The sum of the ages of a man and his wife is six times the sum of the ages of their children. Two years ago the sum of their ages was ten times the sum of the ages of their children. Six years hence the sum of their ages will be three times the sum of the ages of their children. How many children do they have?

a, b, c are three natural numbers such that a x b x c = 27846. If a/6 = b + 4 = c – 4, find a + b + c.

Let a, b, c be real numbers, not all of them are equal. Prove that if a + b + c = 0, then a² + ab + b² = b² + bc + c² = c² + ca + a².

Prove the converse, if a² + ab + b² = b² + bc + c² = c² = ca + a², then a + b + c = 0.

The number of ways in which 26 identical chocolates be distributed between Amy, Bob, Cathy and Daniel so that each receives at least one chocolate and Amy receives more chocolates than Bob is _______.

The four digit number 8ab9 is a perfect square. The value of a² + b² is

(A) 52 

(B) 62 

(C) 54 

(D) 68

The numbers 2, 3, 12, 14, 15, 20, 21 may be divided into two sets so that the product of the numbers in each set is the same. What is this product?

(A) 420 

(B) 1260 

(C) 2520 

(D) 6720

There are 5 cards. Five positive integers (may be different or equal) are written on these cards, one on each card. Abhiram finds the sum of the numbers on every pair of cards. He obtains only three different totals 57, 70, 83. Find the largest integer written on a card.

The difference between the biggest and the smallest three digit number each of which has different digits is

(A) 864 

(B) 875 

(C) 885 

(D) 895

If x²(y + z) = a², y²(z + x) = b², z²(x + y) = c², xyz = a b c prove that a² + b² + c² + 2abc = 1

In an elementary school 26% of the students are girls. If there are 240 less girls than boys, then the strength of the school is _________