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17 Sep 2018, 07:15
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Difficulty:
25%
(medium)
Question Stats:
81% (01:54) correct
19%
(02:02)
wrong
based on 135
sessions
History
Date
Time
Result
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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
A) 3/8
B) 15/16
C) 1
D) 15/14
E) 15/4
17 Sep 2018, 08:19
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GMATPrepNow
Take x as 100..
so 40 percent more than 40 percent of x = \((1+\frac{40}{100})(x*\frac{40}{100})=(1.4)(100*\frac{40}{100})=1.4*40=56\)
now this is equal to 40 percent less than y..
so \(56 = (1-\frac{40}{100})*y=\frac{60y}{100}....y=\frac{560}{6}=\frac{280}{3}\)
so \(\frac{x}{y}=100/(\frac{280}{3})=\frac{300}{280}=\frac{15}{14}\)
D
17 Sep 2018, 14:41
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GMATPrepNow
I will do it step-by-step to help people who eventually tried without success...
\(? = \frac{x}{y}\,\,\,\,\,\,\,\,\left( {y \ne 0\,\,\,\,{\text{implicitly}}} \right)\)
\(40\% \,\,{\text{of}}\,\,x\,\,\, = \frac{2}{5}x\)
\(40\% \,\,{\text{more}}\,\,{\text{than}}\,\,{\text{above}} = {\text{above}} + 40\% \,\,{\text{above}} = \left( {1 + \frac{2}{5}} \right)\,\,{\text{above = }}\left( {\frac{{1 \cdot \boxed5}}{{\boxed5}} + \frac{2}{5}} \right)\,\,\left( {\frac{2}{5}x} \right) = \frac{{14}}{{25}}x\)
\(40\% \,\,{\text{less}}\,\,{\text{than}}\,\,y\,\,\, = \,\,\,60\% \,\,{\text{of}}\,\,y\,\,\, = \,\,\,\frac{3}{5}y\)
\(\frac{{14}}{{25}}x = \frac{3}{5}y\,\,\,\,\,\,\mathop \Rightarrow \limits^{y\,\, \ne \,\,0} \,\,\,\,\,? = \frac{x}{y} = \frac{3}{5} \cdot \frac{{25}}{{14}}\, = \,\frac{{15}}{{14}}\,\,\)
Regards,
Fabio.
