number systems Model Questions & Answers, Practice Test for ibps so prelims

Answer: (a)

If k is any even positive integer, then $(k^2 + 2k)$ is divisible by 8 but may not be divisible by 24.

Let k = 2m, m ∈ N, then

$k^2 + k.2 = 4m^2 + 4m = 4m (m + 1)$

which is divisible by 4.

Answer: (b)

Number of mangoes = 12 dozens

= 12 × 12 = 144

∴ Number of mangoes in 43 boxes

= 43 × 144 = 6192

Answer: (b)

The greatest number that divide 28200, 44333 and 12288 is the H.C.F. of (28200 – 12288, 44333 – 28200, 44333 – 12288) = H.C.F of (15912, 16133, 32045) = 121.

Answer: (a)

The given numbers are two consecutive even numbers, so their HCF = 2

Now, using LCM × HCF = Product of two numbers

LCM × 2 = (…6) × (…8)

It can be seen now that the unit digit of LCM = 4

Answer: (b)

Required time

= L.C.M of 24, 36 and 48

= 144 seconds = 2 minutes 24 seconds