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

Answer: (b)

${x + x + 2 + x + 4 + x + 6}/4 = 27$

$x = {27 × 4 - 12}/4$

$= 96/4 = 24$

∴ Highest number = 24 + 6 = 30

Answer: (d)

If sum of all the digits is divisible by 9 then the number is divisible by 9

Given number is 76 3× 4Y2.

Given number is divisible by 9.

So, 7 + 6 + 3 + X + 4 + Y + 2 = 9k

⇒ 22 + X + Y = 9k

It is clear that LHS is divisible by 9, if X + Y = 5, 14.

Now sum of X and Y is 5, then possible pairs are (1, 4), (4, 1), (2, 3) (3, 2), (0, 5) and (5, 0).

When sum of X and Y is 11, then possible pairs are (5, 9), (9 , 5), (6, 8), (8, 6) and (7, 7).

Total possible pairs are 11.

Answer: (a)

Requirement of bananas for 1 day in the canteen = 13 dozens

∴ Requirement of bananas for 9 weeks i.e. 63 days

= 63 × 13 dozens

= 63 × 13 × 12 = 9828.

Answer: (c)

From equation we have

P = $0.7\ov{3} = {73–7}/90 = 66/90 = 11/15$

Q = $0.5\ov{6} = {56 –5}/90 = 51/90 = 17/30$

∴ Distance between P and Q

= $11/15 - 17/30 = {22 –17}/30 = 5/30 = 1/6$

Answer: (a)

Difference = Sum of digit at odd place – Sum of digit at even place

= (1 + 5 + 9 + 4) – (2 + 4 + 3) = 19 – 9 = 10

In 10, we must add at least 1 so that it is divisible by 11.

So x = 1

Also, the sum of digits of 1254934

= 1 + 2 + 5 + 4 + 9 + 3 + 4 = 28

1254934 will be divisible by 3, after adding y, if the value of y is – 1.

So, x = 1 and y = – 1 is the set of values for x and y.