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If x > y, is x > 6 ? (1) (x - 7)(y - 7) = 0 (2) x >

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Source: — Data Sufficiency |
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Is x> 6?

by GMATGuruNY » Fri Apr 13, 2018 6:45 am
M7MBA wrote:If x > y, is x > 6 ?

(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y
Statement 1: (x - 7)(y - 7) = 0
Case 1: x=7
Here, the answer to the question stem is YES.
Case 2: y=7
Substituting y=7 into x > y, we get:
x > 7.
Thus, the answer to the question stem is YES.
Since the answer is YES in both cases, SUFFICIENT.

Statement 2: x > 18 - 2y
x + 2y > 18
2y > 18 - x
If x=6 in the resulting inequality in blue, then y>6, violating the condition that x>y.
For the value of y to decrease so that x>y, the value of x must INCREASE.
Thus, x>6.
SUFFICIENT.

The correct answer is D.

An algebraic proof for Statement 2:
Multiplying both sides of x > y by 2, we get:
2x > 2y
Adding together 2x > 2y and x > 18 - 2y, we get:
2x + x > 2y + 18 - 2y
3x > 18
x > 6.
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by Vincen » Fri Apr 13, 2018 7:10 am
Hello M7MBA.

This is how would solve it:

(1) (x - 7)(y - 7) = 0

This implies that x=7 or y=7.

If x=7 then x>7, and if y=7 then x>y=7>6. Therefore, this statement is SUFFICIENT.

(2) x > 18 - 2y

Let's suppose for a moment that x=y, then x>18-2x is equivalent to 3x>18 which implies that x>6.
In other words, when "y" take the greatest value that can have (y=x), then the least value for x is 6. Since y<x, then it holds true that x>6.

Therefore, this statement is also SUFFICIENT.

In conclusion, the correct answer is D.

I hope it helps you.
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by Brent@GMATPrepNow » Fri Apr 13, 2018 7:19 am
M7MBA wrote:If x > y, is x > 6 ?

(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y
Target question: Is x > 6 ?

Given: y < x

Statement 1: (x - 7)(y - 7) = 0
There are two possible cases that make this equation true. Either x = 7 OR y = 7
Let's examine each case:
Case a: x = 7. In this case, the answer to the target question is YES, x IS greater than 6
Case b: y = 7. Since it is given that y < x, we can now conclude that 7 < x. The answer to the target question is YES, x IS greater than 6
Both cases yield the SAME answer to the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x > 18 - 2y
Rewrite as 18 - 2y < x
Subtract x from both sides to get: 18 - x < 2y
Add 2y to both sides to get: 18 - x < 2y

IMPORTANT: It is given that y < x
If we multiply both sides by 2 we get another true statement: 2y < 2x
Now add this information to our statement 2 inequality to get: 18 - x < 2y < 2x
This means that 18 - x < 2x
Add x to both sides to get: 18 < 3x
Divides both sides by 3 to get: 6 < x
Perfect.
The answer to the target question is YES, x IS greater than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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