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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Mar 04, 2011 2:03 am
diebeatsthegmat wrote:If y is greater than 110 percent of x, is y greater than 75?
(1) x<75
(2) y - x = 10
y > 110% of x => y > (1.1)x

Statement 1: x < 75
If x = 10 => y > 11 => y may be less than or greater than 75.

Not sufficient

Statement 2: (y - x) = 10
Implies, x = (y - 10)
Hence, y > (1.1)*(y - 10)
=> y > (1.1y - 11)
=> 11 > 0.1y
=> y < (11/0.1) = 110

Not sufficient

1 & 2 Together: x < 75 and y = (x + 10)
If x = 40, y = 50 < 75
If x = 70, y = 80 > 75

Not sufficient

The correct answer is E.
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by rohu27 » Fri Mar 04, 2011 3:02 am
y>1.1x is y>75?
from st 1 x<75, x can be 74 or 1 or any negative number.
not suff
from st 2, y-x=10 implies y=x+10.

x+10>1.1x which says, x<100, similar to 1st statement.
not suff.

so it has to be E

whts OA?
diebeatsthegmat wrote:If y is greater than 110 percent of x, is y greater than 75?
(1) x<75
(2) y - x = 10
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by navami » Thu May 05, 2011 9:41 am
Anurag@Gurome wrote:
diebeatsthegmat wrote:If y is greater than 110 percent of x, is y greater than 75?
(1) x<75
(2) y - x = 10
y > 110% of x => y > (1.1)x

Statement 1: x < 75
If x = 10 => y > 11 => y may be less than or greater than 75.

Not sufficient

Statement 2: (y - x) = 10
Implies, x = (y - 10)
Hence, y > (1.1)*(y - 10)
=> y > (1.1y - 11)
=> 11 > 0.1y
=> y < (11/0.1) = 110

Not sufficient

1 & 2 Together: x < 75 and y = (x + 10)
If x = 40, y = 50 < 75
If x = 70, y = 80 > 75

Not sufficient

The correct answer is E.
Hi Anurag,
For statement 2,
y-x=10, we know y>=(110/100)x,
lets take the worst case, where y=(110/100)x
=>y = 1.1x
putting this in equation y-x=10, x=100 atleast,
now if x>=100, y must be >100 or >75, hence it gives us a sufficent condition.
IMO B.
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by MAAJ » Thu May 05, 2011 4:08 pm
Weird problem... Don't need to use y > 1.1x :D

(1) x < 75 -> x = LT(75)
(2) y - x = 10 -> y = 10 + x

If we combine them: y = 10 + LT(75) = LT(85)
So y must be less than 85

Edit: Also x < 77.27...

y > 1.1x
-y > -85
0 > 1.1x -85
85 > 1.1 x
85/1.1 > x
77.2727 > x
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by rohu27 » Thu May 05, 2011 4:49 pm
navami wrote:
Anurag@Gurome wrote:
diebeatsthegmat wrote:If y is greater than 110 percent of x, is y greater than 75?
(1) x<75
(2) y - x = 10
y > 110% of x => y > (1.1)x

Statement 1: x < 75
If x = 10 => y > 11 => y may be less than or greater than 75.

Not sufficient

Statement 2: (y - x) = 10
Implies, x = (y - 10)
Hence, y > (1.1)*(y - 10)
=> y > (1.1y - 11)
=> 11 > 0.1y
=> y < (11/0.1) = 110

Not sufficient

1 & 2 Together: x < 75 and y = (x + 10)
If x = 40, y = 50 < 75
If x = 70, y = 80 > 75

Not sufficient

The correct answer is E.
Hi Anurag,
For statement 2,
y-x=10, we know y>=(110/100)x,
lets take the worst case, where y=(110/100)x
=>y = 1.1x
putting this in equation y-x=10, x=100 atleast,
now if x>=100, y must be >100 or >75, hence it gives us a sufficent condition.
IMO B.
your euqation of y=1.1x and subsitituion would be correct if X were an integer.
wht if x=.1, then y=.11, doesnt satisfy.
HTH
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