GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Jan 2020, 18:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60480
If b ≠ d, and a/b + c/d = n, is n an integer?  [#permalink]

### Show Tags

02 Dec 2019, 00:27
00:00

Difficulty:

75% (hard)

Question Stats:

38% (01:28) correct 62% (02:00) wrong based on 47 sessions

### HideShow timer Statistics

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.

Are You Up For the Challenge: 700 Level Questions

_________________
VP
Joined: 19 Oct 2018
Posts: 1290
Location: India
Re: If b ≠ d, and a/b + c/d = n, is n an integer?  [#permalink]

### Show Tags

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.

Are You Up For the Challenge: 700 Level Questions
Senior Manager
Joined: 21 Jun 2017
Posts: 395
Location: India
Concentration: Finance, Economics
Schools: IIM
GMAT 1: 620 Q47 V30
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: If b ≠ d, and a/b + c/d = n, is n an integer?  [#permalink]

### Show Tags

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 ??????

Thanks
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9983
Location: Pune, India
Re: If b ≠ d, and a/b + c/d = n, is n an integer?  [#permalink]

### Show Tags

08 Jan 2020, 07:44
1
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.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
VP
Joined: 19 Oct 2018
Posts: 1290
Location: India
Re: If b ≠ d, and a/b + c/d = n, is n an integer?  [#permalink]

### Show Tags

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.
Re: If b ≠ d, and a/b + c/d = n, is n an integer?   [#permalink] 08 Jan 2020, 08:48
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne