NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 21:52 It is currently 23 Apr 2024, 21:52
Decision Tracker
My Rewards
New posts
New comers' posts

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

Which is the least number that must be subtracted from 1856 so that

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
feruz77
Manager
Manager
Joined: 08 Oct 2010
Posts: 171
Own Kudos [?]: 2318 [20]
Given Kudos: 974
Location: Uzbekistan
Concentration: Finance and accounting
Schools:Johnson, Fuqua, Simon, Mendoza
GPA: 4.0
WE 3: 10
Send PM
Which is the least number that must be subtracted from 1856 so that [#permalink] New post   18 Oct 2010, 02:05
1
Kudos
19
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

69% (02:42) correct 31% (02:56) wrong based on 248 sessions
Hide Show timer Statistics
Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 4?

a) 137
b) 1361
c) 140
d) 157
e) 172
ShowHide Answer
Official Answer
E
Most Helpful Reply
avatar
urfrndniks
Intern
Intern
Joined: 08 Jun 2013
Posts: 25
Own Kudos [?]: 21 [7]
Given Kudos: 15
Schools: Olin '19 (A) Fisher '19 (D) UC Davis '19 (A) Arizona State"19 (D) Merage '19 (A$) Carlson '19 (D) Mays '19 (D) Mendoza '19 (WL) McDonough '19 (WL) Anderson '19 (D)
Send PM
Which is the least number that must be subtracted from 1856 so that [#permalink] New post   24 Sep 2016, 05:27
6
Kudos
Bunuel

I solved this with POE, subtracting each option from the original number and dividing it by 7, 12, 16. Solved it under 2 mins though.
A) 1856 - 137 = 1719 ; 1719/7 gives remainder 4 but dividing by 12 it fails, leave it
B) 1856 - 1361 = 495 ; 495/7 fails remainder is 5, leave it
C) 1856 - 140 = 1716; 1716/7 , fails remainder is not 4
D) 1856 - 157 = 1699; 1699/7, fails remainder is not 4
E) 1856-172 = 1684; dividing by all three 7, 12 and 16 gives remainder 4 - CORRECT

Is this approach suitable?
User avatar
shrouded1
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2929 [6]
Given Kudos: 25
Location: London
 Q51  V41
Send PM
GMAT ToolKit User Reviews Badge
Re: Which is the least number that must be subtracted from 1856 so that [#permalink] New post   18 Oct 2010, 02:38
2
Kudos
4
Bookmarks
feruz77 wrote:
Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 4?
a) 137
b) 1361
c) 140
d) 157
e) 172

pls. help with solution method!?


First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}
The largest such number less than or equal to 1856 is 336x5+4 or 1684
To obtain this you need to subtract 172.

Answer is (d)
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618628 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Which is the least number that must be subtracted from 1856 so that [#permalink] New post   25 Sep 2016, 03:02
Expert Reply
urfrndniks wrote:
Bunuel

I solved this with POE, subtracting each option from the original number and dividing it by 7, 12, 16. Solved it under 2 mins though.
A) 1856 - 137 = 1719 ; 1719/7 gives remainder 4 but dividing by 12 it fails, leave it
B) 1856 - 1361 = 495 ; 495/7 fails remainder is 5, leave it
C) 1856 - 140 = 1716; 1716/7 , fails remainder is not 4
D) 1856 - 157 = 1699; 1699/7, fails remainder is not 4
E) 1856-172 = 1684; dividing by all three 7, 12 and 16 gives remainder 4 - CORRECT

Is this approach suitable?

______________
Yes, that;s correct.
User avatar
B
JoeKan1234
Intern
Intern
Joined: 27 Aug 2022
Posts: 40
Own Kudos [?]: 7 [1]
Given Kudos: 130
Send PM
Re: Which is the least number that must be subtracted from 1856 so that [#permalink] New post   19 Mar 2024, 15:48
1
Kudos
Let X be the number

1856 - X =336Q + 4

X = 1852 - 336Q

To minimize X, maximize Q

Max. value of Q = 5

So Min. value of X = 1852 - 336*5 = 172
GMAT Club Bot
gmatclubot
Re: Which is the least number that must be subtracted from 1856 so that [#permalink]
19 Mar 2024, 15:48
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions