BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Number system

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 866
Joined: Mon Aug 02, 2010 6:46 pm
Location: Gwalior, India
Thanked: 31 times

Number system

by goyalsau » Mon Nov 15, 2010 2:42 am
HI! Friends,

Yesterday one of my friend asked one question. It is from Number Properties. Please share your views


One number is {159 * 66 * 99 * 135 * 29 * 34 } What we should subtract from the number to make it divisible by 31 ?

I don't remember the options exactly,

they were like

11
9
3
4

Or may be i am not posting the right options. but i just want to know how to approach these kind of questions. I am completely confused.............
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pm
Location: Milpitas, CA
Thanked: 447 times
Followed by:88 members

by Rahul@gurome » Mon Nov 15, 2010 3:40 am
goyalsau wrote:HI! Friends,

Yesterday one of my friend asked one question. It is from Number Properties. Please share your views


One number is {159 * 66 * 99 * 135 * 29 * 34 } What we should subtract from the number to make it divisible by 31 ?

I don't remember the options exactly,

they were like

11
9
3
4

Or may be i am not posting the right options. but i just want to know how to approach these kind of questions. I am completely confused.............
We have to use modular arithmetic here. According to modular arithmetic, (a mod b) = c means when a is divided by b, the remainder is c. A fundamental formula in modular arithmetic is
  • (ab) mod c = [a mod c * b mod c] mod c
Say, N = 159*66*99*135*29*34
Therefore, (N mod 31) = [{(159 mod 31)*(66 mod 31)*(99 mod 31)*(135 mod 31)*(29 mod 31)*(34 mod 31)} mod 31]

Now,
  • 159 mod 31 = 4
    66 mod 31 = 4
    99 mod 31 = 6
    135 mod 31 = 11
    29 mod 31 = 29
    34 mod 31 = 3
Thus, (N mod 31)
= [{4*4*6*11*29*3} mod 31]
= [{32*99*29} mod 31]
= [{(32 mod 31)*(99 mod 31)*(29 mod 31)} mod 31]
= [{1*6*29} mod 31]
= 174 mod 31
= 19

Therefore we must subtract 19 from N to make it divisible by 31.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Master | Next Rank: 500 Posts
Posts: 437
Joined: Sat Nov 22, 2008 5:06 am
Location: India
Thanked: 50 times
Followed by:1 members
GMAT Score:580

by beat_gmat_09 » Mon Nov 15, 2010 4:19 am
Is this a GMAT question ? Source ?
Hope is the dream of a man awake
Top
User avatar
Legendary Member
Posts: 866
Joined: Mon Aug 02, 2010 6:46 pm
Location: Gwalior, India
Thanked: 31 times

by goyalsau » Mon Nov 15, 2010 4:44 am
beat_gmat_09 wrote:Is this a GMAT question ? Source ?
I don't know buddy one of my friend asked me this question...

Rahul has provided a splendid solution, But the thing is { its very hard to remember formula } approach is good but i don't know will i able to remember it when i will be asked the same question again..........
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
Top
User avatar
Legendary Member
Posts: 866
Joined: Mon Aug 02, 2010 6:46 pm
Location: Gwalior, India
Thanked: 31 times

by goyalsau » Mon Nov 15, 2010 5:16 am
Rahul thanks for the Wonderfull Solution.

can we use this property to solve one more question.

76 ^ 47 is the number and we have to make it divisible by 47

29 ^ 47 mode 47

it can we written as 841 ^ 23 * 29 { 47 * 17 = 799 }

42 ^ 23 * 29 mode 47

1764 ^ 11 * 29 * 42 mode 47

25 ^ 11 * 29 * 42 mode 47

525 ^5 * 29 * 25 * 42 mode 47

8 ^ 5 * 29 * 25 * 42 mode 47

64 ^ 2 * 8 * 29 * 25 * 42 mode 47

27 ^ 2 * 8 * 29 * 25 * 42 mode 47

729 * 8 * 29 * 25 * 42 mode 47

24 * 8 * 29 * 25 * 42 mode 47

192 * 725 * 42 mode 47

4 * 20 * 42 mode 47

80 * 42 mode 47

33 * 42 mode 47

462 * 3 mode 47

39 * 3 mode 47

117 mode 47

23 mode 47

we need to subtract 23 from 76 ^ 47
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
Top
Post new topic Post Reply
• Page 1 of 1