concept regarding numbers giving specific remainders with specific divisors.

Today's concept...an extension of concept regarding numbers giving specific remainders with specific divisors.

Type#5

Smallest no. that must be subtracted from 1000 so that the resultant no. leaves remainders 1,3,4,8 with divisors 2,6,5,13 respectively.

from yesterday's approach, v can find out...the smallest no. satisfying all 4 conditions is 99. now to 99 if v add lcm of 2,6,5,13 i.e. 390, the remainders will remain unchanged.

so v need 99 + 390k such that the resultant value is just below 1000.
easily, for k=2, we get one such value....99+390x2 = 879.

hence, ans is 1000-879=121

Type#6

smallest no. that leaves remainders 3,2,4 when successively divided by 5,6,7 respectively.

for such questions...start approaching from the rear end...

we want 4 remainder with 7...the smallest such no. is 4 itself.

now this 4 must have come after a no. was divided by 6
so the no. must have been 4x6+2(remainder with 6) = 26

now, 26 was the quotient when sum no. was divided by 5
so the no. must have been 26x5 + 3(remainder with 5) = 133

so, the answer is 133.

Type#7

a no. leaves remainder 3 when divided by 5 and remainder 8 when successively divided by 11. what is the remainder when this no. is divided by 55?

look at this question carefully...55 is lcm of earlier divisors 11,5... in such a case...the remainder with lcm as divisor wud be constant.

an easy approach for this problem...start from the rear end...take a small no. that leaves rem. 8 with 11...lets take 8.

this 8 is quotient when the main no. is divided by 5...it also leaves remainder 3.

hence, the main no. is

8x5 + 3 = 43

43%55 = 43 answer.

Type#8

Find the largest no. that leaves same remainder when it divides 3398 and 6578.

the concept is very simple...to leave same remainder...difference between two dividents must be divisible by the divisor.

i.e. 6578-3398 = 3180 shud be divisible by the divisor to leave same remainders.

largest no. that divides 3180 is 3180 itself.

hence, the answer is 3180.

Type#9

Find the largest no. that leaves same remainder when it divides 16009,9009,7509 and 14009.

the approach is same... take difference of the nos in ascending or descending order....
i.e. 16009-14009=2000,
14009-9009=5000
9009-7509=1500.

now to leave same remainder, each of the interval shud be divisible by the divisor.

hence, take hcf of 2000,5000,1500. i.e. 500

so, the answer is 500.


Type#10

If a no. is divided by 15, it leaves a remainder 7, if thrice the no. is divided by 5, then what is the remainder?
options...1,2,3,4,0

such questions are difficult to frame as one has to find a pattern b/w divisors n remainders...i know these questions are easy n v all can crack it easily...but the reason y am putting it here is bcoz i have a very short...practical approach for solving this question..

choose a no. that leaves 7 remainder with 15....lets take 7 only.

thrice 7 = 21

21%5 =1 (edited after vani's post)


since, the no. shud give same result for all values that give 7 rem. with 15, its better to take sum value n solve it instead of takin an algebraic approach...

hence, answer is 1.

Answers for yesterday's questions...

Q1. 2 when divided by 3,5,6 or 9 (other than 2)----92
Q2. 2,5,7 when divided by 7,10 and 12 respectively----415
Q3. 1,2,3,4 with 3,4,5,7 respectively.----298
Q4. 6 with 7,8,9,10 and 3 with 11.----20166
Q5. 3 with 6, 0 with 11, 3 with 5, 7 with 8----1023
Q6. 2 with 5, 7 with 8, 3 with 4, 5 with 7&11----2007
Q7. 1 with 11, 4 with 5, 9 with 10, 7 with 9.----529

kudos to vani for the active participation n gett'n most answers correct.



Today's questions...

1. smallest no. that must be added to 1000 so that the resultant no. leaves remainders 2,3,4,5 with 5,6,7,11 respectivelt

2. smallest no. that leaves remainders 1,2,5,6, when divided successively by 2,3,4,23.

3. smallest no. that leaves remainders 4 everytime when successively divided by 7,5,10,13 respectively.

4. a no. leaves remainders 2,5,3,7 when successively divided by 3,7,6,9. what is the remainder when this no. is divided by 126?

5.find the largest no. that leaves same remainder when it divides 2345,7645,9845,6595 and 10095.

6.a no. when divided 88 leaves remainder 3. what is the remainder when its divided by 11?

7.a no. when divided by 391 leaves rem. of 49. find the remainder when its divided by 39...options 29,10,none of these,cannot be determined.