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# x = y - (50/y), where x and y are both > 0 If the value of y is doubl

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Math Expert
Joined: 02 Sep 2009
Posts: 59730
x = y - (50/y), where x and y are both > 0 If the value of y is doubl  [#permalink]

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14 May 2016, 03:54
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Difficulty:

55% (hard)

Question Stats:

65% (01:59) correct 35% (01:51) wrong based on 100 sessions

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x = y - (50/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will

A. decrease
B. stay the same
C. increase four fold
D. double
E. increase to more than double

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Math Expert
Joined: 02 Aug 2009
Posts: 8326
Re: x = y - (50/y), where x and y are both > 0 If the value of y is doubl  [#permalink]

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14 May 2016, 08:20
Bunuel wrote:
x = y - (50/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will

A. decrease
B. stay the same
C. increase four fold
D. double
E. increase to more than double

hi,

lets see what will happen to each term..
the POSITIVE quantity, y, will double....
the NEGATIVE quantity 50/y will become LESSER as the denominator is doubled..

so OVERALL effect on x will be (DOUBLED positive - LESSER quantity), so x will increase MORE than double..
E

also --
x when y is doubled -
$$x_1= 2y - \frac{50}{2y} = \frac{2y^2-25}{y}$$......... (i)and
$$2x = 2( y-\frac{50}{y}) = \frac{2y^2-100}{y}$$...(ii)
clearly (i) > (ii)
so $$x_1>2x$$
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Re: x = y - (50/y), where x and y are both > 0 If the value of y is doubl  [#permalink]

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14 May 2016, 08:29
1
Bunuel wrote:
x = y - (50/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will

A. decrease
B. stay the same
C. increase four fold
D. double
E. increase to more than double

Alternate approach

Plug in some values of y > 0

Let y = 10

So, x = y - (50/y)

Or, x = 10 - (50/10) => 5

Quote:
If the value of y is doubled

Let y = 20

So, x = y - (50/y)

Or, x = 20 - (50/20) =>17.5

So, x increases from 5 to 17.5

Hence the number increases 3.5 times, thus the correct answer will be (E)
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Re: x = y - (50/y), where x and y are both > 0 If the value of y is doubl  [#permalink]

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04 Oct 2018, 19:33
Bunuel wrote:
x = y - (50/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will

A. decrease
B. stay the same
C. increase four fold
D. double
E. increase to more than double

We can let y = 10; then x = 10 - (50/10) = 5. Now, let’s the double the value of y to 20; now we have x = 20 - (50/20) = 17.5. We see that the value of x increases to more than double.

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Re: x = y - (50/y), where x and y are both > 0 If the value of y is doubl   [#permalink] 04 Oct 2018, 19:33
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