Question: 26 -

A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and the other digits are correct, then the correct answer would be :

555181

555681

553681

556581

Answer:

555681

Solution:

987 = 3 * 7 * 47.
So, the required number must be divisible by each one of 3, 7, 47
553681 => (Sum of digits = 28, not divisible by 3)
555181 => (Sum of digits = 25, not divisible by 3)
555681 is divisible by each one of 3, 7, 47.

Question: 27 -

(51 + 52 + 53 + .........+100) is equal to

3775

4225

4275

3755

Answer:

3775

Solution:

51 + 52 + 53 + ...........+ 100

=> (1 + 2 + 3 + .... + 100) - (1 + 2 + 3 + ...... + 50)

=> It is in the form of  [n(n+1)/2]  series summation
=> n1 = 100 , n2 = 50

=>[100(100+1)/2] − [50(50+1)/2]
=> (5050 - 1275) = 3775

Question: 28 -

A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be:

2

1

3

5

Answer:

1

Solution:

Let the Number be Y.
Then  Y = 296 q + 75
= (37 x 8)q +( 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1

Question: 29 -

The sum of all two digit numbers divisible by 5 is

945

678

439

568

Answer:

945

Solution:

Required numbers are 10,15,20,25,...,95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,then n=18.
Required sum=n/2(a+l)=18/2(10+95)=945.

Question: 30 -

If the product 4864*9 P 2 is divisible by 12, the value of p:

1

3

2

4

Answer:

1

Solution:

clearly 4864 is divisible by 4
So 9 P 2 must be divisible by 3.So(9+P+2) must be
 divisible by 3.
so P=1.