number systems Model Questions & Answers, Practice Test for ssc chsl tier 1

Answer: (b)

Requirement of bananas for 1 day in the canteen = 13 dozens

∴ Requirement of bananas for 9 weeks i.e. 63 days

= 63 × 13 dozens

= 63 × 13 × 12 = 9828.

Answer: (c)

I. f (k) = 4k + 3

For k = 1, f (1) = 4 × 1 + 3 = 7

For k = 2, f (2) = 4 × 2 + 3 = 11

For k = 3, f (3) = 4 × 3 + 3 = 15

Values of f (k) for k = 1, 2, ...... cannot be expressed as sum of squares, since

$1^2 + 2^2 = 5, 1^2 + 3^2 = 10, 2^2 + 3^2$ = 13

II. f (k) = 8k + 1

For k = 1, f (1) = (8 × 1) + 1 = 9 = $(3)^2$

For k = 2, f (2) = (8 × 2) + 1 = 17

For k = 3, f (3) = (8 × 3) + 1 = 25 = $(5)^2$

For k = 4, f (4) = (8 × 4) + 1 = 33

For k = 5, f (5) = (8 × 5) + 1 = 41

f (k) = 8k + 1 is square of an odd integer only for some values of k.

So, only Statement I is correct.

Answer: (d)

The number $17^29 = (18 – 1)^29$ when divided by 18

leaves the remainder $(– 1)^29$ = 18 – 1 = 17

The number $19^29 = (18 + 1)^29$ when divided by 18

leaves the remainder $(1)^29$ = 1

Then after adding these two the remainder will be

17 + 1=18 which is divisible by 18

Hence the remainder will be 0

Answer: (c)

If the number is divisible by 9 the sum of all its digit is divisible by 9

4 + 7 + 9 + 8 + 6 + 5 + A + B = 39 + A + B is divisible by 9

Possible values of B are 1, 3, 5, 7, 9 as it is given that last digit is odd

For B = 1, A = 5

For B = 3, A = 3

For B = 5, A = 1

For B = 7, A = 8

For B = 9, A = 6

Answer: (a)

Through option 4.65 when multiplied by = 20 gives whole number