BTGmoderatorDC wrote:Is \(a^3 + b^2 + 4\) divisible by 6?
(I) b is odd
(II) \(\frac{5a}{b}\) is even
OA C
Source: e-GMAT
For a^3 + b^2 + 4 to be divisible by 6, it must be divisible by 2 as well as 3. Thus, a^3 + b^2 + 4 must be even.
Let's take each statement one by one.
(I) b is odd
If a is even, then a^3 is even and b^2 is odd; thus, a^3 + b^2 + 4 is odd. The answer is no.
If a is odd, say a = b = 1, then, a^3 + b^2 + 4 i= 1^3 + 1^2 + 4 = 6, divisible by 6. The answer is yes.
No unique answer. Insufficient.
(II) 5a/b is even
b can be even or odd.
Say, for example, if a = 2 and b = 1, then a^3 + b^2 + 4 is odd. The answer is no. However, if a = 4 and b = 2, then a^3 + b^2 + 4 = 72, divible by 6. The answer is yes.
No unique answer. Insufficient.
(1) and (2) together
We have b = odd; thus, a is even. This means that a^3 + b^2 + 4 is odd. The answer is no. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations:
GMAT Classes Tampa |
GMAT Tutoring DC |
GRE Prep San Francisco |
TOEFL Prep Classes Chicago | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
