Number System - Online Test
Q1. How many 3 digit numbers are divisible by 6 in all ?
Answer : Option B
Explaination / Solution:
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.
Q2. A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
Answer : Option A
Explaination / Solution:
Q3. 8597 - ? = 7429 - 4358
Answer : Option C
Explaination / Solution:
7429 Let 8597 - x = 3071
-4358 Then, x = 8597 - 3071
---- = 5526
3071
----
Q4. The smallest prime number is:
Answer : Option B
Explaination / Solution:
The smallest prime number is 2.
Q5. (12345679 x 72) = ?
Answer : Option B
Explaination / Solution:
| 12345679 x 72 | = 12345679 x (70 +2) |
| = 12345679 x 70 + 12345679 x 2 | |
| = 864197530 + 24691358 | |
| = 888888888 |
Q6. On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
Answer : Option C
Explaination / Solution:
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.
Q7. If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Answer : Option E
Explaination / Solution:
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
P = 1.
Q8. Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?
Answer : Option B
Explaination / Solution:
When n is odd, (xn + an) is always divisible by (x + a).
Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).
Q9. -84 x 29 + 365 = ?
Answer : Option D
Explaination / Solution:
| Given Exp. | = -84 x (30 - 1) + 365 |
| = -(84 x 30) + 84 + 365 | |
| = -2520 + 449 | |
| = -2071 |
Q10. A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
Answer : Option A
Explaination / Solution:
Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
