Numbers problems
- 1. 107 x 107 + 93 x 93 =?
Options- A. 19578
- B. 19418
- C. 20098
- D. 21908
- E. None of these Discuss
Correct Answer: 20098
Explanation:
| 107 x 107 + 93 x 93 | = (107)2 + (93)2 |
| = (100 + 7)2 + (100 - 7)2 | |
| = 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2) ] | |
| = 20098 |
- 2. On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder?
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
Correct Answer: 1
Explanation:
Number = 269 x 68 + 0 = 18292
67) 18292 (273
134
----
489
469
----
202
201
---
1
---
Therefore, Required remainder = 1
- 3. What least number must be added to 1056, so that the sum is completely divisible by 23?
Options- A. 2
- B. 3
- C. 18
- D. 21
- E. None of these Discuss
Correct Answer: 2
Explanation:
23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
- 4. Which one of the following can't be the square of natural number?
Options- A. 30976
- B. 75625
- C. 28561
- D. 143642
- E. None of these Discuss
Correct Answer: 143642
Explanation:
The square of a natural number nerver ends in 2.
∴ 143642 is not the square of natural number.
- 5. Which one of the following is a prime number?
Options- A. 119
- B. 187
- C. 247
- D. 551
- E. None of these Discuss
Correct Answer: None of these
Explanation:
√551 > 22
All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.
119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.
So, none of the given numbers is prime.
- 6. The sum of first five prime numbers is:
Options- A. 11
- B. 18
- C. 26
- D. 28 Discuss
Correct Answer: 28
Explanation:
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
- 7. The sum all even natural numbers between 1 and 31 is:
Options- A. 16
- B. 128
- C. 240
- D. 512 Discuss
Correct Answer: 240
Explanation:
Required sum = (2 + 4 + 6 + ... + 30)
This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.
Let the number of terms be n. Then,
tn = 30 ⟹ a + (n - 1)d = 30
⟹ 2 + (n - 1) x 2 = 30
⟹ n - 1 = 14
⟹ n = 15
| ∴Sn = | n | (a + l) | = | 15 | x (2 + 30) = 240. |
| 2 | 2 |
- 8. How many prime numbers are less than 50?
Options- A. 16
- B. 15
- C. 14
- D. 18 Discuss
Correct Answer: 15
Explanation:
Prime numbers less than 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Their number is 15
- 9. (51 + 52 + 53 + ... + 100) =?
Options- A. 2525
- B. 2975
- C. 3225
- D. 3775 Discuss
Correct Answer: 3775
Explanation:
S n = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
| = | 100 | x (1 + 100) - | 50 | x (1 + 50) |
| 2 | 2 |
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775.
- 10. How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options- A. 4
- B. 5
- C. 6
- D. 7 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 4
Explanation:
132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 → 11,3,4 (/)
396 → 11,3,4 (/)
462 → 11,3 (X)
792 → 11,3,4 (/)
968 → 11,4 (X)
2178 → 11,3 (X)
5184 → 3,4 (X)
6336 → 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
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