If a is an integer divisible by 3, and b is not divisible by 3, which

Question

If a is an integer divisible by 3, and b is not divisible by 3, which of the following is NOT divisible by 3?

A. a(b - 3)
 
B. ab + 3
 
C. 3(a + b)
 
D. 3a + b
 
E. a + 3b

yashikaaggarwal · Answer

Let a = 3x 
B = 5z
Where X and Z are mutually exclusive.

Putting value of a and b in option:

A. a(b - 3)
=> 3x(5z-3)
=> 15xz - 9x
Which is divisible by 3 (15&9 both are multiple of 3)

B. ab + 3
=> 3x*5z + 3
=> 15xz + 3
Which is divisible by 3 (15&3 both are multiple of 3)

C. 3(a + b)
=> 3(3x+5z)
=> 9x + 15z
Which is divisible by 3 (15&9 both are multiple of 3)

D. 3a + b
=> 3*3x + 5z
=> 9X+ 5Z
Which is not divisible by 3 (5 is not a multiple of 3)

E. a + 3b
=> 3x + 3*5z
=> 3x + 15z
Which is divisible by 3 (15&3 both are multiple of 3)

Answer is D

Posted from my mobile device

Archit3110 · Answer

let a = 6 and b = 5
so for each option except for D ; we get yes
OPTION D is correct

IanStewart · Answer

If you add a multiple of 3, and a non-multiple of 3, you can never get a multiple of 3. If it's not clear why that's true, we can prove it algebraically -- we can write a multiple of 3 as "3m", and a non-multiple of 3 as "3q + R", where R is 1 or 2, the remainder when we divide our non-multiple by 3. Adding, we get 3m + 3q + R = 3(m + q) + R, which is going to have a remainder of R when we divide by 3.

So here, without even looking at the answer choices, we can be sure a+b is not divisible by 3. That's not an answer choice, but 3a is also a multiple of 3, and if b is not a multiple of 3, then 3a + b cannot be a multiple of 3, so D is right.

So here, without even looking at the answer choices, we can be sure a+b is not divisible by 3. That's not an answer choice, but 3a is also a multiple of 3, and if b is not a multiple of 3, then 3a + b cannot be a multiple of 3, so D is right.

If a is an integer divisible by 3, and b is not divisible by 3, which

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a is an integer divisible by 3, and b is not divisible by 3, which

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards