model 2 divisibility, multiples, add and subtract based number system Practice Questions Answers Test with Solutions & More Shortcuts

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.

Answer: (c)

Divisor = 5 × Remainder = 5 × 46 = 230

Quotient = $230/10$ = 23

∴ Dividend = Divisor × Quotient + Remainder

= 230 × 23 + 46

= 5290 + 46 = 5336

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)

A number will be exactly divisible by 18 if it is divisible by 2 and 9 both. Clearly 65043 is not divisible by 2.

∴ Required number = 65043

Answer: (c)

Sum of first 60 numbers

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

The number 1830 is divisible by 61.