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Problems on Numbers

Description: There are 15 question on Numerical Ability for Bank PO/CLERK and Class V to X standard.
Number of Questions: 15
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Tags: MATHS Numerical Ability
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If one-third of one-fourth of a number is 15, then three-tenths of that number is

  1. 35

  2. 36

  3. 45

  4. 54

  5. None of these

Show answer
Correct Option: D
Explanation:

Correct answer. Let the number = x Then, 1/3 of 1/4 of of x = 15 x = 15 x 12 x = 180 So, the required number = (3/10) * 180 = 54

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. What is the number?

  1. 18

  2. 24

  3. 42

  4. 81

  5. None of these

Show answer
Correct Option: B
Explanation:

Let the ten's and unit digit be x and 8/x, respectively. Then, (10x + 8/x) + 18 = 10 x (8/x) + x 10x2 + 8 + 18x = 80 + x2 9x2 + 18x - 72 = 0 x2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = 2. So, unit's digit = 4 and ten's digit = 2 Then, the required number is 24. Therefore, the correct answer is 24.

Three times of the first integer of three consecutive odd integers is 3 more than twice the third. The third integer is

  1. 9

  2. 11

  3. 13

  4. 15

  5. None of these

Show answer
Correct Option: D
Explanation:

Let the three integers be x, x + 2 and x + 4. Then, 3x = 2(x + 4) + 3 x = 11. Third integer = x + 4 = 15. Therefore, 15 is correct answer.

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?

  1. 4

  2. 8

  3. 16

  4. 12

  5. None of these

Show answer
Correct Option: B
Explanation:

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let the ten's and the unit's digits be 2x and x, respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4 Required difference = (2x + x) - (2x - x) = 2x = 8 Therefore, 8 is the correct answer.

The sum of the squares of three positive numbers is 138, while the sum of their products taken two at a time is 131. Their sum is

  1. 20

  2. 30

  3. 40

  4. 50

  5. None of these

Show answer
Correct Option: A
Explanation:

Let the numbers be a, b and c. Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131 (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400 (a + b + c) = 20

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. Which of the following is that number?

  1. 145

  2. 253

  3. 370

  4. 352

  5. None of these

Show answer
Correct Option: B
Explanation:

Let the middle digit be b. Then, 2b = 10 or b = 5. Let the number be abc. Now, 100 a + 10 b + c + 99 = 100 c + 10 b + a Or, a + 1 = c So, the number is  253

The sum of two numbers is 25 and their difference is 13. Find their product.

  1. 104

  2. 114

  3. 315

  4. 325

  5. None of these

Show answer
Correct Option: B
Explanation:

Let the numbers be x and y. Then, x + y = 25 and x - y = 13. 4xy = (x + y)2 - (x- y)2 4xy = (25)2 - (13)2 4xy = (625 - 169) = 456 xy = 114

If the difference of squares of two consecutive even numbers is 84, then what is the sum of the numbers?

  1. 34

  2. 38

  3. 42

  4. 46

  5. None of these

Show answer
Correct Option: C
Explanation:

This is the correct answer. Let the numbers be x and x + 2. 
Then, (x + 2)2 - x2 = 84 4x + 4 = 84  4x = 80  x = 20  The required sum = x + (x + 2) = 2x + 2 = 42

In a two-digit number, its unit's digit exceeds its ten's digit by 2 and the product of the given number and the sum of its digits is equal to 144, then the number is

  1. 24

  2. 26

  3. 42

  4. 46

  5. None of these

Show answer
Correct Option: A
Explanation:

Let the ten's digit be x. Then, unit's digit will be x + 2. The number = 10x + (x + 2) = 11x + 2 The sum of digits = x + (x + 2) = 2x + 2 (11x + 2)(2x + 2) = 144 22x2 + 26x - 140 = 0 11x2 + 13x - 70 = 0 (x - 2)(11x + 35) = 0 x = 2 Hence, the required number = 11x + 2 = 24

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is

  1. 380

  2. 395

  3. 400

  4. 425

  5. None of these

Show answer
Correct Option: C
Explanation:

Let the numbers be x and y. Then, xy = 9375 and x/y = 15 (xy)/(x/y) = 9375/15 y2 = 625 y = 25 x = 15y = (15 x 25) = 375 Sum of the numbers = x + y = 375 + 25 = 400.

Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

  1. 3

  2. 10

  3. 17

  4. 20

  5. None of these

Show answer
Correct Option: A
Explanation:

This is the correct answer for this question. Let the number be x. 
Then, x + 17 = 60/x x2 + 17x - 60 = 0  (x + 20)(x - 3) = 0  x = 3

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. Which of the following can be that two-digit number?

  1. 69

  2. 78

  3. 43

  4. 76

  5. None of these

Show answer
Correct Option: A
Explanation:

Let the ten's digit be x and unit's digit be y. Then, x + y = 15 and x - y = 3 or y - x = 3. Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6. Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9. So, the number is either 96 or 69. Hence, out of the given options, option (1) is correct.  

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

  1. 3

  2. 4

  3. 9

  4. Cannot be determined

  5. None of these

Show answer
Correct Option: B
Explanation:

Let the ten's digit be x and the unit's digit be y. Then, (10x + y) - (10y + x) = 36 9(x - y) = 36 x - y = 4

If the digits of a two-digit number interchange places and the new number is added to the original number, then the resulting number will be divisible by

  1. 3

  2. 5

  3. 9

  4. 11

  5. None of these

Show answer
Correct Option: D
Explanation:

Let the ten's digit be x and the unit's digit be y. Then, the number = 10x + y. The number obtained by interchanging the digits = 10y + x (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

The product of two numbers is 120 and the sum of their squares is 289. The sum of the numbers is

  1. 20

  2. 23

  3. 169

  4. 170

  5. None of these

Show answer
Correct Option: B
Explanation:

This is the correct answer. Let the numbers be x and y. 
Then, xy = 120 and x2 + y2 = 289.  (x + y)2 = x2 + y2 + 2xy               = 289 + (2 x 120)               = 529  x + y  = 23

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