number system Model Questions & Answers, Practice Test for ibps rrb po officer scale 1 prelims 2024

Answer: (c)

He wants to write from 1 to 999. He has to write 9 numbers of one digit, 90 numbers of two digits and 900 numbers of three digits.

Total number of times = 1 × 9 + 2 × 90 + 3 × 900 = 2889

Answer: (c)

Sum of all the number from 100 to 200

= Sum of numbers from 1 to 200

– Sum of numbers from 1 to 99

= ${200 × 201}/2 - {99 × 100}/2$

= $100/2[2 × 201 - 99]$

= 50 × 303 = 15150

Answer: (a)

Any number that are divisible by 33 must be divisible by 3 and 11.

A number that are divisible by 3 have sum of its digit divisible by 3.

∴ x + x + y + x + x = (4x + y) must be divisible by 3

And, For divisibility by 11, (x + y + x) – (x + x) = 0

⇒ y = 0

Now, 4x + y = 4x + 0 = 4x divisible by 3

Only when x = 3, 6 or 9.

Hence, three number are 33033, 66066, 99099.

Answer: (a)

132 = 4 × 3 × 11

264 → 11, 3, 4 (✓); 396 → 11, 3, 4 (✓);

462 → 11, 3 (✓); 792 → 11, 3, 4 (✓);

968 → 11, 4 (X); 2178 → 11, 3 (X);

5184 → 3, 4 (X); 6336 → 11, 3, 4 (✓)

Required number of numbers = 4

Answer: (a)

24162 = 89x + 43

x = (24162 – 43) ÷ 89 = 271