Is a/b an ineger? (1) 4a/b is an ineger (2) 4b/a is an

Question

Is a/b an ineger?

(1) 4a/b is an ineger
(2) 4b/a is an integer

Virtual · Answer

I think can't say by both combined also.

consider a/b = 1/4

both 1) and 2) hold good.

but a/b is not an integer.

Paul · Answer

E is answer
from 1) take a=1 and b=2
4*1 / 2 = 2 --> ok
but a/b = 1/2 --> so answer is no

take a=2 and b=1
4*2 / 1 = 8 --> ok
and a/b = 2/1 --> so answer is yes
Statement 1 is inconclusive

from 2) take a=1 and b=2
4*2 / 1 = 8 --> ok
but a/b = 1/2 --> so answer is no

take a=2 and b=1
4*1 / 2 = 2 --> ok
and a/b = 2/1 --> so answer is yes
Statement 2 alone is inconclusive

Both statements together
take a=1 and b=2
4*2 / 1 = 8 --> ok
4*1 / 2 = 2 --> ok
but a/b = 1/2 --> not ok

take a=4 and b=2
4*4 / 2 = 8 --> ok
4*2 / 4 = 2 --> ok
and a/b = 4/2 --> ok
So both statements together is inconclusive

vivek_dj · Answer

E...with Paul providing so many examples...need anyone say more.

Vivek.

anandnk · Answer

a) 4 * a/b is an integer. if a/b = 0.25 4*a/b = 1 which is an integer but a/b is not an integer. If a/b = 1 then 4*a/b = 4 which is an integer.
So Insufficient.

b) if 4 *b/a is an integer then fractional part of b/a could be 0.5 or 0.25
 for example 2.5 *4 = 10 but 1/2.5 is not an integer

combine both of them
a/b = 0.25 and b/a = 4 or a/b = 1 or b/a = 1
So cannot be determined.
Answer is E.

hallelujah1234 · Answer

Is a = 0 (mod b) ?

(1) 4a = 0 (mod b)
(2) 4b = 0 (mod a)

1. 4a = 0 (mod b)
 2a = 0 (mod b/2) or a = 0 (mod b/4)
We dont know whether b is multiple of 2 or of 4. 

2. 4b = 0 (a)
 2b = 0 (mod a/2) or b = 0 (mod a/4)
We dont know about a either.

Combining (1) and (2): (2) does not tell whether b is a multiple of 2 or of 4.

Answer is E.

Is a/b an ineger? (1) 4a/b is an ineger (2) 4b/a is an

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