Numbers problems
- 1. 3251 + 587 + 369 -? = 3007
Options- A. 1250
- B. 1300
- C. 1375
- D. 1200
- E. None of these Discuss
Correct Answer: 1200
Explanation:
3251 Let 4207 - x = 3007 + 587 Then, x = 4207 - 3007 = 1200 + 369 ---- 4207 ----
- 2. The sum of first 45 natural numbers is:
Options- A. 1035
- B. 1280
- C. 2070
- D. 2140 Discuss
Correct Answer: 1035
Explanation:
Let S n =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
| Sn = | n | [2a + (n - 1)d] | = | 45 | x [2 x 1 + (45 - 1) x 1] | = | ❨ | 45 | x 46 | ❩ | = (45 x 23) |
| 2 | 2 | 2 |
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
Shorcut Method:
| Sn = | n(n + 1) | = | 45(45 + 1) | = 1035. |
| 2 | 2 |
- 3. The difference between the place values of two sevens in the numeral 69758472 is
Options- A. 0
- B. 6993
- C. 699930
- D. None of these Discuss
Correct Answer: 699930
Explanation:
Required difference = (700000 - 70) = 699930
- 4. If the number 653 xy is divisible by 90, then (x + y) =?
Options- A. 2
- B. 3
- C. 4
- D. 6 Discuss
Correct Answer: 4
Explanation:
90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653x0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.
- 5. The smallest 3 digit prime number is:
Options- A. 101
- B. 103
- C. 109
- D. 113 Discuss
Correct Answer: 101
Explanation:
The smallest 3-digit number is 100, which is divisible by 2.
∴ 100 is not a prime number.
√101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
∴101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
- 6. The difference between the place value and the face value of 6 in the numeral 856973 is
Options- A. 973
- B. 6973
- C. 5994
- D. None of these Discuss
Correct Answer: 5994
Explanation:
(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
- 7. Which one of the following can't be the square of natural number?
Options- A. 32761
- B. 81225
- C. 42437
- D. 20164
- E. None of these Discuss
Correct Answer: 42437
Explanation:
The square of a natural number never ends in 7.
∴42437 is not the square of a natural number.
- 8. What is the unit digit in the product (365 x 659 x 771)?
Options- A. 1
- B. 2
- C. 4
- D. 6 Discuss
Correct Answer: 4
Explanation:
Unit digit in 3 4 = 1 ⟹ Unit digit in (3 4 ) 16 = 1
∴ Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3
Unit digit in 659 = 6
Unit digit in 74 ⟹ Unit digit in (74)17 is 1.
Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3
∴ Required digit = Unit digit in (3 x 6 x 3) = 4.
- 9. How many 3 digit numbers are divisible by 6 in all?
Options- A. 149
- B. 150
- C. 151
- D. 166 Discuss
Correct Answer: 150
Explanation:
Required numbers are 102, 108, 114, ... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then,
a + (n - 1)d = 996
⟹ 102 + (n - 1) x 6 = 996
⟹ 6 x (n - 1) = 894
⟹ (n - 1) = 149
⟹ n = 150.
- 10. The smallest 6 digit number exactly divisible by 111 is:
Options- A. 111111
- B. 110011
- C. 100011
- D. 110101
- E. None of these Discuss
Correct Answer: 100011
Explanation:
The smallest 6-digit number 100000.
111) 100000 (900
999
-----
100
---
Required number = 100000 + (111 - 100)
= 100011.
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