H.C.F and L.C.M Aptitude Test Paper 3

Answer: C

Explanation:

Let the two numbers be x and (1000 - x)

∴ x * (1000 - x) = 8919
     1000x - x² = 8919
     -x² + 1000x -8919 = 0
     -x² + ( 991 + 9)x - 8919 = 0
     -x² + 991x +9x - 8919 = 0
     -x(x - 991) + 9(x - 991) = 0
     (x - 991) (-x + 9) = 0

∴ (x - 991) = 0
     X = 991, and
     (-x + 9) = 0
     -x = -9
     X = 9
So, the required numbers are 991 and 9.

Answer: D

Explanation:

Apply Formula: HCF x LCM = First number x Second number
                            2 x 70 = 140 (product of two numbers)
The option D satisfies the given condition, as 14 * 10 = 140. So, the required numbers are 14 and 10.

Answer: C

Explanation: For the capacity of the biggest container, we have to find the HCF.
HCF: By Long Division method
First find the HCF of two numbers, 496 and 403

The HCF of 496 and 403 = 31
Now find the HCF of 31 and 713

HCF of 713 and 31 is 31
So, the maximum capacity is 31 liters.

Answer: B

Explanation:

LCM of 2, 3, 4, 5, 6

LCM = 2 x 2 x 3 x 5 = 60

Now, 60 x 1 + 1 = 61 is not divisible by 7

60 x 2 + 1 = 121 is not divisible by 7

60 x 5 + 1 = 301 is divisible by 7

Hence 301 is the number.

Answer: A

Explanation:

Greatest three digit number = 999
LCM of 6, 9 and 12

LCM = 2 x 2 x 3 x 3 = 36

On dividing 999 by 36,

Remainder = 27.

∴ The greatest three digit number divisible by 6, 9, and 12

      = (999 - 27) = 972

As per the question, the required number is (972 + 3) = 975.