## Number System Questions MCQs

### Total Questions : 531

Page 1 of 27 pages
Question 1. A 9 digit number in which zero does not appear and no digits are repeated has the following properties: The number comprising the left most two digits is divisible by 2, that comprising the left most three digits is divisible by 3, and so on
1.    183654729
2.    381654729
3.    983654721
4.    981654723
Question 2. The remainder obtained when any prime number greater than 6 is divided by 6 must be :
1.    either 1 or 2
2.    either 1 or 3
3.    either 1 or 5
4.    either 3 or 5
Question 3. If the sum of two numbers is 14 and their difference is 10, find the product of these two numbers.
1.    18
2.    20
3.    24
4.    22
Question 4. The greatest number by which the product of three consecutive multiples of 3 is always divisible is :
1.    54
2.    81
3.    162
4.    243
Question 5. The smallest number which must be subtracted from 8112 to make it exactly divisible by 99 is :
1.    91
2.    92
3.    93
4.    95
Question 6. If p3 - q3 = (p - q) (p - q)2 - xpq, then find the value of x :
1.    1
2.    - 3
3.    3
4.    - 1
Question 7. If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true ?
I. n is odd
II. n is prime
III. n is a perfect square
1.    I only
2.    I and II only
3.    I and III only
4.    None of these
Question 8. If the seven digit number 876p37q is divided by 225, then the value of p and q respectively are :
1.    0 and 0
2.    9 and 0
3.    0 and 5
4.    9 and 5
Question 9. What is the remainder when 231 is divided by 5 ?
1.    1
2.    2
3.    3
4.    4
Question 10. (800 ÷ 64) × (1296 ÷ 36) = ?
1.    420
2.    460
3.    500
4.    540
5.    None of these
Question 11. The number of times 99 is subtracted from 1111 so that the remainder is less then 99 is :
1.    10
2.    11
3.    12
4.    13
Question 12. If p is a positive fraction less than 1, then
1.    $$\frac{1}{p}$$ is less than 1
2.    $$\frac{1}{p}$$ is a positive integers
3.    p2 is less than p
4.    $$\frac{2}{p}$$ - p is a positive number
Question 13. Given that (12 + 22 + 32 + ..... + 202) = 2870, the value of (22 + 42 + 62 + ... + 402 ) is :
1.    2870
2.    5740
3.    11480
4.    28700
Question 14. If the number 357*25* is divisible by both 3 and 5, then the missing digits in the unit's place and the thousandth's place respectively are :
1.    0, 6
2.    5, 1
3.    5, 4
4.    None of these
Question 15. In the relation x > y + z, x + y > p and z < p, which of the following is necessarily true ?
1.    y > p
2.    x + y > z
3.    y + p > x
4.    Insufficient data
Question 16. (xn - an) is divisible by (x - a)
1.    for all values of n
2.    only for even values of n
3.    only for odd values of n
4.    only for prime values of n
Question 17. 8 + 88 + 888 + 8888 + 88888 + 888888 = ?
1.    897648
2.    896748
3.    986748
4.    987648
5.    None of these
Question 18. If a + b + c = 0, (a + b) (b + c) (c + a) equals
1.    ab (a + b)
2.    (a + b + c)2
3.    - abc
4.    a2 + b2 + c2