Last visit was: 03 Jun 2026, 09:11 It is currently 03 Jun 2026, 09:11
Home
Messages
MBA Fair
Tests
Schools
Events
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 03 Jun 2026
Posts: 1,862
Own Kudos:
2,802
Given Kudos: 234
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,862
Kudos: 2,802
In other words, how many distinct values can x/y have if x Updated on: 05 Jul 2006, 22:30
Originally posted by kevincan on 05 Jul 2006, 06:44.
Last edited by kevincan on 05 Jul 2006, 22:30, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
How many distinct quotients can be obtained if both the dividend and the divisor are integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
acfuture
User avatar
Joined: 19 Apr 2006
Last visit: 23 Jun 2007
Posts: 118
Own Kudos:
9
Posts: 118
Kudos: 9
In other words, how many distinct values can x/y have if x 05 Jul 2006, 17:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
How many distinct quotients can be obtained if both the dividend and the divisor are positive digits?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71
Show more


i have tried, and I dont' think that I understand the question...
my answer is not one of the five listed above.

If I may ask, is this a GMAT question? I looked up "quotient" and still don't have an answer... :oops:
lets wait for one of the math gurus...
User avatar
giddi77
User avatar
Joined: 21 Sep 2003
Last visit: 02 Jan 2018
Posts: 526
Own Kudos:
257
Location: USA
Posts: 526
Kudos: 257
In other words, how many distinct values can x/y have if x 05 Jul 2006, 17:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is there something missing..??

How many distinct quotients can be obtained if both the dividend and the divisor are positive digits?

Can you clarify the red part.
Thx!
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 03 Jun 2026
Posts: 1,862
Own Kudos:
2,802
Given Kudos: 234
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,862
Kudos: 2,802
In other words, how many distinct values can x/y have if x 05 Jul 2006, 22:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In other words, how many distinct values can x/y have if x and y are both integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71

My apologies for the error in the original!

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
535
Posts: 695
Kudos: 535
In other words, how many distinct values can x/y have if x 05 Jul 2006, 22:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
In other words, how many distinct values can x/y have if x and y are both integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71

My apologies for the error in the original!
Show more


total = 100

1/1 or 1 = 10 times but count only once.
1/2 = 2/4 = 4/8 = 3/6 = 5/10 = 5 times so count only once.
1/3 = 2/6 = 3/9 = 3 times but count only once.
.
.
.
.
.
10/9 = only once

i willl correct if any, i found 67.

eager to know the elegant approach......
User avatar
Zooroopa
User avatar
Joined: 09 Apr 2006
Last visit: 07 Sep 2008
Posts: 114
Own Kudos:
4
Location: Somewhere in Wisconsin!
Posts: 114
Kudos: 4
In other words, how many distinct values can x/y have if x 06 Jul 2006, 21:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I tried this. But my method was very time consuming. What is the source of this problem?

All possible combinations - 10*10 = 100.
Now start pairing possible duplicates:
(1/2,2/4,3/6,4/8,5/10) and their reciprocals.
(1/3,2/6,3/9) and their reciprocals.
(1/4,2/8) and their reciprocals.
(1/5,2/10) and their reciprocals.
(2/3,4/6,6/9) and their reciprocals.
(2/5,4/10) and their reciprocals.
(3/4,6/8) and their reciprocals.
(3/5,6/10) and their reciprocals.
(1/1,2/2,....10/10).

Subtract and get the answer. I am feeling too tired to do so!

Hint: You would need to consider at least one member from each group and the corresponding group of its reciprocals.
User avatar
Zooroopa
User avatar
Joined: 09 Apr 2006
Last visit: 07 Sep 2008
Posts: 114
Own Kudos:
4
Location: Somewhere in Wisconsin!
Posts: 114
Kudos: 4
In other words, how many distinct values can x/y have if x 06 Jul 2006, 21:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I posted a solution.

https://www.gmatclub.com/phpbb/viewtopic.php?t=31482

Is that correct?
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
535
Posts: 695
Kudos: 535
In other words, how many distinct values can x/y have if x 07 Jul 2006, 00:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zooroopa
I tried this. But my method was very time consuming. What is the source of this problem?

All possible combinations - 10*10 = 100.
Now start pairing possible duplicates:
(1/2,2/4,3/6,4/8,5/10) and their reciprocals.
(1/3,2/6,3/9) and their reciprocals.
(1/4,2/8) and their reciprocals.
(1/5,2/10) and their reciprocals.
(2/3,4/6,6/9) and their reciprocals.
(2/5,4/10) and their reciprocals.
(3/4,6/8) and their reciprocals.
(3/5,6/10) and their reciprocals.
(1/1,2/2,....10/10).

Subtract and get the answer. I am feeling too tired to do so!

Hint: You would need to consider at least one member from each group and the corresponding group of its reciprocals.
Show more


you are missing 4/5, 8/10 and their reciprocals.
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
535
Posts: 695
Kudos: 535
In other words, how many distinct values can x/y have if x 07 Jul 2006, 00:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MA
kevincan
In other words, how many distinct values can x/y have if x and y are both integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71

My apologies for the error in the original!

total = 100

1/1 or 1 = 10 times but count only once.
1/2 = 2/4 = 4/8 = 3/6 = 5/10 = 5 times so count only once.
1/3 = 2/6 = 3/9 = 3 times but count only once.
.
.
.
.
.
10/9 = only once

i willl correct if any, i found 67.

eager to know the elegant approach......
Show more

but i guess it is 65.
1/2 5 4
1/3 3 2
1/4 2 1
1/5 2 1
2/3 2 1
2/5 2 1
3/4 2 1
3/5 2 1
4/5 2 1
13
the reciprocals also have the same number of occurances = 13
sum of these two's = 26
add 9 for ten (10) 1's = 26+9 = 35
so distinct values for x/y = 100-35 = 65.
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 03 Jun 2026
Posts: 1,862
Own Kudos:
2,802
Given Kudos: 234
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,862
Kudos: 2,802
In other words, how many distinct values can x/y have if x 07 Jul 2006, 01:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MA
MA
kevincan
In other words, how many distinct values can x/y have if x and y are both integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71

My apologies for the error in the original!

total = 100

1/1 or 1 = 10 times but count only once.
1/2 = 2/4 = 4/8 = 3/6 = 5/10 = 5 times so count only once.
1/3 = 2/6 = 3/9 = 3 times but count only once.
.
.
.
.
.
10/9 = only once

i willl correct if any, i found 67.

eager to know the elegant approach......
but i guess it is 65.
1/2 5 4
1/3 3 2
1/4 2 1
1/5 2 1
2/3 2 1 (no, 2/3=4/6=6/9!)
2/5 2 1
3/4 2 1
3/5 2 1
4/5 2 1
13
the reciprocals also have the same number of occurances = 13 (correct 14)
sum of these two's = 26 (28)
add 9 for ten (10) 1's = 26+9 = 35 (37)
so distinct values for x/y = 100-35 = 65 (63).
Show more


Excellent approach, but 2/3=4/6=6/9, so there are a total of 14*2=28
fractions that can be simplified. Therefore OA= 63 (A)
User avatar
Zooroopa
User avatar
Joined: 09 Apr 2006
Last visit: 07 Sep 2008
Posts: 114
Own Kudos:
4
Location: Somewhere in Wisconsin!
Posts: 114
Kudos: 4
In other words, how many distinct values can x/y have if x 07 Jul 2006, 04:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
You are right the list was so long that I forgot noting down a few while I replied to the answer. I have them in my scratchpad!! :)

Is there a shorter method?
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
535
Posts: 695
Kudos: 535
In other words, how many distinct values can x/y have if x 07 Jul 2006, 06:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
MA
MA
kevincan
In other words, how many distinct values can x/y have if x and y are both integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71

My apologies for the error in the original!

total = 100

1/1 or 1 = 10 times but count only once.
1/2 = 2/4 = 4/8 = 3/6 = 5/10 = 5 times so count only once.
1/3 = 2/6 = 3/9 = 3 times but count only once.
.
.
.
.
.
10/9 = only once

i willl correct if any, i found 67.

eager to know the elegant approach......
but i guess it is 65.
1/2 5 4
1/3 3 2
1/4 2 1
1/5 2 1
2/3 2 1 (no, 2/3 = 4/6 = 6/9!)
2/5 2 1
3/4 2 1
3/5 2 1
4/5 2 1
13
the reciprocals also have the same number of occurances = 13 (correct 14)
sum of these two's = 26 (28)
add 9 for ten (10) 1's = 26+9 = 35 (37)
so distinct values for x/y = 100-35 = 65 (63).

Excellent approach, but 2/3=4/6=6/9, so there are a total of 14*2=28
fractions that can be simplified. Therefore OA= 63 (A)
Show more


yup. thats correct. so tedious problem that i was messed up with the numbers....
User avatar
laxieqv
User avatar
Joined: 24 Sep 2005
Last visit: 24 Jun 2011
Posts: 831
Own Kudos:
1,537
Posts: 831
Kudos: 1,537
In other words, how many distinct values can x/y have if x 07 Jul 2006, 07:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
In other words, how many distinct values can x/y have if x and y are both integers from 1 to 10?

(A) 63 (B) 65 (C) 67 (D) 69 (E) 71

My apologies for the error in the original!
Show more


This is really a gripping question! :)

We know that all pairs of (x,y) in which x and y have only 1 as their common factor form distinct values for x/y --> consider (x,y) in which x,y have common factor other than 1. They're:
(2,4) , (2,6) ,(2,8) , (2,10) , (3,6), (3,9), (4,6) , (4,8) , (4,10), (5,10) , (6,8) , (6,9), (6,10) , (8,10)
Each of these form 2 indistinct x/y --> 14*2= 28 indistinct x/y

2/2, 3/3, ......10/10 also form indistinct x/y --> 9 such x/y

---> the number of distinct x/y= 100 - 28- 9= 63

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
User avatar
acfuture
User avatar
Joined: 19 Apr 2006
Last visit: 23 Jun 2007
Posts: 118
Own Kudos:
9
Posts: 118
Kudos: 9
In other words, how many distinct values can x/y have if x 07 Jul 2006, 17:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevin,

do you have OA and OE?

I would really like to know how this works...

thanks...



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
111042 posts