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2+2=?

If you form a subset of integers chosen from between 1 to 3000, such that no two integers add up to a multiple of nine, what can be the maximum number of elements in the subset. (Include both 1 and 3000.)

(a) 1668 (c) 1333

(b) 1332 (d) 1336

The series. of numbers. (1,1/2,1/3,1/4 .............1/1972) is taken. Now two numbers are taken from this series (the first two) say x, y. Then the operation x+y+x.y is performed to get a consolidated number. The process is repeated. What will be the value of the set after all the numbers are consolidated into one number?

(a)1970 (b)1971
(c)1972 (d)none of these

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The price of raw materials in a company has gone up by 20%. Also, the labour cost has increased to
1/4th of the total cost of production which was earlier 1/6th of the total cost of production. By how
much percent should the company reduce its usage of raw materials to keep the total cost of production
same as before?

The price of raw materials in a company has gone up by 20%. Also, the labour cost has increased to
1/4th of the total cost of production which was earlier 1/6th of the total cost of production. By how
much percent should the company reduce its usage of raw materials to keep the total cost of production
same as before?