Arithmetic - Problem Set 1

Friday, May 05, 2006

Problems are based on what we learned in topics under Arithmetic - Addition, Subtraction, Division and Multiplication.

Problems:

Q1) For a number to be divisible by 77 it should be:
a) Divisible by 7.
b) Divisible by 7 and 22.
c) Divisible by 7 and 11.
d) None of the above.

Q2) On dividing 5678 by 22, what is the quotient, divisor, dividend and the remainder?

Q3) A123 is exactly divisible by 9. Find A.

Q4) 12Y3 is divisible by 11. Find Y.

Q5) A12345987B is divisible by 18. Find A and B.

Q6) Find the largest 4 digit number exactly divisible by 12.

Q7) Find the smallest 4 digit number exactly divisible by 11.

Q8) A number, when divided by 19, leaves a remainder 3, what will be the remainder when the same number is divided by 297?

Solutions:

A1): c, The number should be divisible by both 7 and 11 (co-primes)

A2): Divisor = 22, Divident = 5678, Quotient = 258, Remainder = 1. This was a silly question. ;)

A3): For a number to be divisible by 9, sum of its digits should be divisible by 9, hence A + 1 + 2 + 3 = 9, A + 6 = 9, A = 9 - 6 = 3. Hence the answer, 3.

A4): For a number to be divisible by 11, the difference of the sum of its even and odd numbers should be either 0 or divisible by 11, hence (2 + 3) - (1 + Y) = 0 or divisible by 11, 4 - Y = 0. Hence Y = 4. Try to do all this in your mind.

A5): For a number to be divisible by 18, it should be divisible by both 9 and 2. Hence the number A12345987B should be divisible by both 9 and 2. B can be 2, 4, 6, 8 or 0. Let's add up the digits, A + 1 + 2 + 3 + 4 + 5 + 9 + 8 + 7 + B = A + B + 39. Now lets replace B with 2, then our A will be, A + 41, A + 5 = 9, A = 4, why? because we added all the digits, which to make divisible by 9, 4 was required. Try other numbers for B.

A6): The largest 4 digit number is 9999, divide it by 12, the remainder is 3, subtract 3 from 9999, we get our number, i.e 9996. Just think why we did this. To make the dividend fully divisible by divisor we just subtract the remainder from the dividend.

A7): The smallest 4 digit number is 1000, which when divided by 11, the remainder is 10. Add the divident to the difference of divisor and remainder, i.e 1000 + (11 - 10) = 1001, which is exactly divisible by 11.

A8): Tricky, there is a formula for this. rl = 2x + rs, where x is the smaller divisor, rs is remainder when divided by smaller divisor i.e x, and rl is the remainder when divided by larger divisor. So by substituting the values in the formula, rl = 2 x 19 + 3 = 38 + 3 = 41. Try to explain me the formula if you get it ;)