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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
If y is greater than 110 percent of x, is y greater than 75  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:35) correct 27% (01:49) wrong based on 1064 sessions

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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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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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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: If y is greater than 110 percent of x, is y greater than 75  [#permalink]

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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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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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1
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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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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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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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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1
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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GMAT 1: 700 Q50 V34 Re: If y is greater than 110 percent of x, is y greater than 75  [#permalink]

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

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srikanth9502 wrote:
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??

Can someone please explain? Why is y>110 incorrect?
Intern  B
Joined: 21 Jun 2017
Posts: 7
Re: If y is greater than 110 percent of x, is y greater than 75  [#permalink]

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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! Is it ok to say that 110>y and because of that, B is no sufficient?

Thank you in advance!
Intern  B
Joined: 13 Dec 2018
Posts: 10
If y is greater than 110 percent of x, is y greater than 75  [#permalink]

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1
srikanth9502 wrote:
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??

Hi srikanth9502 , Xin Cho

We have given y>1.1x
It means y can be 1.2x, 1.3x and so on...

Now as a limiting case i.e. y=1.1x
you already got y>110 .
But what about other cases i.e. when y=1.2x, 1.3x, 1.4x

Now if you will check for all values you will see the value of x keep on decreasing and so on for y.
Hence it(y>75) is not true in every case. That's why B is insufficient.

Hope it helps

Let me know for anything else.
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Concentration: Finance, Strategy
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Re: If y is greater than 110 percent of x, is y greater than 75  [#permalink]

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Aha, I missed this. Thank you for the explanation a12bansal. Re: If y is greater than 110 percent of x, is y greater than 75   [#permalink] 18 Aug 2019, 08:12
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