Q 01/05

Which product of three consecutive primes gives 1001, the trick behind the 7, 11 and 13 divisibility test?

A) 3 × 7 × 11

B) 11 × 13 × 17

C) 7 × 11 × 13

D) 5 × 7 × 11

Answer · why

C) 7 × 11 × 13

That is why splitting a number into three-digit blocks and alternately adding and subtracting them tests all three primes at once. 1001 is also the fi...

Q 02/05

Multiplying 142857 by which single digit gives 999999?

A) 7

B) 8

C) 9

D) 11

Answer · why

A) 7

142857 is the repeating block of 1/7 and the best-known cyclic number: multiplying it by 1 to 6 just rotates its digits.

Q 03/05

Using the difference-of-two-squares shortcut, 27 × 33 equals what?

A) 891

B) 901

C) 911

D) 921

Answer · why

A) 891

Both numbers sit 3 away from 30, so the product is 30² minus 3², or 900 minus 9. The trick works whenever two numbers have an easily squared average.

Q 04/05

Which four-digit number, when multiplied by 9, gives its own digits reversed?

A) 1089

B) 1098

C) 1189

D) 1809

Answer · why

A) 1089

1089 × 9 = 9801. It is also 33 squared and the number that ends the classic 'reverse and subtract, then reverse and add' parlour trick.

Q 05/05

Plato praised 5040 as an ideal city population because it is divisible by every number from 1 to 12 except which?

A) 11

B) 7

C) 9

D) 10

Answer · why

A) 11

It is also 10 × 9 × 8 × 7, the number of ways to arrange 4 items from 10, and one less than the square 71².