If x y, is x 6 ? (1) (x - 7)(y - 7) = 0 (2) x 18 - 2y

Question

If x > y, is x > 6 ?

(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y

Source: Gmatclasses, Madrid

BrentGMATPrepNow · Accepted Answer

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 RELATED VIDEOS FROM OUR COURSE https://www.youtube.com/watch?v=Od98BOicIq4 https://www.youtube.com/watch?v=S_fjYmCtvy0

chetan2u · Answer

Hi,
since there is not much info in Q apart from x>y, lets see the statements..

(1) (x - 7)(y - 7) = 0
this will be possible , if either of x and y is 7..
if x is 7, x>6...
if y=7. x>y so x>7 and hence x>6..
Sufficient

(2) x > 18 - 2y
this can be written as x+2y>18..
x>y, but lets take they are almost equal in the worst possible scenario..
so x+2x>18..
3x>18..x>6..
hence Sufficient

ans D

mvictor · Answer

1. either x-7=0 or y-7=0, 1st case -> x=7, so yes, x>6. second case y=7. since x>y, then yes, x>6.

2. x>18-2y
note that if y is negative, x is always positive
now we need to see whether are options where x=<6.
suppose x=5, then y must be >6.5 but this is impossible, since x>y.
another case: x=6 -> y >6 - again impossible.
so x MUST be > than 6.

souvonik2k · Answer

x>y
S1 => (x - 7)(y - 7) = 0
i.e. x=7 or y=7
In either case x>6
Sufficient.

S2 => x > 18 - 2y --------------(1) 
Since x > y
Multiplying both sides by 2, we get 2x > 2y ------(2)
Adding inequalities (1) and (2)
3x > 18
x > 6.
Sufficient.

Answer D.

SalahT · Answer

1) either x>7 or y>7 in both cases X>6

2) x>18-2y
lets plug values in the above in equation:
for y is negative x>6
for y is zero x>6
for y is positive x>6 (as long as the constrain x>y maintained)

IMO Answer is D

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If x > y, is x > 6 ? (1) (x - 7)(y - 7) = 0 (2) x > 18 - 2y

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