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For all numbers x, the operation <> is defined by <x> = x - x/5. If <<

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Math Expert
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Joined: 02 Sep 2009
Posts: 49300
For all numbers x, the operation <> is defined by <x> = x - x/5. If <<  [#permalink]

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New post 18 Jan 2018, 03:20
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (01:24) correct 13% (01:24) wrong based on 97 sessions

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Re: For all numbers x, the operation <> is defined by <x> = x - x/5. If <<  [#permalink]

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New post 18 Jan 2018, 04:58
1
Bunuel wrote:
For all numbers x, the operation <> is defined by <x> = x - x/5. If <<w>> = 32, then what is the value of w ?

(A) 15
(B) 25
(C) 35
(D) 50
(E) 60


Instead of solving explicitly, we'll just try the different answers.
This is an Alternative approach.

Let's start with the median - C.
If w = 35 then <w> = 35 - 7 = 28 so <<w>> must be smaller than 28.
Impossible! (C) is eliminated along with the smaller (A) and (B).
Let's try (D): if w=50 then <w> = 50 - 10 = 40 and <<w>> = 40 - 8 = 32.
Yes!

(D) is our answer.
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For all numbers x, the operation <> is defined by <x> = x - x/5. If <<  [#permalink]

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New post 18 Jan 2018, 09:24
1) w'-w'/5 = 32 <=> 4w' = 160 <=> w'=40
2) w-w/5 = 40 <=> 4w=200 <=> w = 50

Answer (D)
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Re: For all numbers x, the operation <> is defined by <x> = x - x/5. If <<  [#permalink]

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New post 18 Jan 2018, 09:49
1
Simple:

<x>=(4/5)*x

<<w>>=(4/5)*<w>=(4/5)*(4/5)*w=(16/25)*w

=>(16/25)*w=32

=>w=50
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Re: For all numbers x, the operation <> is defined by <x> = x - x/5. If <<  [#permalink]

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New post 20 Jan 2018, 07:37
Bunuel wrote:
For all numbers x, the operation <> is defined by <x> = x - x/5. If <<w>> = 32, then what is the value of w ?

(A) 15
(B) 25
(C) 35
(D) 50
(E) 60


We can create the equation:

<w> = w - w/5, so <<w>> is:

w - w/5 - (w - w/5)/5 = 32

Multiplying by 5 we have:

5w - w - (w - w/5) = 160

4w - w + w/5 = 160

3w + w/5 = 160

Multiplying by 5 again, we have:

15w + w = 800

16w = 800

w = 50

Answer: D
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Re: For all numbers x, the operation <> is defined by <x> = x - x/5. If << &nbs [#permalink] 20 Jan 2018, 07:37
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