lcm and hcf Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Answer: (c)

We know that product of two numbers

= LCM × HCF of those numbers

So, product of numbers = 11 × 385

= 11 × 7 × 5 × 11

Since one of them lies between 75 and 125

So this number would be = 11 × 7 = 77

So the number is 77.

Answer: (b)

∵ ${13}/8 = {13}/8 × {125}/{125} = {1625}/{1000}$ = 1.625

$3/{16} = {3 × 625}/{16 × 625} = {1875}/{10000}$ = 0.1875

${137}/{25} = {137 × 4}/{25 × 4} = {548}/{100}$ = 5.48

It is clear that all of these are terminating and decimals.

Hence, $3/{11}$ is a non-terminating and repeating decimal.

Answer: (d)

x + k is the HCF of given expression, then

x = – k, root of the function

Now, a $(– k)^2 – ak + b = 0 = k^2$ – ck + d

⇒$k^2$ (a – 1) – (a – c) k + b – d = 0

⇒k = ${(a - c) ± √{(a - c)^2 - 4 (a - 1)(b - d)}}/{2(a - 1)}$

Answer: (c)

It is given that the remainder is 25 in each case when we divide 1305, 4665 and 6905 by k.

So, subtracting 25 from each of the numbers, we get 1280, 4640 and 6880.

HCF (1280, 4640 and 6880) = 160

So the greatest number is 160.

So k = 160

Sum of its digit = 1 + 6 + 0 = 7

So the answer is 7.

Answer: (a)

Given that $x^3 – 27 = (x – 3) (x^2$ + 9 + 3x)

Hence the value of k should be 9.