Problems on Numbers
- 1. The sum of two number is 25 and their difference is 13. Find their product.
Options- A. 104
- B. 114
- C. 315
- D. 325 Discuss
Correct Answer: 114
Explanation:
Then, x + y = 25 and x - y = 13.
4xy = (x + y)2 - (x- y)2
= (25)2 - (13)2
= (625 - 169)
= 456
∴ xy = 114.
- 2. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options- A. 24
- B. 26
- C. 42
- D. 46 Discuss
Correct Answer: 24
Explanation:
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
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, required number = 11x + 2 = 24.
- 3. 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. The number is:
Options- A. 145
- B. 253
- C. 370
- D. 352 Discuss
Correct Answer: 253
Explanation:
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
- 4. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
Options- A. 3
- B. 5
- C. 9
- D. 11 Discuss
Correct Answer: 11
Explanation:
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
∴ (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
- 5. 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. The number is:
Options- A. 18
- B. 24
- C. 42
- D. 81 Discuss
Correct Answer: 24
Explanation:
| Let the ten's and unit digit be x and | 8 | respectively. |
| x |
| Then, | ❨ | 10x + | 8 | ❩ | + 18 = 10 x | 8 | + x |
| x | x |
⟹ 10x2 + 8 + 18x = 80 + x2
⟹ 9x2 + 18x - 72 = 0
⟹ x2 + 2x - 8 = 0
⟹ (x + 4)(x - 2) = 0
⟹ x = 2.
- 6. 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:
Options- A. 380
- B. 395
- C. 400
- D. 425 Discuss
Correct Answer: 400
Explanation:
| Then, xy = 9375 and | x | = 15. |
| y |
| xy | = | 9375 |
| (x/y) | 15 |
⟹ y2 = 625.
⟹ y = 25.
⟹ x = 15y = (15 x 25) = 375.
∴ Sum of the numbers = x + y = 375 + 25 = 400.
- 7. 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:
Then, (10x + y) - (10y + x) = 36
⟹ 9(x - y) = 36
⟹ x - y = 4.
- 8. 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:
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.
- 9. 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:
| Then, | 1 | of | 1 | of x = 15 ⟺ x = 15 x 3 x 4 = 180. |
| 3 | 4 |
| So, required number = | ❨ | 3 | x 180 | ❩ | = 54. |
| 10 |
- 10. 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:
Then, 3x = 2(x + 4) + 3 ⟺ x = 11.
∴ Third integer = x + 4 = 15.
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