Question 1

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 2

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 3

7, 16, 36, 78, 144, ? which number come in place of question mark

Accepted Answer

222

Question 4

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 5

The largest 4 digit number exactly divisible by 88 is ?

Accepted Answer

The largest 4 digit number is = 9999 After dividing 9999 with 88, we get 55 as remainder so largest 4 digit number divisible by 88 = 9999-55 = 9944.

Question 6

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 7

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 a and b are the numbers.Then a+b is 12 and ab is 35. a+b/ab = 12/35 1/b + 1/a = 12/35

Question 8

What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?

Accepted Answer

6)4456(742 42 -------- 25 24 ------- 16 12 ----- 4 ------ Required number = (6-4) = 2.

Question 9

How many of the following numbers are divisible by 132? 264,396,462,792,968,2178,5184,6336

Accepted Answer

132 = 4 x 3 x 11, So if the number is divisible by all three numbers 4,3 and 11,then the number is divisible by 132 also. 264 => 4,3,11(/) 396 => 4,3,11(/) 462 => 11,3 792 => 4,3,11(/) 968 => 11,4 2178 => 11,3 5184 => 3,4 6336 => 4,3,11(/) Required number of numbers=4.

Question 10

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

Accepted Answer

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = ( 22 + x ), which must be divisible by 3. When x=2. [(22 + 2) = 24 is divisible by 3] So, the answer is 2

Question 11

A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?

Accepted Answer

The maximum number of bows will be 4 yards (= 4 x 36 inches) divided by 15 inches. This gives 9.6. But as a fraction of a bow is no use, we can only make 9 bows.

Question 12

Find the unit digit of 4198 + 612345 + 34866 + 2411 + 1.

Accepted Answer

Given that, 4 198 + 6 12345 + 348 66 + 24 11 + 1 Now Power Cycle of 4 is 4, 6 6 is 6 8 is 8, 4, 2, 6 1 is 1 4 198 - 198 is even number , So the unit digit value is 6 6 12345 - It is always 6 348 66 - 66/4 the remainder is 2 , So the second value is 4 24 11 - 11 is odd number, So the unit digit value is 4 1 - It is always 1 Total = 21 Therefore, The unit digit is 1

Question 13

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n is divided by 4 ?

Accepted Answer

Let n=4*q + 3. Then, 2*n = 8*q + 6 = 4(2*q + 1) + 2. Thus when 2*n is divided by 4, the reminder is 2.

Question 14

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 15

Which natural number is nearest to 8485, which is completely divisible by 75 ?

Accepted Answer

On dividing we get 75)8485(113 75 ------ 98 75 ------ 235 225 ------ 10 ------ Required number = (8485-10)=8475.

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

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x+y is equal to ?

Accepted Answer

Since 653xy is divisible by 5 as well as 2, so y = 0. Now, 653x0 must be divisible by 8. So, 3x0 must be divisible by 8. This happens when x = 2 x + y = (2 + 0) = 2.

Question 18

How many terms are in the G.P. 3, 6, 12, 24, ......., 384 ?

Accepted Answer

Here a = 3 and r = 6/3 = 2. Let the number of terms be n. Then, t = 384 => a * r^(n-1) = 384 => 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7) => n-1 = 7 => n = 8.

Question 19

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 20

What will come in place of the question mark (?) in the following questions ? 22% of ? + 166.64 = 340

Accepted Answer

(kx22)/100 = 340 - 166.64 = 173.36 k = (173.36 x 100)/22 k = 788

Numbers Questions