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M21-14

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M21-14 [#permalink]

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New post 16 Sep 2014, 01:10
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Re M21-14 [#permalink]

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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 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
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Re: M21-14 [#permalink]

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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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Re: M21-14 [#permalink]

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New post 03 Oct 2014, 11:50
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Expert's post
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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Re: M21-14 [#permalink]

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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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M21-14 [#permalink]

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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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Re: M21-14 [#permalink]

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New post 11 Jul 2015, 08:49
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: http://www.wolframalpha.com/input/?i=1. ... an+1%2F1.8
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Re: M21-14 [#permalink]

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New post 02 Aug 2016, 08:02
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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Re: M21-14 [#permalink]

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why is the equation=1/x +1/x*224/100 and not =1/x*224/100?
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Re: M21-14 [#permalink]

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New post 22 Nov 2017, 03:47
+1 for D. The number is 1.8. x=(3.24/x). i.e, x^2 = 3.24. x is 1.8
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M21-14 [#permalink]

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New post 22 Nov 2017, 09:04
Convert 224% GREATER to algebraic expression
We know that 100% GREATER means X * 2 (twice as large)

Therefore 224% GREATER means X * 3.24

Based on this:
X = 1/X (3.24)

X^2 = 3.24

X must be between 1 and 2 so eliminate A and E

1.1 is unlikely. Eliminate B

1.5^2 = (3/2)^2 = 9/4...this is 2.25 so elim C

Answer must be D

To check: (9/5)^2 = 81/25 which is 3 and 6/25 = 3.24
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Re: M21-14 [#permalink]

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New post 22 Nov 2017, 11:12
manchitkapoor wrote:
why is the equation=1/x +1/x*224/100 and not =1/x*224/100?


Because the question is asking for a number 224% greater than its reciprocal and not 224% of its reciprocal.
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Re: M21-14 [#permalink]

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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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New post 04 Jan 2018, 20:32
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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M21-14   [#permalink] 04 Jan 2018, 20:32
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