mrunal [aptitude] remainder_ one number and two divisors (number theory)

[Aptitude] Remainder: One number and two divisors (Number Theory)

Intro. question1.DemoQ: 13s2.Demo Q: 19s3.DemoQ: 31s (with shortcut)4.Complex situation: higher number5.Mock questions6.

Intro. question

If a number divided by 56, leaves remainder 29. If the same number is divided by 8,then what will be the remainder? This type of questions is quite common in SSC exam.

Suppose we divide 9 by 4, then what will be the situation? We know that 4 x 2=8And 8 +1=9. Therefore,(4 x 2) + 1 =9. It means 1 is the remainder.Similarly, if unknown number N is divided by 58 and we are getting 29 as remainder,we can write this as

(56 x q) + 29 = N

Distribute these things into green and red buckets in following manner.

Green Red Total (Green + Red)56 x q 29 N

Now forget the last column (total N).Just concentrate on green and red bucket. Assume theyre filled with chocolates.

Mrunal [Aptitude] Remainder: One number and two divisors (Number Th... http://mrunal.org/2013/01/aptitude-remainder-one-number-and-two-diviso...

1 of 6 7/28/2014 10:39 AM

There is only one rule:Whatever number of chocolates can be perfectly divided by 8, must stay in greenbucket. Everything else goes in red bucket.First check the green bucket itself.Divide 56 x q by 8.We know that 56 = 8 x 7. Therefore 56 x q will always be divisible by 8.

Green Red Total (Green + Red)8 x 7 x q 29 NPerfectly divisible by 8

How about red bucket: 29 chocolates? Divide them with 8 you get29 = (8 x 3) + Remainder 5So shift (8 x 3) number of chocolates from red bucket to green bucket.

Green Red Total (Green + Red)8 x 7 x q + 8 x 3 5 NPerfectly divisible by 8 This is our remainder!

We are left with only 5 chocolates in red bucket. Therefore final answer= 5.

DemoQ: 13s

Q. A number when divided by 65 gives the remainder of 43. If this same number isdivided by 13, whatll be the remainder?

Ans. if an unknown number N is divided by 65 and we are getting 43 as remainder,we can write it as (65 x q)+ 43=Nagain, Visualize there are two buckets: green bucket and red bucket.


2 of 6 7/28/2014 10:39 AM

Green Red Total (Green + Red)65xq 43 N

There is only one rule: Whatever number of chocolates are perfectly divisible by 8, muststay in green bucket. Everything else goes in red bucket.But I know that 65=13 x 5

Green Red total13 x 5 x q 43 NPerfectly Divisible by 13 Yet to check

Now check the red bucket. Divide it with 13but 43= (13 x3)+4= (if youre unsure, just divide 43 by 13 and get the remainder).it means 133 number of chocolates can be shifted from red to green bucket.

Green Red total(13 x 5 x q) + (13 x 3) 4 NDivisible by 13 Not divisible by 13.

Thats it. Red bucket is our remainder = 4.Lets try one more

Demo Q: 19s

If a number divided by 114, leaves remainder 21. If the same number is divided by 19,then the remainder will be(114 x q) + 21 = unknown number N


Divide these buckets with 19. Whatever number of chocolates are perfectly divisible by19, must stay in green bucket.First the green bucket itself.114 = 19 x 6

Green Red Total (Green + Red)19 x 6 x q 21 NPerfectly divisible by 19

How about red bucket: 21 chocolates? Divide them with 19 you get21 = (19 x 1) + Remainder 2So shift (19 x 1) number of chocolates from red bucket to green bucket.

Green Red Total (Green + Red)19 x 6 x q + 19 x 1 2 NPerfectly divisible by 19 This is our remainder!


3 of 6 7/28/2014 10:39 AM

So whats the theme/trend/moral of these type of questions?Youve three numbers A > B > CIf A is perfectly divisible by CThen just divide B by C and whether remainder you get, is your answer.

DemoQ: 31s (with shortcut)

A Number divided by 899 leaves remainder of 65. When this number is divided by 31,what will be the remainder?Arrange A> B> C899 > 65 > 31Check: is 899 perfectly divisible by 31? Yes. 31 x 29 =899. (if youre not comfortablewith such two digit division, go through previous article click me)Now divide 65 (B) by 31 and whatever remainder you get, is your answer.65 = (31 x 2) + 3Therefore, final answer (remainder is 3)Lets complicate the situation

Complex situation: higher number

A number when divided by 31, leaves a remainder of 29. Find the remainder whensame number is divided by 62

29a.60b.Either a or bc.None of above.d.

Well have go back to red bucket, green bucket concept.Question says A number when divided by 31 gives 29 remainderTherefore: (31 x q) + 29 = N


Now divide both buckets with 62. Whatever if perfectly divisible by 62, must be shiftedto green bucket.First check the green bucket, is it perfectly divisible by 62?

Green Red Total (Green + Red)31 x q 29 NCant say unless we know the value of q Not divisible

Two things can happen: either q=1 or q=2,3,..or some big number.If q=1

Situation 1: q=1


4 of 6 7/28/2014 10:39 AM

Green Red Total (Green + Red)31 x 1 29 NBut this is not divisible by 62! Not divisible

Since 31 is not divisible by 62, it cannot stay in green bucket.It must be shifted to red bucket.

Green Red Total (Green + Red)0 29+31=60 N

Not divisible by 62

Thus in first situation (when q=1) we get remainder 60.

Situation#2: q=2

Green Red Total (Green + Red)31 x 2=62 29 NThis is perfectly divisible by 62. Not divisible by 62

In this case, you get remainder =29.Similarly, in any other situation like q=3 or q=5, 7, 9you get remainder 29. Note:youll get same remainder 29, if q=0.Therefore, two remainders are possible: Either 60 or 29

Mock questions

If a number divided by 27, leaves remainder 23. If the same number is divided by9, then what will be the remainder? This type of questions is quite common inSSC exam.

1.

If a number divided by 30, leaves remainder 17. If the same number is divided by15, then what will be the remainder? This type of questions is quite common inSSC exam.

2.

A number when divided by 551, leaves a remainder of 31. Find the remainderwhen same number is divided by 29

3.

A number when divided by 9, leaves a remainder of 7. Find the remainder whenthe same number is divided by 18

4.


5.


6.

A number when divided by 28, leaves a remainder of 7. Find the remainder whenthe same number is divided by 35.

7.

Answers

Q.No. Answer1 52 2


5 of 6 7/28/2014 10:39 AM

3 24 7 or 165 5, 16 or 276 5, 18, 31 or 447 0, 7, 14, 21 or 28

URL to article: http://mrunal.org/2013/01/aptitude-remainder-one-number-and-two-divisors-number-theory.html

Posted By Mrunal On 26/01/2013 @ 21:29 In the category Aptitude


6 of 6 7/28/2014 10:39 AM

mrunal [aptitude] remainder_ one number and two divisors (number theory)

Documents