The three digit positive integer N = a2b is both a multiple

Question

The three digit positive integer N = a2b is both a multiple of 3 and a multiple of 5. What is N?

(1) a + b is an even integer 
(2) a/b = 1

Bunuel · Answer

The three digit positive integer N = a2b is both a multiple of 3 and a multiple of 5. What is N?

N=a2b
N is a multiple of 3 --> a + 2 + b = {a multiple of 3}.
N is a multiple of 5 --> b = 0 or b = 5.

If b = 0, then a can be 1, 4, or 7 (as a+2+b must be multiple of 3).
If b = 5, then a can be 2, 5, or 8 (for the same reason).

Total of 6 pairs of a and b thus 6 possible values of N.

(1) a + b is an even integer --> two pairs satisfy this b=0, a=4: N=420 OR b=5, a=5: N=525. Not sufficient.

(2) a/b = 1 --> only one possible combination for a and b: a=5, b=5 --> N=525. Sufficient.

Answer: B.

gmattokyo · Answer

another bingo! I think it's the dagger in your hand. Helps chop at these dodgy problems

+1

hgp2k · Answer

Statement 1) Insufficient
b must be 0 or 5, multiple possibilities for a (a+2+b must be divisible by 3)

Statement 2) Sufficient
Only one possibility a=b=5 (As a and b can not be 0). So N is 525.

Answer is B.

Target760 · Answer

Another way to solve it

since the number is both multiple of 3 and 5, therefore the Least common multiple would be 15 i.e. a2b has to be a multiple of 15.

so possible 2 digits numbers, that are multiple of 15, with 2 in tens place = {120, 225, 420, 525, 720, 825}

Statement 1: a + b is even; not sufficient; as with both 420 and 525 "a + b" is even
Statement 2: a/b=1; sufficient; as only 525 has a = b

Therefore answer is B

Bunuel · Answer

Bumping for review and further discussion.

thefibonacci · Answer

My take is B

for a2b to be a multiple of 5, it can be:

(i) a25 or (ii) a20

for a25 to be a multiple of 3, it can be --> 120, 420, 720. 
for a20 to be a multiple of 3, it can be --> 225, 525, 825.

stmnt 1) a+b = even 
here 420 and 525 both hold true. (so insufficient)

stmnt2) a/b = 1
here only 525 holds. (hence 2 alone is sufficient)

purijasv123 · Answer

I dont understand how is that you have deduced that b must be a 0 or 5. I realize that any multiple of 5 has to have for its last digit either a 0 or 5. But here N = a2b is simply N = (a) (2) (b) and thus could have been written in a number of other ways. For example, N = 2ba.

Bunuel · Answer

N = a2b means that: 
a = hundreds digit; 
2 = tens digit;
b = units digit.

Hope it's clear.

gmatkum · Answer

MO B

N = a2b, where N is a multiple of 3 and a multiple of 5 
so b must be 5 or 0

1)a+b is an even integer 
when b=5, a=5 
when b=0, a =4 
not sufficient

2)a/b=1 
in this case b not equal to 0. so b must be 5 and hence a must be 5 
N is 525 
sufficient

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The three digit positive integer N = a2b is both a multiple

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 Data Sufficiency (DS) Questions

The three digit positive integer N = a2b is both a multiple

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