The percent change from 29 to 43 is approximately what...?

Question

The percent change from 29 to 43 is approximately what percent of the percent change from 43 to 57?

(A) 50%
(B) 66%
(C) 110%
(D) 133%
(E) 150%

Please explain the fastest way to think throw this problem. I know that this type of question can give you some extra time on harder problems during the test.
Please give your opinion about the difficult level of the question.

ENGRTOMBA2018 · Answer

This question should be a 600-700 level just because of the care you have to take in order to arrive at the correct solution.

%age change = \frac{(final value - initial value)*100}{initial value}

Thus, %age change from 29 to 43 = 14/29  \approx  50% or 0.5 (we can approximate in this question as the options given are far apart).

%age change from 43 to 57 = 14/43  \approx 0.33

Thus, the required value = 50/33 = 1+17/33  \approx  1+0.5 = 1.5 or 150%

E is thus the correct answer.

Hope this helps.

Aves · Answer

You can set an equation like this,

\frac{(43 - 29)}{29} = \frac{x}{100}\frac{(57-43)}{43}

\frac{14}{29} =\frac{x}{100} \frac{14}{43}

Divide both side by 14, and multiply both side by 43x100, you get

x = \frac{(43)(100)}{29}

x is approximately  \frac{(45)(100)}{30}  which is  150

chetan2u · Answer

Hi,
the change is 14 in both cases, so it boils down to bases..
(14/29)/(14/43)=43/29= nearly 7*6/7*4= 6/4, %=100*3/2 which is 150%

Blackbox · Answer

Lesson learnt:   Always approximate the value to the hundredth decimal. I stopped long division of 43/29   to the tenth decimal and arrived at 1.4 and I thought 1.4 was closer to 133% than it was to 150% (although technically, it is mid-point) . Little did I know that quotient is actually 1.48. Yeap...mistake.

saukrit · Answer

In case the question stem says approximately (or any synonym of it) , never look for exact computations, do what the question says, approximate

For example

\frac{(43-29)}{29} = \frac{14}{29} ~=1/2 
 \frac{(53-43)}{43} = \frac{14}{43} ~=1/3

Required percent =  (\frac{1}{2})/(\frac{1}{3}) *100= \frac{3}{2} * 100= 150%

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The percent change from 29 to 43 is approximately what...?

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The percent change from 29 to 43 is approximately what...?

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