What is the value of p? (1) 5|q + 1| = p - 5 (2) |p + 5| = 16

Question

What is the value of p?

(1) 5|q + 1| = p - 5
(2) |p + 5| = 16

AndrewN · Answer

Statement (1)  is clearly NOT sufficient, since it invokes a second variable about which we can deduce nothing. We are left with no way of correlating the two unknowns.

Statement (2)  is a run-of-the-mill absolute value equation, and looking at it for a few seconds should allow you to figure out that  p  has two solutions, 11 and -21. Of course, you could solve for the second solution more formally if you were uncomfortable with absolute values: -(p + 5) = 16. Since there are two valid solutions to the question, this statement is NOT sufficient.

Together, the statements allow us to rule out -21, since

5|q + 1| = (-21) - 5

will not produce a valid equation. The right-hand side cannot be negative. Thus,  p  can only equal 11, and   the answer must be (C)  . (The other variable was in the equation as a red herring.)

- Andrew

MBAHOUSE · Answer

Absolute value questions are among the hardest questions in the GMAT test

Kinshook · Answer

Asked: What is the value of p?

(1) 5|q + 1| = p - 5
Since 5|q+1|>=0
p-5>=0
p>=5
NOT SUFFICIENT

(2) |p + 5| = 16
Case 1: p>=-5; p +5 = 16; p = 11
Case 2: p<-5; -p-5 = 16; p = -16-5=-21
p = 11 or -21
NOT SUFFICIENT

(1) + (2)
(1) 5|q + 1| = p - 5
since 5|q+1|>=0
p -5 >=0
p>=5
(2) |p + 5| = 16
Case 1: p>=-5; p +5 = 16; p = 11
Case 2: p<-5; -p-5 = 16; p = -16-5=-21; But p>=5; Invalid
p = 11
SUFFICIENT

IMO C

What is the value of p? (1) 5|q + 1| = p - 5 (2) |p + 5| = 16

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