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CAT 2002 — QA Question 36

Number TheoryEasy
Passage / Data

Sum of first n natural numbers = S(n)

Sum given by student = 575

S(10) = 10×112= 55

S(20) = 20×212= 210

S(30) = 30×312= 465

S(40) = 40×412= 820

∴ The student stopped counting somewhere between 30 and 40.

Consider S(35) = 36×352= 630

The student stopped somewhere before 35.

∴ S(31) = 496, S(32) = 528, S(33) = 561 and S(34) = 595

But the student gave 575 as the sum, so the student missed on the number 20.

Hence, option 4.

A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked. "How many gold coins do we have?" After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 48 times the difference of the numbers is equal to the difference of their squares. The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins the merchant has?

Answer & solution

  • 48

  • B

    96

  • C

    32

  • D

    36

Solution

Let the two unequal numbers be x and y.

∴ 48(x – y) = x2 – y2

∴ 48(x – y) = (x + y) (x – y)

∴ (x + y) = 48

∴ Total number of coins is 48.

Hence, option (a).

CAT 2002 QA Q36: A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife a — Solution | TheCATExam