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

Answer: (b)

(H) Hens has one head and two feet.

(G) Goats has one head and four feet.

According to question,

H + G = 90 ...... (i)

2H + 4G = 248 ..... (ii)

Multiplying by 2 in equation (i) and subtract

∴ G = 34

∴ Number of goats = 34

Put the value of G in equation (i)

H + 34 = 90 ⇒ H = 56

Answer: (a)

Let the original number be x

ATQ

$8x – x/8 = 2016$

$x[63/8] = 2016$

8 by solving

x = 256

Answer: (d)

$(2457)^754$

We know that a unit digit of $(7)^4$ is 1.

Unit digit of $(2457)^754 = (2457)^{188 × 4 + 2}$

= $(2457)^{188 × 4} . (2457)^2 → [(2457)^4]^188. 9 → (1)^188 .9→ 9$

Answer: (d)

The no. can be 2 or 3 digit.

Firstly let n be the two digit no.

Therefore, n = 10x + y

$p_n + s_n$ = n ⇒ xy + x + y = 10 x + y

⇒ xy – 9x = 0 ⇒ y = 9 as x ≠ 0

So the numbers can be 19, 29.........99, i.e., 9 values.

For 3 digits n = 100x + 10y + z

⇒ xyz + x + y + z = 100x + 10y + z

⇒ xyz = 99x + 9y or xz = ${9(11x + y)}/y$

It can be verified using various values of y that this equation do not have any solution.

E.g. : For y = 9, x(z – 11) = y

which is not possible.

So in all 9 integers.

Answer: (a)

Suppose the number is x.

$2x^2 – 11x = 21$

$2x^2 – 11x – 21$ = 0

$2x^2 – 14x + 3x – 21$ = 0

2x (x – 7) + 3(x – 7) = 0

(x – 7) (2x + 3) = 0

∴ $x = 7$ or $- 3/2$