model 2 divisibility, multiples, add and subtract based number system Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Sum of first 60 numbers

= ${60(60+ 1)}/2$ = ${60× 61}/2$ = 1830

The number 1830 is divisible by 61.

Answer: (d)

First number (X) = 17x + 13

Second number (Y) = 17y + 11

∴${X + Y}/17$ = ${17(x + y)}/17 + {13 + 11}/17$

∴Required remainder = Remainder obtained on dividing

11 + 13

i.e. 24 by 17 = 7

Answer: (a)

Required remainder = 16 – 12 = 4

(because 24 is a multiple of 12.)

Answer: (b)

1000 = (45 × 22) + 10

∴ 45 – 10 = 35 to be added.

So, the smallest number to be added to 1000 to make the sum exactly divisible by 45 is 35.

Answer: (c)

Divisor = 5 × Remainder = 5 × 46 = 230

Quotient = $230/10$ = 23

∴ Dividend = Divisor × Quotient + Remainder

= 230 × 23 + 46

= 5290 + 46 = 5336

Answer: (c)

The number (x y z x y z) can be written, after giving corresponding weightage of the places at which the digits occur, as 100000 x + 10000y + 1000z + 100x + 10y + z

= 100100x + 10010y + 1001z

= 1001 (100x + 10y + z)

Since 1001 is a factor, the number is divisible by 1001.

7 × 11 × 13 = 1001

As the number is divisible by 1001, it will also be divisible by all three namely, 7, 11 and 13 and not by only one of these because all three are factors of 1001.

So, the answer is 1001.