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- Question
How many 3 digit numbers are divisible by 6 in all?
Options- A. 149
- B. 150
- C. 151
- D. 166
- Correct Answer
- 150
Explanation
Required numbers are 102, 108, 114, ... , 996This 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.
- 1. What is the unit digit in the product (365 x 659 x 771)?
Options- A. 1
- B. 2
- C. 4
- D. 6 Discuss
- 2. 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
- 3. 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
- 4. The smallest 3 digit prime number is:
Options- A. 101
- B. 103
- C. 109
- D. 113 Discuss
- 5. If the number 653 xy is divisible by 90, then (x + y) =?
Options- A. 2
- B. 3
- C. 4
- D. 6 Discuss
- 6. The smallest 6 digit number exactly divisible by 111 is:
Options- A. 111111
- B. 110011
- C. 100011
- D. 110101
- E. None of these Discuss
- 7. The largest 4 digit number exactly divisible by 88 is:
Options- A. 9944
- B. 9768
- C. 9988
- D. 8888
- E. None of these Discuss
- 8. Which one of the following is a prime number?
Options- A. 161
- B. 221
- C. 373
- D. 437
- E. None of these Discuss
- 9. In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?
Options- A. 0
- B. 12
- C. 13
- D. 20 Discuss
- 10. On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder?
Options- A. 0
- B. 3
- C. 5
- D. 11 Discuss
Numbers problems
Search Results
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.
Correct Answer: 42437
Explanation:
The square of a natural number never ends in 7.
∴42437 is not the square of a natural number.
Correct Answer: 5994
Explanation:
(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
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.
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.
Correct Answer: 100011
Explanation:
The smallest 6-digit number 100000.
111) 100000 (900
999
-----
100
---
Required number = 100000 + (111 - 100)
= 100011.
Correct Answer: 9944
Explanation:
Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
Correct Answer: 373
Explanation:
√437 > 22
All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, and 221 is divisible by 13.
373 is not divisible by any of the above prime numbers.
∴373 is prime.
Correct Answer: 20
Explanation:
Number = (12 x 35)
Correct Quotient = 420 ? 21 = 20
Correct Answer: 5
Explanation:
Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
∴Required remainder = 5.
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