## is y greater than 75?

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### is y greater than 75?

by LulaBrazilia » Tue Mar 11, 2014 7:03 pm
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 Patrick_GMATFix » Tue Mar 11, 2014 7:16 pm
The prompt data allows us to write y > 1.1x, and therefore ask is 1.1x > 75? --> is x > 75/1.1 --> is x > 750/11? Rephrase: is x > 68 and 2/11 ?

Statement (1) clearly answers the question, but what about (2)? The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App). -Patrick

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by theCodeToGMAT » Tue Mar 11, 2014 9:58 pm
y > 110/100 * x

TO find: y > 75

Statement 1:
x > 75
lets say x=75, then
y > 110/100 * 75 = 330/4 = 82
SUFFICIENT

Statement 2:
y - x = 10
y - 10 = x
y > 11/10 * (y-10)
y > 11y/10 - 11
y - 11y/10 > -11
-y/10 > -11
y < 110
We are not sure whether y > 75
INSUFFICIENT

[spoiler]{A}[/spoiler]
R A H U L

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by [email protected] » Tue Mar 11, 2014 10:42 pm
Hi LulaBrazilia,

This DS question can be solved by TESTing Values...

We're told that Y is greater than 110% of X. We're asked "is Y > 75?" This is a YES/NO question.

Fact 1: X > 75

Since we know that X is greater than 75 AND we know that Y is greater than 110% of X, then at the minimum we'd have...

X = 75.1
Y > 1.1(75.1) ------> Don't waste time on this math....You KNOW that Y > 75.

As X gets bigger, then Y will get even bigger (and will ALWAYS be > 75)
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: Y - X = 10

Let's TEST Values....

If....
X=1
Y=11
110% of X = 1.1
Y IS greater than 110% of X
Is Y > 75? The answer to the question is NO.

If...
X=70
Y=80
110% of X = 77
Y IS greater than 110% of X
Is Y > 75? The answer to the question is YES.
Fact 2 is INSUFFICIENT.

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### Re: is y greater than 75?

by [email protected] » Wed Jun 16, 2021 3:08 am
LulaBrazilia wrote:
Tue Mar 11, 2014 7:03 pm
If y is greater than 110 percent of x, is y greater than 75?

1) x > 75

2) y-x = 10
Solution:

Question Stem Analysis:

We need to determine whether y is greater than 75, given that it’s greater than 110% of x.

Statement One Alone:

Since x > 75 and y > 1.1x, then y > 1.1(75) = 82.5. Since y > 82.5, then y > 75. Statement one alone is sufficient.

Statement Two Alone:

Since y = x + 10 and y > 1.1x, we have:

x + 10 > 1.1x

10 > 0.1x

100 > x

We see that x < 100. However, we can’t determine whether y > 75. For example, if x = 70, then y = 1.1x = 77. However, if x = 60, then y = 1.1x = 66. In the former case, y > 75; in the latter case, y < 75. Statement two alone is not sufficient.