JMO --- numbers

Find the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers?

JMO - division

Find the remainder when 7187 is divided by 800.

JMO

What is the Remainder in  7⁵ ÷ 6

JMO

For what value of 'n' will the remainder of 351n and 352n be the same when divided by 7?

JMO

What is the unit's digit of the number 6256–4256

JMO

What is the remainder when 91+92+93+....+98 is divided by 6?

JMO

Find the remainder when 3164 is divided by 162

division

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

division and numbers

If the number 5a8b7c is completely divisible by 66 and if b + c = 11 and a + b = 14, then find the value of (a – b).

47^th question of MAT 2014 STD V and STD VI

Answer:

The sum of the numbers = 5 + 8 + 7 + a + b + c = 20 + a + b + c   ------------------------- (1)

Substituting (a + b) = 14 in equation 1 we get 

The sum of the numbers = 20 + 14 + c = 34 + c

Now since the number is completely divisible by 66, it must be divisible by 2, 3 and 11.

If the number is divisible by 2 then “c” has to be an even number or 0.

Also, since the number is divisible by 3, hence sum of numbers must be divisible by 3

c	Sum of the numbers = 34 + c	Selection
0	34	3 + 4 = 7 => not divisible by 3
2	36	3 + 6 = 9 => divisible by 3
4	38	3 + 8 = 11 => not divisible by 3
6	40	4 + 0 = 4 => not divisible by 3
8	42	4 + 2 = 6 => divisible by 3

Therefore, c can have only 2 possible values of 2 and 8 to satisfy the divisibility test of 2 and 3.

Now we have to check the divisibility test of 11.

i.e. the sum of the numbers in the even place – the sum of the numbers in the odd place should be a multiple of 11.

Now, sum of the numbers in the even place = 7 + 8 + 5 = 20

Sum of the numbers in the odd place = a + b + c = 14 + c

c	Sum of the numbers in even place  - sum of number in odd place = absolute { 20 – (14 + c) }	Selection
2	4	=> not multiple of  11
8	2	=> not multiple of  11

So, I think no answer is possible with the given set of conditions.

division

If 3²⁰¹¹ is divided by 5 what is the Remainder.

JMO divisibility

What is the remainder when 17²⁰⁰ is divided by 18 ?

JMO STD VII and STD VIII

JMO STD V and STD VI - divisibility

What is the unit digit in (6324)¹⁷⁹⁷ × (615)³¹⁶ × (341)⁴⁷⁶

^{JMO STD V and STD VI}

JMO --- Divisibility test

When (63⁶³ +63) is divided by 64, the remainder is........................

for JMO STD VII and STD VIII

JMO -- DIvisibility

Which are the two numbers less than 260 that exactly divides

 2³² – 1?

JMO – VII and VIII

number and division

Show that the number 444²⁰¹⁰ + 9 is divisible by 5.

division

 

Divisibility

Show that  3¹ + 3² +... 3²⁰¹⁰ is divisible by 363.

number and divisibility

Prove that 2⁰ + 2¹ + 2² + 2³ + …. 2⁹⁸ is divisible by 7

number, divisibility

Prove that if x and y are both odd positive integers, 

then x² + y² is even but not divisible by 4.

number, divisibility

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q