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

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Bunuel
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If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   02 Dec 2019, 00:27
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E

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36% (01:44) correct 64% (01:51) wrong based on 80 sessions
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If \(b\neq d\), 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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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   02 Dec 2019, 12:10
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


Bunuel wrote:
If \(b\neq d\), 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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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   08 Jan 2020, 03:55
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 ??????



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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   08 Jan 2020, 07:44
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ShankSouljaBoi wrote:
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


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.
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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   08 Jan 2020, 08:48
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


VeritasKarishma wrote:
ShankSouljaBoi wrote:
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


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.
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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   22 Feb 2020, 14:32
Could we get clarification regarding the OA? I thought answer was E....
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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   22 Feb 2020, 22:25
VeritasKarishma wrote:
ShankSouljaBoi wrote:
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


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.

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, \(\frac{a}{b} + \frac{c}{d} = \frac{3}{2} + \frac{2}{4} = 2\)
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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   22 Feb 2020, 23:03
GCD(c,d)= GCD(2,4)= 2
c/d has to be in the simplest form, if GCD of c and d is 1.

AnirudhaS wrote:
VeritasKarishma wrote:
ShankSouljaBoi wrote:
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


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.

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


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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink] New post   30 Jun 2021, 15:16
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Re: If b d, and a/b + c/d = n, is n an integer? [#permalink]
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