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

Answer: (a)

LCM of [${x^2 – (y + z)^2}, {(x + z)^2 – y^2}, {(x – y)^2 – z^2}]$

= LCM of [(x + y + z) (x – y – z), (x + z + y) (x + z – y), (x – y + z) (x – y – z)]

= (x + y + z) (x – y – z) (x – y + z)

Answer: (b)

Let the numerator and denominator of a fraction are x and y, respectively,

According to question,

${x - 1}/y = 1/3$⇒3x - 3 = y⇒3x - y = 3 .....(i)

and $x/{y + 5} = 1/4$⇒4x - y = 5 ....(ii)

On solving eqs. (i) and (ii), we get

x = 2 and y = 3

∴ Required fraction = ${x - 1}/{y + 5} = {2 - 1}/{3 + 5} = 1/8$

Answer: (e)

1008 × $7/8 -968$ × $3/4$

882 – 726 = 156

Answer: (a)

From formula,

∴ (HCF to two numbers) × (LCM of two numbers)

= (First number) × (Second number)

∴ Second number = ${33 × 2376}/{297}$ = 264

Answer: (a)

Here, (x – 6) is the HCF of $x^2 – 2x – 24 and x^2$ – kx – 6

So, that (x – 6) is a factor of both expression.

According to question,

⇒$f(x_1) = f(x_2) at (x_1 = x_2 = 6)$

⇒$(6)^2 – 2(6) – 24 = (6)^2$ – k(6) – 6 (By condition)

⇒36 – 12 – 24 = 36 – 6k – 6

⇒0 = 30 – 6k⇒6k = 30

∴ k = 5