(a) The sum of three consecutive odd numbers is 273. What are the three odd numbers? (b) Find the missing number in the given series: (i) 4, 16, 36, 64, ?, 144 (ii) 30, 29, 27, ?, 20, 15 (iii) 1, 7, 15, 25, ?, 51 (iv) 0, 2, 6, 12, 20, 30, ? (v) 48, 24, 72, 36, 108, ? (c) Find out the correct word from the given jumbled spellings: (i) THRSI (ii) GNDREA (iii) SCHAMOT (iv) ONLNDO (v) HIODALY. (d) Sara's mother is 6 times older than Sara, whereas her brother Ali is twice as old as Sara. In three years' time the sum of their ages will be 72. How old are Sara, Ali and their mother now?

(a) Three consecutive odd numbers

Consecutive odd numbers differ by 2, so let them be x, x + 2 and x + 4.

x + (x + 2) + (x + 4) = 273, so 3x + 6 = 273, 3x = 267, and x = 89.

The numbers are 89, 91 and 93.

(b) Number series

(i) The answer is 100. These are squares of even numbers: 2², 4², 6², 8², 10², 12².

(ii) The answer is 24. The differences are −1, −2, −3, −4, −5: 30, 29, 27, 24, 20, 15.

(iii) The answer is 37. The differences are +6, +8, +10, +12, +14: 1, 7, 15, 25, 37, 51.

(iv) The answer is 42. The differences are +2, +4, +6, +8, +10, +12: 30 + 12 = 42.

(v) The answer is 54. The pattern alternates ÷ 2 and × 3: 48, 24, 72, 36, 108, and then 108 ÷ 2 = 54.

(c) Jumbled words

(i) THRSI = SHIRT (ii) GNDREA = GARDEN (the same letters also make DANGER and GANDER) (iii) SCHAMOT = STOMACH (iv) ONLNDO = LONDON (v) HIODALY = HOLIDAY

(d) Ages

Let Sara's present age be s. Her mother is 6s, and Ali is 2s. This reads '6 times older' in its usual exam sense of six times as old.

In three years, each of the three is 3 years older, so the sum grows by 9.

s + 2s + 6s + 9 = 72, so 9s = 63, and s = 7.

Sara is 7, Ali is 14, and their mother is 42.

Check: in three years, the ages will be 10 + 17 + 45 = 72.