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by Brent@GMATPrepNow » Tue Dec 16, 2008 8:07 am
If x and y are integers and 2x – y = 11, then 4x + y CANNOT be
(A) –5
(B) 1
(C) 13
(D) 17
(E) 55

Answer: D
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by joanjgonzalez » Tue Dec 16, 2008 8:17 am
2x – y = 11

then

2x = 11+y
4x = 22+2y

substituting in the equation:

4x+y --> 22+2y+y --> 22+3y

therefore whe should check if -22 + result given in each answer is divisible by 3 (so as to get an integer for y)

a. y=-27 Ok
b. y= -21 Ok
c. y= -9 Ok
d. y= -5 No Ok
e. y = -33 OK

Therefore D
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by 4meonly » Tue Dec 16, 2008 9:24 am
2x – y = 11,
y=2x-11

then 4x + y = 4x + 2x-11 =6x-11
So, we should find the number that with addition of 11 will not yield a number divisible by 6

(A) –5+11 =6 divisible by 6 CROSS OFF
(B) 1+11 =12 divisible by 6 CROSS OFF
(C) 13+11 =24 divisible by 6 CROSS OFF
(D) 17 +11 =28 NOT divisible by 6 TAKE IT
(E) 55+11 =66 divisible by 6 CROSS OFF

D

Actually the same logic as above
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by vittalgmat » Wed Dec 17, 2008 11:01 pm
Treat the two equations as simultaneous eqns

ie
2x -y = 11
4x +y = k , where k is an integer

solving,
6x = 11+k
or x = (11 +k)/6 ------- 1

Now plugin the values from the choices starting from E, the criteria
being that x should be an integer.
Only choice D does not result in an integer, others all end up such
that (11 +k) is a multiple of 6.


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