M21-14

Question

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

Bunuel · Answer

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

safaria25 · Answer

Hi Bunuel,

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

Thank you

Bunuel · Answer

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.

buddyisraelgmat · Answer

Brilliant way to solve this question !!! I was manually backsolving by plugging in nos - Took ~ 3 Mins

WillGetIt · Answer

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.

Bunuel · Answer

1.8 is 224% greater than 1/1.8: https://www.wolframalpha.com/input/?i=1. ... an+1%2F1.8

harshanitr · Answer

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

KillerGMAT · Answer

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.

Bunuel · Answer

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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

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M21-14

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