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Challenge question: If 40 percent more than 40 percent of x

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Challenge question: If 40 percent more than 40 percent of x

by Brent@GMATPrepNow » Mon Sep 17, 2018 6:14 am

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If 40 percent more than 40 percent of x is equal to 40 percent less than y, what is the value of x/y?

A) 3/8
B) 15/16
C) 1
D) 15/14
E) 15/4

Answer: D
Difficulty level: 600 - 650
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Challenge question: If 40 percent more than 40 percent of x

by fskilnik@GMATH » Mon Sep 17, 2018 1:33 pm
Brent@GMATPrepNow wrote:If 40 percent more than 40 percent of x is equal to 40 percent less than y, what is the value of x/y?

A) 3/8
B) 15/16
C) 1
D) 15/14
E) 15/4
Source: www.gmatprepnow.com
Very nice and important problem.... why nobody posted a solution till now? :(

I will do it step-by-step to help people who eventually tried without success...
\[? = \frac{x}{y}\,\,\,\,\,\,\,\,\left( {y \ne 0\,\,\,\,{\text{implicitly}}} \right)\]
\[40\% \,\,{\text{of}}\,\,x\,\,\, = \frac{2}{5}x\]
\[40\% \,\,{\text{more}}\,\,{\text{than}}\,\,{\text{above}} = {\text{above}} + 40\% \,\,{\text{above}} = \left( {1 + \frac{2}{5}} \right)\,\,{\text{above = }}\left( {\frac{{1 \cdot \boxed5}}{{\boxed5}} + \frac{2}{5}} \right)\,\,\left( {\frac{2}{5}x} \right) = \frac{{14}}{{25}}x\]
\[40\% \,\,{\text{less}}\,\,{\text{than}}\,\,y\,\,\, = \,\,\,60\% \,\,{\text{of}}\,\,y\,\,\, = \,\,\,\frac{3}{5}y\]
Finally,
\[\frac{{14}}{{25}}x = \frac{3}{5}y\,\,\,\,\,\,\mathop \Rightarrow \limits^{y\,\, \ne \,\,0} \,\,\,\,\,? = \frac{x}{y} = \frac{3}{5} \cdot \frac{{25}}{{14}}\, = \,\frac{{15}}{{14}}\,\,\]

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Brent@GMATPrepNow » Tue Sep 18, 2018 1:50 pm
Brent@GMATPrepNow wrote:If 40 percent more than 40 percent of x is equal to 40 percent less than y, what is the value of x/y?

A) 3/8
B) 15/16
C) 1
D) 15/14
E) 15/4
--------ASIDE--------------------
40% MORE THAN k = k + (40% of k)
= k + 0.4x
= 1.4x

40% LESS THAN Q = Q - (40% of Q)
= Q - 0.4Q
= 0.6Q
----NOT ONTO THE QUESTION!!-----------


40 percent of x is the same as 0.4x
So, 40 percent more than 40 percent of x is the same as (1.4)(0.4x)

40 percent less than y is the same as 0.6y

So, we can write: (1.4)(0.4x) = 0.6y
Divide both sides by 0.4 to get: (1.4)(x) = (0.6y)/(0.4)
0.6/0.4 = 6/4 = 1.5, so we can write: 1.4x = 1.5y
Divide both sides by 1.4 to get: x = 1.5y/1.4
Divide both sides by y to get: x/y = 1.5/1.4

Since 1.5/1.4 = 15/14, we can write: x/y = 15/14

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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