leaves the same remainder

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GoMBA: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Tue Jun 24, 2008 8:36 am

by GoMBA » Tue Aug 19, 2008 8:23 am

Can someone help with a technique to solve this and similar type questions....

Find the greatest number, which will divide 215,167 and 135 so as to leave the same remainder in each case?

a. 64
b. 32
c. 24
d. 16
e. 8

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Source: Beat The GMAT — Problem Solving | Tue Aug 19, 2008 8:23 am

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

Re: leaves the same remainder

by sudhir3127 » Tue Aug 19, 2008 8:37 am

GoMBA wrote:Can someone help with a technique to solve this and similar type questions....

Find the greatest number, which will divide 215,167 and 135 so as to leave the same remainder in each case?

a. 64
b. 32
c. 24
d. 16
e. 8

My answer is D. 16i hope i will be a help:)

the technique is to understand the question .. the "greatest number " u need to find the GCD of mod ( c-a),mod ( a-b), mod ( b-c) thats it ..

hence the numbers are 80, 32,48.

GCD of them is 16. thats it ...

If he asks u the least number .. then do an LCM...

do let me know if u have any doubts,,,

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GoMBA: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Tue Jun 24, 2008 8:36 am

Re: leaves the same remainder

by GoMBA » Tue Aug 19, 2008 8:44 am

Taking the GCD because its asking for the greatest number is something i was also able to guess. But how did you arrive at taking the GCD for (c-a), (a-b), (b-c)? And also i didnt understand what do you mean by mod(c-a)?

Thanks.

sudhir3127 wrote:
GoMBA wrote:Can someone help with a technique to solve this and similar type questions....

Find the greatest number, which will divide 215,167 and 135 so as to leave the same remainder in each case?

a. 64
b. 32
c. 24
d. 16
e. 8
My answer is D. 16i hope i will be a help:)

the technique is to understand the question .. the "greatest number " u need to find the GCD of mod ( c-a),mod ( a-b), mod ( b-c) thats it ..

hence the numbers are 80, 32,48.

GCD of them is 16. thats it ...

If he asks u the least number .. then do an LCM...

do let me know if u have any doubts,,,

Like this post

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

Re: leaves the same remainder

by sudhir3127 » Tue Aug 19, 2008 8:49 am

GoMBA wrote:Taking the GCD because its asking for the greatest number is something i was also able to guess. But how did you arrive at taking the GCD for (c-a), (a-b), (b-c)? And also i didnt understand what do you mean by mod(c-a)?

Thanks.

sudhir3127 wrote:
GoMBA wrote:Can someone help with a technique to solve this and similar type questions....

Find the greatest number, which will divide 215,167 and 135 so as to leave the same remainder in each case?

a. 64
b. 32
c. 24
d. 16
e. 8
My answer is D. 16i hope i will be a help:)

the technique is to understand the question .. the "greatest number " u need to find the GCD of mod ( c-a),mod ( a-b), mod ( b-c) thats it ..

hence the numbers are 80, 32,48.

GCD of them is 16. thats it ...

If he asks u the least number .. then do an LCM...

do let me know if u have any doubts,,,

I am sorrie abt that.. Mod mean Absolute.. thats the formula...

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Thu Aug 21, 2008 7:13 am

why we should find GCD of the difference?

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GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Aug 21, 2008 8:10 am

If we write out what the question is saying, where d is the divisor, and r the remainder, we have:

1. 215 = ad + r
2. 167 = bd + r
3. 135 = cd + r

If you subtract these in pairs (subtract 2. from 1., 3. from 2., and 3. from 1.) we have:

48 = (a-b)d
32 = (b-c)d
80 = (a-c)d

That is, 48, 32 and 80 are all multiples of d. The largest possible value of d is the GCD of 48, 32 and 80, which is 16.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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