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CAT 2002 — QA Question 35

Permutation & CombinationEasy
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.

In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column?

Answer & solution

  • A

    32

  • B

    96

  • C

    24

  • None of these

Solution

The number of ways of selecting 1 black square is 32.

∵  8 white squares in the corresponding row and column cannot be selected.

∴ The number of ways of selecting the white square is 24.

∴ Total number of required ways = 32 × 24 = 768

Hence, option (d).

CAT 2002 QA Q35: In how many ways, we can choose a black and a white square on a chess board such that the two are not in the s — Solution | TheCATExam