## Data Sufficiency

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### Data Sufficiency

by DAM1997 » Fri Nov 27, 2020 11:58 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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### Re: Data Sufficiency

by [email protected] » Mon Jun 20, 2022 2:50 am
DAM1997 wrote:
Fri Nov 27, 2020 11:58 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.