Question 1

The sum of all two digit numbers divisible by 5 is

Accepted Answer

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 2

On dividing 2272 as well as 875 by 3-digit number N,we get the same remainder.The sum of the digits of N is:

Accepted Answer

(2272-875) = 1397, is exactly divisible by N. Now , 1397 = 11 x 127 The required 3-digit number is 127,the sum of digits is 10.

Question 3

The difference between the squares of two consecutive odd integers is always divisible by ?

Accepted Answer

Let the two consecutive odd integers be (2x + 1) and (2x + 3) Then, (2x + 3)2 - (2x + 1)2 = (2x + 3 + 2x + 1) (2x + 3 - 2x - 1) = (4x + 4)(2) = 8 (x + 1), which is always divisible by 8

Question 4

On dividing 4150 by a certain number , the quotient is 55 and the remainder is 25, the divisor is

Accepted Answer

Let Divisor be x. We know that Dividend = Remainder+Divisor×Quotient So Divisor = (Dividend - Remainder)/Quotient ⇒ x = (4150 - 25)/55 ⇒ x = 4125/55 ⇒ x = 75 Hence Divisor is 75.

Question 5

Find the next number in the series 125, 80, 45, 20, ....

Accepted Answer

The pattern is -45, -35, -25, -15 The next number = 20-15= 5

Question 6

The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

Accepted Answer

Let the required fraction be x. Then 1 - x = 9 x 20 ∴ 1 - x2 = 9 x 20 ⟹ 20 - 20x2 = 9x ⟹ 20x2 + 9x - 20 = 0 ⟹ 20x2 + 25x - 16x - 20 = 0 ⟹ 5x(4x + 5) - 4(4x + 5) = 0 ⟹ (4x + 5)(5x - 4) = 0 x = 4 5

Question 7

If 60% of 35 of a number is 36, then the number is

Accepted Answer

Let the number be x.Then 60% of 3 5 of x=36. => 60 100 * 3 5 * x = 36 => 9 x 25 = 36 => x= 25 * 36 9 = 100 Required number is 100.

Question 8

Find the next number in the series 14, 916, 2536,......

Accepted Answer

The pattern is 1 2 2 2 , 3 2 4 2 , 5 2 6 2 , ∴ The next number= 7 2 8 2 = 4964

Question 9

476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:

Accepted Answer

Let the number be 476ab0 476ab0 is divisible by 3 => 4 + 7 + 6 + a + b + 0 is divisible by 3 => 17 + a + b is divisible by 3 ------------------------(i) 476ab0 is divisible by 11 [(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11 => [3 + (b - a)] is 0 or divisible by 11 --------------(ii) Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2. if a=6 and b=2, 17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer if a=8 and b=2, 17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i) [3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer if a=6 and b=5, 17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer if a=8 and b=5, 17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1 [3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2 Since these values satisfies both equation 1 and equation 2, this is the answer

Question 10

Which one of the following cannot be the square of a natural number?

Accepted Answer

The square of a natural number never ends in 7. 42437 is not the square of a natural number

Question 11

How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?

Accepted Answer

LCM of 2, 3, 7 is 42. => (700 – 300)/42 = 9 22/42 => 9 Numbers.

Question 12

The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?

Accepted Answer

Let the numbers be a and b . Then, a + b = 12 and ab = 35. ∴ a + b = 12 ⟹ ❨ 1 + 1 ❩ = 12 ab 35 b a 35 ∴ Sum of reciprocals of given numbers = 12 35

Question 13

A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?

Accepted Answer

9

Question 14

If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

Accepted Answer

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x ), which must be divisible by 3. ∴ x = 2.

Question 15

At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ?

Accepted Answer

Let, no. of rice bowl = x no. of dal bowl = y no. of meat bowl = z Then, x + y + z = 65 ....(1) Also given that, 2x = 3y = 4z substituting value of y & z in terms of x i.e. y = 2x/3 and z = x/2 in eq (1), We get x = 30. As 1 rice bowl is shared between 2 guests, Therefore, there are 60 guests.

Question 16

Find the next number in the series 3, 4, 5, 5, 12, 13, 7, 24, 25, 8, 15, ...

Accepted Answer

The pattern is 3 2 + 4 2 = 5 2 , 5 2 + 12 2 = 13 2 , 7 2 + 24 2 = 25 2 The next number = 8 2 + 15 2 = 17 2 i.e. 17

Question 17

The difference of two numbers is 11 and (1/5)th of their sum is 9. The numbers are

Accepted Answer

28, 17

Question 18

About 4 out of 5 students are left handed. If there are totally 40 students in an class. How many would be left handed ?

Accepted Answer

Probability of left handed = 4/5 total student = 40 total left handed = 40 x(4/5) = 32

Question 19

What will come in place of the question mark (?) in the following number series? 3240, 540, 108, 27, ?, 4.5

Accepted Answer

Ans. 540 = 3240/6 108 = 540/5 27 = 108/4 ? = 27/3, i.e. ? = 9

Question 20

The sum of three consecutive odd numbers is 93. What is the middle number?

Accepted Answer

Let the three consecutive odd numbers be x, x+2, x+4 Then, x + x + 2 + x + 4 = 93 => 3x + 6 = 93 => 3x = 87 => x = 29 => 29, 31, 33 are three consecutive odd numbers. Therefore, the middle number is 31.

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