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

Answer: (b)

Let the number be p.

According to the question,

∴ $\text"p + 12"/6 = 112$

⇒   p + 12 = 672

⇒   p = 672 – 12 = 660

∴  Correct answer = $\text"600"/6 = 112$

Correct answer =  110 + 12 = 122

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: (d)

Let the total number of members be X.

Then, each member's contribution =Rs. 2X

Given, X × 2X = 3042

⇒ 2X² = 3042

⇒ X² = 1521

⇒ X = 39

Answer: (b)

Here, the first divisor (91) is a multiple of the second divisor (13).

∴ Required remainder = Remainder obtained on dividing 17 by 13

⇒ 17 = ( 13 × 1 ) + 4

Hence Required remainder = 4

Answer: (c)