Discussion
Home ‣ Aptitude ‣ Problems on Numbers Comments
- Question
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?
Options- A. 4
- B. 8
- C. 16
- D. None of these
- Correct Answer
- 8
ExplanationSince 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 ten's and 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.
Problems on Numbers
Search Results
- 1. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
Options- A. 20
- B. 23
- C. 169
- D. None of these Discuss
Correct Answer: 23
Explanation:
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 = √529 = 23.
- 2. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Options- A. 9
- B. 11
- C. 13
- D. 15 Discuss
Correct Answer: 15
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.
- 3. If one-third of one-fourth of a number is 15, then three-tenth of that number is:
Options- A. 35
- B. 36
- C. 45
- D. 54 Discuss
Correct Answer: 54
Explanation:
Let the number be x.Then, 1 of 1 of x = 15 ⟺ x = 15 x 3 x 4 = 180. 3 4 So, required number = ❨ 3 x 180 ❩ = 54. 10 - 4. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
Options- A. 69
- B. 78
- C. 96
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: Cannot be determined
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, the number cannot be determined.
- 5. 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?
Options- A. 3
- B. 4
- C. 9
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 4
Explanation:
Let the ten's digit be x and unit's digit be y.Then, (10x + y) - (10y + x) = 36
⟹ 9(x - y) = 36
⟹ x - y = 4.
- 6. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
Options- A. 20
- B. 30
- C. 40
- D. None of these Discuss
Correct Answer: 20
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) = √400 = 20.
- 7. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
Options- A. 3
- B. 10
- C. 17
- D. 20 Discuss
Correct Answer: 3
Explanation:
Let the number be x.Then, x + 17 = 60 x ⟹ x2 + 17x - 60 = 0
⟹ (x + 20)(x - 3) = 0
⟹ x = 3.
- 8. What is the sum of two consecutive even numbers, the difference of whose squares is 84?
Options- A. 34
- B. 38
- C. 42
- D. 46 Discuss
Correct Answer: 42
Explanation:
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.
- 9. 4.036 divided by 0.04 gives :
Options- A. 1.009
- B. 10.09
- C. 100.9
- D. None of these Discuss
Correct Answer: 100.9
Explanation:
4.036 = 403.6 = 100.9 0.04 4 - 10.
The value of (0.96)3 - (0.1)3 is: (0.96)2 + 0.096 + (0.1)2
Options- A. 0.86
- B. 0.95
- C. 0.97
- D. 1.06 Discuss
Correct Answer: 0.86
Explanation:
Given expression = (0.96)3 - (0.1)3 (0.96)2 + (0.96 x 0.1) + (0.1)2 = ❨ a3 - b3 ❩ a2 + ab + b2 = (a - b) = (0.96 - 0.1) = 0.86
Comments
There are no comments.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.