Problems on Numbers
- 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:
Then, xy = 120 and x2 + y2 = 289.
∴ (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
∴ x + y = √529 = 23.
- 2. 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 Discuss
Correct Answer: 8
Explanation:
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.
- 3. 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:
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.
- 4. 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:
| Then, x + 17 = | 60 |
| x |
⟹ x2 + 17x - 60 = 0
⟹ (x + 20)(x - 3) = 0
⟹ x = 3.
- 5. 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:
Then, (x + 2)2 - x2 = 84
⟹ 4x + 4 = 84
⟹ 4x = 80
⟹ x = 20.
∴ The required sum = x + (x + 2) = 2x + 2 = 42.
- 6. Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500 .The smallest numbers is
Options- A. 4
- B. 5
- C. 6
- D. 10 Discuss
Correct Answer: 5
- 7. The largest 4 digit number exactly divisible by 88 is
Options- A. 8888
- B. 9999
- C. 9944
- D. 9988 Discuss
Correct Answer: 9944
Explanation:
To find the largest 4 digit number exactly divisible by 88,
We should divide the largest possible 4 digit number by 88, and if we get any remainder than subtract it from that largest number.
The largest possible 4 digit number is 9999
Now,
88) 9999 (113
88
_______
119
88
_______
319
264
_______
55
_______
Therefore, the largest 4 digit number exactly divisible by 88 is given by
9999 - 55 = 9944.
- 8. What is the place value of 6 in 64?
Options- A. 6
- B. 60
- C. 64
- D. 10 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 60
Explanation:
We know that,
? Each digit has a fixed position called its place.
? Each digit has a value depending on its place called the place value of the digit.
? The face value of a digit for any place in the given number is the value of the digit itself
? Place value of a digit = (face value of the digit) × (value of the place).
Hence, the place value of 6 in 64 = 6 x 10 = 60.
- 9. In a two-digit number, the digit in the unit's place is more than twice the digit in ten's place by 1. If the digits in the unit's place and the ten's place are interchanged,difference between the newly formed number and the oiginal number is less than the original number by 1. What is the original number ?
Options- A. 35
- B. 36
- C. 37
- D. 39 Discuss
Correct Answer: 37
Explanation:
Let the ten's digit be x. Then, unit's digit = 2x + 1.
[10x + (2x + 1)] - [{10 (2x + 1) + x} - {10x + (2x + 1)}] = 1
<=> (12x + 1) - (9x + 9) = 1 <=> 3x = 9, x = 3.
So, ten's digit = 3 and unit's digit = 7. Hence, original number = 37.
- 10. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is :
Options- A. 12
- B. 137
- C. 14
- 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.
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