number systems Model Questions & Answers, Practice Test for ssc mts paper 1

Answer: (c)

Total number of candles = 15 × 12 × 39 = 7020

Answer: (d)

Last digit of $3^4798$

We know that 3 is cyclic of its unit digit at 4 times.

So, we divide 4798 by 4

= $3^4798 = 3^{1199 × 4 + 2} = (3^{1199 × 4}) .3^2 = 9$

Answer: (d)

The remainder when a number is divided by 16 is given by the remainder of the last 4 digits divided by 16

(because 10000 is a multiple of 16. This principle is very similar in logic to why we look at last 2 digits for divisibility by 4 and the last 3 digits for divisibility by 8.)

Thus, the required answer would be the remainder of 4950/16 which is 6.

Answer: (c)

Since two hands are interchange their positions so sum of the angles subtended at the centre by hour hand and minute hand = 360°

Let us suppose that she was out of house for t min.

So the sum of angles subtended at the centre by the hour hand and minute hand.

Angle made by hour hand.

i.e., 12h → 360°

⇒ 1h = $360/12$ =30°

⇒ 1min = $30/60$ = 0.5 min

Angle made by minute hand.

60 min = 360° ⇒ 1 min = 60

⇒ (0.5)t + (6 × t)° = 360°

⇒ 6.5t = 360 ⇒ t = 55.38 min.

∴ Option (a) is correct.

Answer: (b)

If a number is divisible by 88, it should be divisible by 8 and 11.

In a given option, number 9944 and 8888 is divisible by 88.

Hence, largest number is 9944.