Problem Solving

BTGmoderatorLU wrote:If x is negative and y is positive, which of the following must be positive?

A. x/y
B. xy
C. 2y + x
D. (x + y)^2 +1
E. 3x/y

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.
For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

E. 3x/y
Since 3 is positive, we can rewrite this as: (POSITIVE)(NEGATIVE)/POSITIVE
In the numerator, we have (POSITIVE)(NEGATIVE), which becomes NEGATIVE
So, we get: NEGATIVE/POSITIVE, which evaluates to be NEGATIVE
So, answer choice E is negative
ELIMINATE E

D. (x + y)^2 +1
Recognize that something^2 is always greater than or equal to zero.
So, we can say: (x + y)^2 +1 = something^2 + 1
= (some number greater than or equal to 0) + 1
= a POSITIVE number

Answer: D

Cheers,
Brent

BTGmoderatorLU wrote:If x is negative and y is positive, which of the following must be positive?

A. x/y
B. xy
C. 2y + x
D. (x + y)^2 +1
E. 3x/y

The OA is D.

I'm confused with this Ps question, option C can be positive too but the OA is D. Can anyone assist me, please? Thanks!

The key word here is MUST.
So, we're looking for an expression that must always be positive

C. 2y + x
If y = 10 and x = -1, then 2y + x = 2(10) + (-1) = 19. So, 2y + x CAN be positive.
However, if y = 3 and x = -7, then 2y + x = 2(3) + (-7) = -1. So, 2y + x CAN be negative.
Since we're looking for an expression that MUST be positive, we must eliminate C

Cheers,
Brent

BTGmoderatorLU wrote:If x is negative and y is positive, which of the following must be positive?

A. x/y
B. xy
C. 2y + x
D. (x + y)^2 +1
E. 3x/y

Solution:

Scanning our answer choices, we see that (x + y)^2 must be nonnegative, and then when we add 1 to (x + y)^2, (x + y)^2 + 1 MUST be positive.

Answer: D