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# If x,y and z are positive numbers and y<100, then the number obtained

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Senior Manager
Joined: 13 Jun 2013
Posts: 275
If x,y and z are positive numbers and y<100, then the number obtained  [#permalink]

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20 Jan 2015, 01:07
2
4
00:00

Difficulty:

75% (hard)

Question Stats:

59% (02:46) correct 41% (02:47) wrong based on 99 sessions

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If x,y and z are positive numbers and y<100, then the number obtained by increasing z by x% and decreasing the result by y% exceeds z if and only if

a) $$x>y$$

b) $$x> \frac{y}{100-y}$$

c) $$x>\frac{y}{1-y}$$

d) $$x> \frac{100y}{100+y}$$

e) $$x>\frac{100y}{100-y}$$
Senior Manager
Joined: 13 Jun 2013
Posts: 275
Re: If x,y and z are positive numbers and y<100, then the number obtained  [#permalink]

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21 Jan 2015, 01:20
1
the number obtained when z is increased by x% is = z(1+x/100)

now, this new number is decreased by y%= z(1+x/100) - z(1+x/100)y/100

and we are told that this number is greater than z. thus we have

z(1+x/100) - z(1+x/100)y/100 >z

(1+x/100)(1-y/100)>1

(1+x/100)>1/(1-y/100)

1+x/100 > 100/(100-y)

x/100 > {100/(100-y)} -1

x/100 > y/100-y

x> 100y/(100-y)

hence E.
Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: If x,y and z are positive numbers and y<100, then the number obtained  [#permalink]

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21 Jan 2015, 06:45
E....... when z is increased by x% is z(100+x)/100 and when this new number is decreased by y%: z{(100+x)/100 }{(100-y)/100}
and as this number is greater than z.... z{(100+x)/100 }{(100-y)/100} >z

u get the ans by solving eq
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x,y and z are positive numbers and y<100, then the number obtained  [#permalink]

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28 Dec 2017, 12:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x,y and z are positive numbers and y<100, then the number obtained &nbs [#permalink] 28 Dec 2017, 12:15
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