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

Answer: (c)

Let two numbers are 12a and 12b.

Such that H.C.F = 12.

then L.C.M = 12.a.b

Here, L.C.M of these two number must be divisible by 12.

'80' is not divisible by 12, so can not be L.C.M

Answer: (c)

$x^2 + 2x – 8 = x^2$ + 4x – 2x – 8

= x (x + 4) – 2 (x + 4) = (x – 2) (x + 4)

$x^3 – 4x^2 + 4x = x^3 – 2x^2 – 2x^2$ + 4x

= $x^2$ (x – 2) – 2x (x – 2)

= ($x^2$ – 2x) (x – 2) = x (x – 2) (x – 2)

$x^2$ + 4x = x (x + 4)

So, LCM of ($x^2 + 2x – 8), (x^3 – 4x^2$ + 4x) and

($x^2$ + 4x) = x (x – 2) (x + 4) (x – 2)

= x (x + 4) $(x – 2)^2$

Answer: (b)

LCM of 8, 12 and 16 = 48. Such numbers are (48 × 1 + 3) = 51, (48 × 2 + 3) = 99, which is divisible by 11.

∴ the required number = 9.

Answer: (b)

length of each room = 6 m

breadth of each room = 4 m

height of each room = 2.5 m

area of walls of each room = 2(6 + 4) × 2.5 = 50 $m^2$

Total area of walls of 5 rooms = 5 × 50 = 250 $m^2$

According to the question

1 l = 20 $m^2$

Required paint = ${250}/{20}$ = 12.5 l

Hence, 13 cans are required.

Answer: (a)

Let the age of Ram = x and Rakesh = y

then $x/y=6/11$

∴ x= ${6y}/11$

According to question, ${x-4}/{y-4}=1/2$

2x – 8 = y – 4

$2 × {6y}/11$ - 8 = y - 4 or ${12y}/11$ - y = -4 + 8 or $y/11 = 4$

∴y = 44 yr.

∴ Age of Rakesh after 5 yr = 44 + 5 = 49 yr.