, so if 224%=~225% then it should be 4.5 times.


No. 100% more is *2 (1 + 1), 200% more is *3 (1 + 2), 300 more is *4 (1 + 3), ... 224% more is *(1 + 2.24) = *3.24.
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Re: M21-14 [#permalink] New post  30 Aug 2023, 01:23
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re M21-14 [#permalink] New post  21 Nov 2023, 13:58
I think this is a high-quality question and I agree with explanation.
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Re M21-14 [#permalink]
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