number system Model Questions & Answers, Practice Test for ssc cgl tier 2

Answer: (c)

Let the even consecutive numbers are 2n–2, 2n, 2n + 2 (2n – 2) × (2n) × (2n + 2) = 4032 ...(1)

Product of 1st even number third even number = 252

Putting this in equation ...(1)

252 × 2n = 4032 ⇒ n = 8

Numbers are 14, 16, 18

Five times of 2nd number is = 5 × 16 = 80

Answer: (d)

Given number is 222222.

Sum of digits = 2 + 2 + 2 + 2 + 2 + 2 = 12 which is divisible by 3.

So, number is also divisible by 3.

Sum of odd terms of digits – Sum of even terms of digits = 6 – 6 = 0, it is divisible by 11.

In a number a digit repeated six times, then this number is divisible by 7, 11 and 13.

Hence, the given number is divisible by 3, 7 and 11

Answer: (d)

Let us assume that he was out of house for 't' min.

So angle formed by min. hand = 6 × t

Angle formed by hour hand = 0.5 × t

Now, 0.5 × t + 6 × t = 360

⇒ 6.5 t = 360

$t = 360/{6.5} = 55.38$ min

Answer: (b)

Following are the numbers between – 11 and 11 which are multiples of 2 or 3?

– 10, – 9, – 8, – 6, – 4, – 3, – 2, 0, 2, 3, 4, 6, 8, 9,10

So ,the numbers of multiples 2 or 3, between – 11 and 11 are 15.

Alternative Method:

Numbers between 0 and 11 which are multiples of 2 or 3

$11/2 + 11/3 - 11/6$ = 5 + 3 – 1 = 7

Numbers between 0 and – 11

$11/2 + 11/3 - 11/6$ = 7

So, the numbers are 14 and 0.

Answer: (d)

According to question.

⇒ 3x + 2y = $5k_1$ + 2 ----------(i)

⇒ 2x + 3y = $5k_2$ + 3 ----------(ii)

eq(i)-eq(ii)

⇒ x – y = 5$(k_1 – k_2)$ – 1

so when (x – y) is divided by 5 remainder will be

5 + (–1) = 4

At x = 5, y = 1, Remainder = 4

At x = 6, y = 5, Remainder = 1

So, option (b) and (c) both are is correct