Algebra Play — Practice

Question 1

A two-digit number is reversed and the smaller is subtracted from the larger. The result is always divisible by:

Accepted Answer

9

Question 2

In a number pyramid each box is the sum of the two below it. If the bottom row is a, b, c, the number at the top is:

Accepted Answer

a + 2b + c

Question 3

Using each of the digits 3, 5 and 9 exactly once in (two-digit number) × (one-digit number), the largest possible product is:

Accepted Answer

477

Question 4

A 6-digit number of the form abcabc is always divisible by:

Accepted Answer

7, 11 and 13

Question 5

The four numbers of a 2 × 2 block on a calendar page add up to 36. What is the top-left number?

Accepted Answer

5

Question 6

Take any 3-digit number abc and form bca and cab by cycling the digits. Prove that abc + bca + cab is always divisible by 37, and say whether it is always divisible by 3.

Accepted Answer

The sum is 111(a + b + c) = 3 × 37 × (a + b + c), so it is divisible by both 37 and 3

Question 7

A farm has horses and hens with 55 heads and 150 legs in total. Find the number of each, first with algebra and then without using letters.

Accepted Answer

20 horses and 35 hens

Question 8

A dosa cart costs ₹5000 a day in rent and ₹10 to make each dosa. If customers will pay only ₹50 a dosa, how many must be sold daily to make a profit of ₹2000?

Accepted Answer

175 dosas

Practice — Algebra Play

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