a, and b are integers, is a factor of b?

Question

a and b are integers, is a factor of b?

(1) a is a factor of 2b
(2) 2a is a factor of b

chaoswithin · Answer

Original statement asks is "a" a factor of "b".

which means is b/a = an integer.

Statement 1:

a is factor of 2b. so 2b/a = an integer.

which means "a" has to be a multiple of 2. so if b is 3 or any other prime a cannot be a factor of b, but otherwise, a can be a factor of b.

For ex. if b =3 and a = 2. 2b = 6. so "a" is a factor of 2b, but a is not a factor of "b".
if b = 4 and a = 2. 2b = 8. so "a" is a factor of 2b and a factor of "b".

Insufficient.

Statement 2:

2a is a factor of b. so b / 2a is an integer.

which means "b" has to be a multiple of 2 and "a" so "a" naturally becomes a factor of "b"

Sufficient.

My answer is B.

KarishmaB · Answer

Statement 1: a is a factor of 2b. Not sufficient.
e.g. If b = 9, 2b = 18
a, factor of 18, could be 3 (in which case it is a factor of b) or could be 18 (in which case it is not a factor of b i.e. 9)

Statement 2: 2a is a factor of b. Sufficient.
If 2a is already a factor of b, all factors of 2a will be factors of b. Since a will be a factor of 2a, it will be a factor of b.
e.g. If a = 6, 2a = 12. Now, 12 is a factor of 24 (= b), hence 6 will also be a factor of 24.

prashantbacchewar · Answer

Even though I have solved this problem earlier. It took me 5.5 mins to arrive at the correct ans.
I was plugging different numbers to arrive at the solution.

Can anybody pls suggest where I am going wrong as it is said that one should be able to find solution for GMAT problem within 2 mins. I think I am missing something or not applying my knowlege correctly.

In general I have even seen on my GMAT prep whenever I come across a number property question my mind stops working. Can someboby pls suggest some way to answer the number properties questions.

KarishmaB · Answer

Plugging numbers should generally be the last option. Sometimes you forget to consider numbers from one particular range, sometimes you make silly mistakes in calculation and sometimes you just plain and simple, get lost.

Focus on statement 1: 'a' is a factor of 2b. 'a' is a factor of a bigger number than we need. 'a' could be 2b. Will it be a factor of 'b' then? No. But 'a' could be very small as well and be a factor of 'b' also. So not sufficient.
Now focus on statement 2: 2a is a factor of 'b'. A number bigger than 'a' is a factor of 'b'. Will 'a' be a factor of 'b'? Since 'a' is a factor of 2a and 2a is a factor of 'b', 'a' will be a factor of 'b'. Sufficient.

When I think factors, I like to say to myself "Smaller numbers", when I say multiples, I like to say to myself "Bigger numbers"... It helps me imagine the scenario quickly.

(Of course factors can be equal and multiples can be 0 and negative and a smaller number needn't be a factor of a bigger number etc etc etc but this thought always puts me in the right frame of mind)

EMPOWERgmatRichC · Answer

HI All,

This question can be easily solved by TESTing VALUES, but you have to be thorough (and not random) with your TESTs.

We're told that A and B are integers. We're asked if A is a factor of B. This is a YES/NO question.

Fact 1: A is a factor of 2B

IF....
A = 1
B = 2
1 is a factor of 2 and the answer to the question is YES.

Before TESTing another set of VALUES, take note of what we've done SO FAR. We used 1 (which is a factor of ALL integers) and we used B=2 (2B = 4) - numbers that only have EVEN FACTORS (beyond the number 1). With our next TEST, we should look to try something different....

IF...
A = 2
B = 3
2 is NOT a factor of 3 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: 2A is a factor of B

Here, we have a variety of Number Properties at play (and a great Number Property 'shortcut'): since we know that A and B are INTEGERS and now we know that 2A is a factor of B.....we know that....

2A is an EVEN integer (2 x integer = even)
B MUST be an EVEN integer, since 2A (which is EVEN) is a factor
Since 2A is a factor, B MUST BE divisible by BOTH 2 and A.

eg. 
B = 20
2A = 4
A = 2
With this combination of "rules", by definition, A will ALWAYS be a factor of B
Fact 2 is SUFFICIENT

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

bumpbot · Answer

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a, and b are integers, is a factor of b?

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