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# If 40 percent more than 40 percent of x is equal to

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CEO
Joined: 12 Sep 2015
Posts: 3020
If 40 percent more than 40 percent of x is equal to  [#permalink]

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17 Sep 2018, 07:15
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15% (low)

Question Stats:

96% (01:27) correct 4% (00:00) wrong based on 26 sessions

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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

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Brent Hanneson – GMATPrepNow.com

Math Expert
Joined: 02 Aug 2009
Posts: 6961
Re: If 40 percent more than 40 percent of x is equal to  [#permalink]

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17 Sep 2018, 08:19
2
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

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
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Re: If 40 percent more than 40 percent of x is equal to  [#permalink]

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17 Sep 2018, 14:41
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

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.
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CEO
Joined: 12 Sep 2015
Posts: 3020
Re: If 40 percent more than 40 percent of x is equal to  [#permalink]

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18 Sep 2018, 14:51
Top Contributor
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

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

Re: If 40 percent more than 40 percent of x is equal to &nbs [#permalink] 18 Sep 2018, 14:51
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