# Practice Test:Number System

- If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?

a.16 b.24 c.18 d.30

2. P and q when divided by 17, we get remainder as 9 and 11, so what will be the remainder when (p-q)^{2} is divided by 17

a. 4 b. 8 c. 6 d. 2

3. A rectangle is such that it can be perfectly cut into smaller squares of a maximum possible side of length 12 units. It is also known that the perimeter of such a rectangle is 384 units.How many distinct rectangles are there which satisfy the criteria given

a.4 b.8 c.7 d.None

4.What number should be subtracted fromx3+4×2−7x+12if it is to be perfectly divisible by x + 3

a42 b. 39 c. 13 d.None

5.A girl counts all the numbers from 100 to 999. The number of zeroes that she gets is ‘a’, the number of 5’s that he uses is ‘b’ and the number of 8’s he uses is ‘c’. What is the value of b+c-a?

a.280 b. 380 c. 480 d.580

5.Find the unit’s digit in264102+264103

a. 0 b 2 c. 4 d. 6

6.The largest number amongst the following that will perfectly divide101100–1 is:

a.100 b. 1 c. 10,000 d.100,000

7.N is the smallest number that has 5 factors. How many factors does (N – 1) have?

a.2 b.3 c.4 d.5

8. Find the sun of the digits of the least natural number P, such that the sum of the cubes of the four smallest distinct divisors of P equals 2P

a. 7 b. 8 c. 9 d. 10

9. n sq – 81n =199 is prime for n equal to

a.78 b.79 c.80 d.81

10. Consider 4 digit number for which first digits are equal, also last two digits are equal.How many such numbers are perfect square.

a. 3 b.2 c.4 d. 0