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# If y is greater than 110 percent of x, is y greater than 75

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If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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17 Jan 2014, 01:29
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If y is greater than 110 percent of x, is y greater than 75 ?

(1) x > 75
(2) y -x = 10

Data Sufficiency
Question: 42
Category: Arithmetic; Algebra Percents; Inequalities
Page: 156
Difficulty: 600

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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17 Jan 2014, 01:30
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SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $$y>1.1x$$.
Question: is $$y>75$$? Or is $$x\geq{\frac{75}{1.1}}$$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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17 Jan 2014, 10:53
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If y is greater than 110 percent of x, is y greater than 75 ?

(1 ) x > 75
(2) y -x = 10

y > 1.1 * x

Statement 1) x > 75 as y > 1.1 * 75, definitely we can say y > 75. Sufficient

Statement 2) y - x = 10 => y = 10 + x . As we don't know the value of x, we cannot determine if y > 75. Not Sufficient.

Hence Option A)
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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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17 Jan 2014, 21:48
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If y is greater than 110 percent of x, is y greater than 75 ?

(1 ) x > 75
(2) y -x = 10

SOl:We need to find whether y>75 and we know y>1.1x

St 1: Clearly sufficient cause if x>75 and y>1.1*75. B,C and E ruled out

St 2: y= 10+x and also y>1.1x so 10+x>1.1x -----> 100>x....So can can take any value and therefore Y can have any value
Ans A
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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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18 Jan 2014, 04:23
SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $$y>1.1x$$.
Question: is $$y>75$$? Or is $$x\geq{\frac{75}{1.1}}$$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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23 May 2014, 09:55
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If y is greater than 110 percent of x, is y greater than 75 ?

1. x > 75
2. y -x = 10

Ans:

1: Clearly sufficient

2: y= 10+x => x=y-10 and also y>1.1x so y>1.1(y-10) -----> 110>y. Thus not sufficient.

A it is!
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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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23 May 2014, 10:03
If y is greater than 110 percent of x, is y greater than 75 ?

1. x > 75
2. y -x = 10

1. Is sufficient enough to declare that y>75

2. In-sufficient

Hence, I go with option A.

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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23 May 2014, 10:47
If y is greater than 110 percent of x, is y greater than 75 ?

Looking at options
(1). x> 75
As y >1.1 x --> y >75. Sufficient

(2). y -x =10
As y >1.1 x --> x = y/1.1 - d where d >0
So, (2) --> y - y/1.1 + d = y/11 + d = 10 --> y = 110 - 11d
So, y > 75 will depend on the value of d; Not sufficient
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If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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07 Dec 2014, 10:20
What we know from the test of the problem: y > 1.1x

1) x > 75 and y > 75*1.1
So y > 82.5 and the statement is sufficient.

2) y - x = 10 and, since we are interested in the limiting case, y = 1.1*x
So 1.1x - x = 10, x = 100 and y = 110, leading to y > 110.

Why the reasoning behind the second point is wrong according to the GMAT Quant Review?

Only now I saw why.

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If y is greater than 110 percent of x, is y greater than 75 ? [#permalink]

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07 Jun 2015, 03:30
Y>1.1X,
Is Y > 75?

1. X>75
Put x=75, Y>82.5, definitely y is greater than 75

Sufficient

2. Y-X= 10
X=Y-10
Y>1.1(Y-10)
Y>1.1Y - 11
0.1Y<11
Y<110
Not Sufficient

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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15 Aug 2015, 02:07
Bunuel wrote:
SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $$y>1.1x$$.
Question: is $$y>75$$? Or is $$x\geq{\frac{75}{1.1}}$$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

Bunuel Sir

The question says y>1.1 x (here we don't know the sign of x and y) . Now I'd like to discuss statement II here

II says y - x = 10
And if I re frame my stem its given that y > 1.1 x
or y > x + 0.1 x
or y - x > 0.1x
Now y - x = 10 from statement 2
10 > 0.1x
10 > x/10
x < 100
This means y <110

So, we are not sure

Have i done it correctly ?

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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Re: If y is greater than 110 percent of x, is y greater than 75 [#permalink]

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30 Aug 2017, 19:34
Bunuel wrote:
SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $$y>1.1x$$.
Question: is $$y>75$$? Or is $$x\geq{\frac{75}{1.1}}$$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

Hi Bunuel,

Can you pls point out the flaw in my reasoning.
Given that y>1.1x
As a limiting case, suppose y=1.1x
So, if y-x=10
0.1x=10
x=100
y>1.1x -> y>110
Isn't it suff??

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Re: If y is greater than 110 percent of x, is y greater than 75   [#permalink] 30 Aug 2017, 19:34
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