If a, b, and c are positive integers such that a is divisible by b, an

Question

If a, b, and c are positive integers such that a is divisible by b, and c is divisible by a, which of the following is NOT necessarily an integer?

A. (a + c)/b
B. (c - a)/b
C. ca/b
D. (c + b)/a
E. cb/a

rohit8865 · Answer

If a, b, and c are positive integers such that a is divisible by b, and c is divisible by a, which of the following is NOT necessarily an integer?

A. (a + c)/b
B. (c - a)/b
C. ca/b
D. (c + b)/a
E. cb/a

Ans:-D

a=bx.........(1)
c=aY.........(2)

a. (A+C)/B = (bx+ay)/b = (bx+ bxy)/b =x+xy=integer
b. (c-a)/b = (ay-a)/b = a(y-1)/b = bx(y-1)/b = integer.

similarly

All options were integer except D.

d.(c+b)/a
 ay+b)/a .....not integer......

Ans D

CounterSniper · Answer

as per the question.

let a be 15
 b be 5
and c be 45

plugging in the values in answer choices only option D turns out not to be an integer.

verify the result by plugging in a=9,b=3 and c=27 or a=14, b =7 and c=35

starktony3000 · Answer

From the question. 
a,b,c are integers

And a is divisible by b => \frac{a}{b} = I (integer)

Similarly,
c is divisible by a => \frac{c}{a} = I

Now multiple the two we have
\frac{a}{b} x \frac{c}{a} = \frac{c}{b} = I

Now check each option. If you get any of these fractions in calculations, it will be an integer.

Correct answer is D.

Posted from my mobile device

sjeffry · Answer

We are looking for which fraction is not "necessarily" an integer, given that a/b and c/a are integers.
That tells us that b is a factor of a AND a is a factor of c, thus: b < a < c

Process of elimination is an easy approach here:
A) a+c/b -> we know a is divisible by b, and a is also a factor of c, so b can divide into both a and c = Cross out A

B) c-a/b -> same reasoning as A) and because we know c > a, b is still divisible by the difference = Cross out B

C) ca/b -> it is given that a is divisible by b, so any integer multiplied by a is divisible by b = Cross out C

D) c+b/a-> we know a is a factor of c, but not a factor of b and b<a so b is NOT divisible by a = D is our answer

E) cb/a -> same reason as C) c is divisible by a, so all products of c are divisible by a = Cross out E

My first reply on GMAT Club, please point out errors if you see them!

RC3 · Answer

I assumed the values as following b=3 a=6 c=36

then i tried option and D did not work, so I chose D

is the approach right?

Bunuel · Answer

Yes, your plug-in approach is fine here. With b = 3, a = 6, c = 36 (which satisfy a divisible by b and c divisible by a), D fails while all others are integers. That correctly shows D is not necessarily an integer.

If a, b, and c are positive integers such that a is divisible by b, an

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If a, b, and c are positive integers such that a is divisible by b, an

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