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Is x > 6 ?

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Joined: 30 Aug 2007
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Is x > 6 ?  [#permalink]

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New post 26 Jan 2016, 02:52
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (01:54) correct 52% (01:53) wrong based on 102 sessions

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If x > y, is x > 6 ?

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


Source: Gmatclasses, Madrid
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Re: Is x > 6 ?  [#permalink]

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New post 26 Jan 2016, 03:12
kevincan1 wrote:
If x > y, is x > 6 ?

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


Source: Gmatclasses, Madrid


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
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Re: Is x > 6 ?  [#permalink]

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New post 24 Mar 2016, 18:41
kevincan1 wrote:
If x > y, is x > 6 ?

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


Source: Gmatclasses, Madrid


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.
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Is x > 6 ?  [#permalink]

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New post 13 Apr 2018, 08:22
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1
kevincan1 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

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Re: Is x > 6 ?  [#permalink]

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New post 13 Apr 2018, 09:07
kevincan1 wrote:
If x > y, is x > 6 ?

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


Source: Gmatclasses, Madrid


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.
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Re: Is x > 6 ? &nbs [#permalink] 13 Apr 2018, 09:07
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