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# The price of a pair of earrings is x percent more than the price of a

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Math Expert
Joined: 02 Sep 2009
Posts: 60515
The price of a pair of earrings is x percent more than the price of a  [#permalink]

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19 Nov 2019, 01:48
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55% (hard)

Question Stats:

60% (02:16) correct 40% (02:33) wrong based on 24 sessions

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The price of a pair of earrings is x percent more than the price of a bracelet, and the price of a necklace is y percent less than the price of the earrings. Is the price of the bracelet less than the price of the necklace?

(1) $$\frac{xy}{100} < x-y$$

(2) $$x-y > 0$$

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Re: The price of a pair of earrings is x percent more than the price of a  [#permalink]

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19 Nov 2019, 07:26
1
The price of a pair of earrings is x percent more than the price of a bracelet,----$$p*(1+\frac{x}{100})$$ and
the price of a necklace is y percent less than the price of the earrings.----$$p*(1+\frac{x}{100})(1-\frac{y}{100})$$
Is the price of the bracelet less than the price of the necklace? Is $$p<p*(1+\frac{x}{100})(1-\frac{y}{100})....1<(\frac{100+x}{100})(\frac{100-y}{100})............10000<100x-100y-xy+10000.......xy<100(x-y)$$

(1) $$\frac{xy}{100} < x-y.........xy<100(x-y)$$..Yes..Suff

(2) $$x-y > 0$$.....
xy<100(x-y).....say x-y=1
x=3 and y=2.....3*2<100(3-2)
x=100 and y=99...100*99>100(100-99)
Insuff

A
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Re: The price of a pair of earrings is x percent more than the price of a  [#permalink]

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21 Nov 2019, 06:33
Bunuel wrote:
The price of a pair of earrings is x percent more than the price of a bracelet, and the price of a necklace is y percent less than the price of the earrings. Is the price of the bracelet less than the price of the necklace?

(1) $$\frac{xy}{100} < x-y$$

(2) $$x-y > 0$$

$$e=(1+x/100)b…b=100e/(100+x)… n=(1-y/100)e$$
$$b<n…100e/(100+x)<(1-y/100)e…100/(100+x)<(1-y/100);$$
$$10^4<(100-y)(100+x)…10^4-10^4<100x-100y-xy…xy<100(x-y)$$

(1) $$\frac{xy}{100} < x-y$$ sufic

$$xy<100(x-y)…xy/100<(x-y)$$

(2) $$x-y > 0$$ insufic

$$x-y>0…x>y:(x,y)=(5,4)…xy<100(x-y)…20/100<1=yes$$
$$x-y>0…x>y:(x,y)=(5,4.99)…xy<100(x-y)…24.95/100<(0.01)=no$$

Ans (A)
Re: The price of a pair of earrings is x percent more than the price of a   [#permalink] 21 Nov 2019, 06:33
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