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# The product of x and y is a constant. If the value of x is increased b

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
The product of x and y is a constant. If the value of x is increased b  [#permalink]

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02 Feb 2016, 01:02
00:00

Difficulty:

25% (medium)

Question Stats:

84% (01:23) correct 16% (01:11) wrong based on 76 sessions

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The product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?

A. 50%
B. 40%
C. 33 1⁄3%
D. 25%
E. 12 1⁄2%

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Re: The product of x and y is a constant. If the value of x is increased b  [#permalink]

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02 Feb 2016, 01:06
1
Product of x and y = xy
If the value of x is increased by 50% , value of y needs to be = xy/(1.5 x ) = 2/3 y
Decrease in value of y = y - 2/3 y = 1/3 y
% decrease in value of y = (1/3 y)/y * 100%
=33 1⁄3%

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Re: The product of x and y is a constant. If the value of x is increased b  [#permalink]

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02 Feb 2016, 22:47
1
Say xy=a
Then 50% increase in x =150x/100=1.5x
Hence, 1.5xy=1.5a
To maintain the constant as a, we shud multiply it by 1/1.5;
So 1.5xy*1/1.5= a
1/1.5 is equivalent to 0.667
Therefore,y scud be decreased by 0.33
Or 33.33%
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Re: The product of x and y is a constant. If the value of x is increased b  [#permalink]

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03 Feb 2016, 00:25
Bunuel wrote:
The product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?

A. 50%
B. 40%
C. 33 1⁄3%
D. 25%
E. 12 1⁄2%

x*y = constt.

Let x = y = 100 in beginning

i.e. x*y = 100*100 = 10000

x (100) ---becomes---> 1.5x (150)

i.e. 150*New 'y' = 10000
i.e. New 'y' = 10000/150 = 66.66

i.e. y decreases from 100 to 66.66 i.e. Decrease of 33.33%

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Re: The product of x and y is a constant. If the value of x is increased b  [#permalink]

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03 Feb 2016, 00:47
Let x be 4 and y be 6, therefore xy = 24

50% increase in X is 4 x1.5 = 6
To maintain the constant of 24, Y will need to reduce to 4
so to calculate the % decrease in y, we use New Value - Old Value / Old Value
% Decrease in Y = 4-6/6 => 2/6 => 1/3
Convert 1/3 to % => 33.3%
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Re: The product of x and y is a constant. If the value of x is increased b  [#permalink]

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04 Feb 2016, 22:20
Hi All,

This question is based on a 'math truism' that shows up most often in certain types of "Distance Formula" questions. Here's a link to a question that's based on the exact SAME idea:

john-would-have-reduced-the-time-it-took-him-to-drive-from-his-home-to-210670.html?hilit=truism

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The product of x and y is a constant. If the value of x is increased b  [#permalink]

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21 Aug 2018, 21:13
Bunuel wrote:
The product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?

A. 50%
B. 40%
C. 33 1⁄3%
D. 25%
E. 12 1⁄2%

Let $$x = 10$$ and $$y = 10$$ and $$xy = 100$$

If $$x$$ is increased by $$50$$% its value is $$15$$

So, The value of $$y$$ is $$\frac{100}{15} = 6.67$$

So, The value of y must be decreased by 33 1⁄3% , Answer must be (C)
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Re: The product of x and y is a constant. If the value of x is increased b  [#permalink]

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21 Aug 2018, 21:47
The ans is C 33$$\frac{1}{3}$$
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Re: The product of x and y is a constant. If the value of x is increased b &nbs [#permalink] 21 Aug 2018, 21:47
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