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07 Nov 2019, 03:04
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:45) correct 34% (01:36) wrong based on 38 sessions

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A and B brought a radio each for the same price, $z. A and B sold their radio for$x and $y respectively. If x>y>z, A’s profit is what percent greater than B’s? (1) x – y = 20 (2) x – z = 40 Are You Up For the Challenge: 700 Level Questions Math Expert Joined: 02 Aug 2009 Posts: 8284 A and B brought a radio each for the same price,$z. A and B sold thei  [#permalink]

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07 Nov 2019, 21:14
Bunuel wrote:
A and B brought a radio each for the same price, $z. A and B sold their radio for$x and $y respectively. If x>y>z, A’s profit is what percent greater than B’s? (1) x – y = 20 (2) x – z = 40 Are You Up For the Challenge: 700 Level Questions A's profit = $$\frac{x-z}{z}$$, and B's profit = $$\frac{y-z}{z}$$ % change of A over B = $$\frac{A's.profit-B's.profit}{b"s.profit}*100...........\frac{\frac{x-z}{z}-\frac{y-z}{z}}{\frac{y-z}{z}}*100=\frac{\frac{x-y}{z}}{\frac{y-z}{z}}*100=\frac{x-y}{y-z}*100$$... Hence, we require values of x, y and z OR values of x-y and y-z We have some fractions for A’s and B’s profit. When we substitute it in the formula $$\frac{\frac{(x-z)}{z}-\frac{(y-z)}{z}}{(\frac{y-z}{z})}=\frac{\frac{(x-z-(y-z))}{z}}{\frac{((y-z)}{z)}}=\frac{(x-z-y+z)}{y-z}=\frac{(x-y)}{(y-z)}$$ Now we know x-y and y-z can be found from the two statements. Subtract statement I from ii $$(x-z)-(x-y)=40-20=20....y-z=20$$ Statement I and II give us these values when combined Answer = $$\frac{20}{20}*100=100%$$ y-z can be found by subtracting Statement I from statement II C _________________ Intern Joined: 15 Jun 2015 Posts: 2 Re: A and B brought a radio each for the same price,$z. A and B sold thei  [#permalink]

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25 Nov 2019, 22:17
chetan2u : I have a doubt, the stmt. 2 says "x-z = 40", I'm wondering how was it substituted into "y-z", please help me with this as I'm stuck at this point when I solved it myself.
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Joined: 24 Sep 2019
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29 Nov 2019, 09:57
1
pkky wrote:
chetan2u : I have a doubt, the stmt. 2 says "x-z = 40", I'm wondering how was it substituted into "y-z", please help me with this as I'm stuck at this point when I solved it myself.

Hi

We have some fractions for A’s and B’s profit. When we substitute it in the formula
$$\frac{\frac{(x-z)}{z}-\frac{(y-z)}{z}}{(\frac{y-z}{z})}=\frac{\frac{(x-z-(y-z))}{z}}{\frac{((y-z)}{z)}}=\frac{(x-z-y+z)}{y-z}=\frac{(x-y)}{(y-z)}$$
Now we know x-y and y-z can be found from the two statements.
Subtract statement I from ii
$$(x-z)-(x-y)=40-20=20....y-z=20$$
_________________
A and B brought a radio each for the same price, $z. A and B sold thei [#permalink] 29 Nov 2019, 09:57 Display posts from previous: Sort by # A and B brought a radio each for the same price,$z. A and B sold thei

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