If x > y, is x > 6 ?
(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y
The OA is D
I don't know how to prove that the second statement is sufficient. I need some help. Please.
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If x > y, is x > 6 ? (1) (x - 7)(y - 7) = 0 (2) x >
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GMATGuruNY
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Statement 1: (x - 7)(y - 7) = 0M7MBA wrote:If x > y, is x > 6 ?
(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y
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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Vincen
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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.
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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Target question: Is x > 6 ?M7MBA wrote:If x > y, is x > 6 ?
(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y
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
