If b d, and a/b + c/d = n, is n an integer?

Question

If  b
eq d , and  \frac{a}{b}+\frac{c}{d}=n , is n an integer?

(1) The greatest common divisor of a and b is 1.

(2) The greatest common divisor of c and d is 1.

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nick1816 · Answer

Statement 1-

Case 1-  a=1; b=1; c=3; and d=2

a/b+c/d= 2.5 (not an integer)

Case 2-  a=1; b=1; c=4; and d=2

a/b+c/d= 3 (integer)

Insufficient

Statement 2-

Case 1-  a=3; b=2; c=1; and d=1

a/b+c/d= 2.5 (not an integer)

Case 2-  a=4; b=2; c=1; and d=1

a/b+c/d= 3 (integer)

Insufficient

Combining 2 statements

Case 1-  a=1; b=1; c=3; and d=2

a/b+c/d= 2.5 (not an integer)

Case 2-  a=1; b=1; c=2; and d=-1

a/b+c/d= -1 (integer)

Insufficient

E

ShankSouljaBoi · Answer

Let a=4 b =3 c= 4 d = 3 so n = 4/3 + 3/4 = not an integer.
Let a = 3 b = 4 and c =3 and d = -4 so n = 3/4 - 3/4 = 0 = an integer.

VeritasKarishma   chetan2u  Please help with this question. Is the OA fine ??????

Thanks

KarishmaB · Answer

The problem is with d taking a negative value. When we deal with GCD and factors, we are dealing with positive numbers only. But then, I would like it to be specified in the question.

nick1816 · Answer

It should be mentioned in the question that a, b, c and d are all positive. IMO OA is wrong. Here is the link for the GCD of negative numbers. https://proofwiki.org/wiki/GCD_for_Negative_Integers

OpenInitials · Answer

Could we get clarification regarding the OA? I thought answer was E....

AnirudhaS · Answer

Well its not only with negatives. The question does not mention c/d is in its simplest form.

For example, a=3, b=2, c=2, d=4. Now technically, b ≠ d

So,  \frac{a}{b} + \frac{c}{d} = \frac{3}{2} + \frac{2}{4} = 2

nick1816 · Answer

GCD(c,d)= GCD(2,4)= 2
c/d has to be in the simplest form, if GCD of c and d is 1.

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If b d, and a/b + c/d = n, is n an integer?

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