Last visit was: 22 Apr 2026, 17:50 It is currently 22 Apr 2026, 17:50
Home
Messages
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
Back to Forum
Create Topic
User avatar
puma
User avatar
Joined: 23 Mar 2008
Last visit: 11 Oct 2008
Posts: 153
Own Kudos:
1,619
 [80]
Posts: 153
Kudos: 1,619
 [80]
If n is a positive integer, which of the following is a poss Updated on: 29 Jul 2013, 05:41
Originally posted by puma on 19 Jun 2008, 13:57.
Last edited by Bunuel on 29 Jul 2013, 05:41, edited 2 times in total.
Edited the question and moved to PS forum.
8
Kudos
Add Kudos
72
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

80% (01:51) correct 20% (01:58) wrong based on 1364 sessions

History

Date
Time
Result
Not Attempted Yet
If n is a positive integer, which of the following is a possible value of |56 - 5n| ?

A. 7
B. 9
C. 12
D. 15
E. 20
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,754
Own Kudos:
810,671
 [26]
Given Kudos: 105,823
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,754
Kudos: 810,671
 [26]
If n is a positive integer, which of the following is a poss 29 Jul 2013, 05:41
11
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
sophietrophy
brokerbevo
puma
If n is a positive integer, which of the following is a possible value of I56-5nI?

A) 7
B) 9
C) 12
D) 15
E) 20

|56-5n| can be written as 2 equations --> 56-5n = a AND 56-5n = -a where a = one of the answer choices
Then just plug in the answer choices and see which one works:

A) 56 - 5n = 7 --> 5n = 49 (not a multiple of 5) AND 56 - 5n = -7 --> 5n = 63 (not a multiple of 5)
B) 56 - 5n = 9 --> 5n = 47 (not a multiple of 5) AND 56 - 5n = -9 --> 5n = 65 (IS A MULTIPLE OF 5) Thus this is the answer!!
C) 56 - 5n = 12 --> 5n = 44 (not a multiple of 5) AND 56 - 5n = -12 --> 5n = 68 (not a multiple of 5)
D) 56 - 5n = 15 --> 5n = 41 (not a multiple of 5) AND 56 - 5n = -15 --> 5n = 71 (not a multiple of 5)
E) 56 - 5n = 20 --> 5n = 36 (not a multiple of 5) AND 56 - 5n = -20 --> 5n = 76 (not a multiple of 5)


I'm sorry if this is a ridiculous question but how do we know that the answer we're looking for must be a multiple of 5? I understand 5n will be a multiple of 5 but I can't see anywhere a statement regarding the answer being a multiple of 5. I would greatly appreciate it if you could explain. Thank you in advance.
Show more

The correct answer must not be a multiple of 5.

If n is a positive integer, which of the following is a possible value of |56 - 5n| ?
A. 7
B. 9
C. 12
D. 15
E. 20

When 56>5n, then |56 - 5n| = 56 - 5n = (55-5n) + 1 = {multiple of 5} + 1
When 56<=5n, then |56 - 5n| = -(56 - 5n) = (5n-55) - 1 = {multiple of 5} - 1

So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.

Answer: B.

Hope it's clear.
User avatar
brokerbevo
User avatar
Joined: 11 Apr 2008
Last visit: 14 Jan 2009
Posts: 47
Own Kudos:
238
 [14]
Location: Chicago
Posts: 47
Kudos: 238
 [14]
If n is a positive integer, which of the following is a poss Updated on: 19 Jun 2008, 14:49
Originally posted by brokerbevo on 19 Jun 2008, 14:10.
Last edited by brokerbevo on 19 Jun 2008, 14:49, edited 4 times in total.
5
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
puma
If n is a positive integer, which of the following is a possible value of I56-5nI?

A) 7
B) 9
C) 12
D) 15
E) 20
Show more

|56-5n| can be written as 2 equations --> 56-5n = a AND 56-5n = -a where a = one of the answer choices
Then just plug in the answer choices and see which one works:

A) 56 - 5n = 7 --> 5n = 49 (not a multiple of 5) AND 56 - 5n = -7 --> 5n = 63 (not a multiple of 5)
B) 56 - 5n = 9 --> 5n = 47 (not a multiple of 5) AND 56 - 5n = -9 --> 5n = 65 (IS A MULTIPLE OF 5) Thus this is the answer!!
C) 56 - 5n = 12 --> 5n = 44 (not a multiple of 5) AND 56 - 5n = -12 --> 5n = 68 (not a multiple of 5)
D) 56 - 5n = 15 --> 5n = 41 (not a multiple of 5) AND 56 - 5n = -15 --> 5n = 71 (not a multiple of 5)
E) 56 - 5n = 20 --> 5n = 36 (not a multiple of 5) AND 56 - 5n = -20 --> 5n = 76 (not a multiple of 5)
General Discussion
User avatar
fluke
User avatar
Retired Moderator
Joined: 20 Dec 2010
Last visit: 24 Oct 2013
Posts: 1,095
Own Kudos:
5,167
 [3]
Given Kudos: 376
Posts: 1,095
Kudos: 5,167
 [3]
If n is a positive integer, which of the following is a poss 11 Feb 2011, 06:09
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
If n is a positive integer, which of the following is a possible value of |56 - 5n|?
A. 7
B. 9
C. 12
D. 15
E. 20

The units place of 5n will either be 5 or 0.
The units place of 56 is always 6.

So; the possible values for units place of |56-5n| are:

6: 6-0=6 {for all 5n where units place of 5n is 0 and 5n<56 or n<12}
1: 6-5=1 {for all 5n where units place of 5n is 5 and 5n<56 or n<12}
9: 5-6=15-6=9 {for all 5n where where units place of 5n is 5 and 5n>56 or n>=12}
4: 0-6=10-6=4 {for all 5n where where units place of 5n is 0 and 5n>56 or n>=12}

Only number with above criteria is 9.

Ans: "B"
User avatar
sophietrophy
User avatar
Joined: 29 Jun 2013
Last visit: 18 Nov 2014
Posts: 8
Own Kudos:
13
Given Kudos: 21
WE:Law (Law)
Posts: 8
Kudos: 13
If n is a positive integer, which of the following is a poss 29 Jul 2013, 05:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
brokerbevo
puma
If n is a positive integer, which of the following is a possible value of I56-5nI?

A) 7
B) 9
C) 12
D) 15
E) 20

|56-5n| can be written as 2 equations --> 56-5n = a AND 56-5n = -a where a = one of the answer choices
Then just plug in the answer choices and see which one works:

A) 56 - 5n = 7 --> 5n = 49 (not a multiple of 5) AND 56 - 5n = -7 --> 5n = 63 (not a multiple of 5)
B) 56 - 5n = 9 --> 5n = 47 (not a multiple of 5) AND 56 - 5n = -9 --> 5n = 65 (IS A MULTIPLE OF 5) Thus this is the answer!!
C) 56 - 5n = 12 --> 5n = 44 (not a multiple of 5) AND 56 - 5n = -12 --> 5n = 68 (not a multiple of 5)
D) 56 - 5n = 15 --> 5n = 41 (not a multiple of 5) AND 56 - 5n = -15 --> 5n = 71 (not a multiple of 5)
E) 56 - 5n = 20 --> 5n = 36 (not a multiple of 5) AND 56 - 5n = -20 --> 5n = 76 (not a multiple of 5)
Show more


I'm sorry if this is a ridiculous question but how do we know that the answer we're looking for must be a multiple of 5? I understand 5n will be a multiple of 5 but I can't see anywhere a statement regarding the answer being a multiple of 5. I would greatly appreciate it if you could explain. Thank you in advance.
User avatar
aeglorre
User avatar
Joined: 12 Jan 2013
Last visit: 21 Sep 2014
Posts: 103
Own Kudos:
228
Given Kudos: 47
Posts: 103
Kudos: 228
If n is a positive integer, which of the following is a poss 16 Dec 2013, 11:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
^Yeah.. That was an amazing method which I would never have thought of.

The method I used was that subtraction with multiples of 5 follow a pattern: they either end in 1 or 6 (for positive numbers). My problem was that I din't count the negative subtractions.. But they are either 9 or 4 and thus B) is the only valid choice.

The "good" thing about the method I used is that it covers the same reasoning you used; they are (a multiple of 5) +/- 1 and thus only one of them could be an alternative.

However I do not think this method is wise to employ in general since it doesn't have to work in general for all multiples of integer x.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,045
 [7]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,045
 [7]
If n is a positive integer, which of the following is a poss 21 Feb 2015, 18:29
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Hi All,

While it's nice to know an "elegant" approach to solving problems, the practical approach to any question will likely involve the easiest work possible. If you have to stare at this question for 2 minutes to come up with the 'elegant' approach, then your'e wasting time. Here, we can get to the correct answer in under a minute (doing math that children can do) with "brute force":

We're told that N is a POSITIVE INTEGER. We're asked for a possible value of |56 - 5N|.

IF....
N = 1, then the answer is 51
N = 2, then the answer is 46
N = 3, then the answer is 41
N = 4, then the answer is 36

At this point, you might recognize that the pattern (so far) is that the answer will end in 1 or 6. Taking a quick look at the answers, you'll see that NONE of them fits this pattern. We're not wrong though....so there MUST be more work to be done. Remember that absolute value signs turn NEGATIVE results into POSITIVE ones....

Let's leap-frog a few of the numbers and continue working...
IF.....
N = 11, then the answer is 1
N = 12, then the answer is |-4| = 4
N = 13, then the answer is |-9| = 9

And now we have the answer.

Final Answer:
Show Spoiler
B

GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
If n is a positive integer, which of the following is a poss 08 Apr 2026, 20:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109754 posts
Krunaal
Tuck School Moderator
853 posts