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CAT 2002 — QA Question 30

TrianglesEasy
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.

The area of the triangle with the vertices (a, a), (a + 1, a) and (a, a + 2) is

Answer & solution

  • A

    a3

  • 1

  • C

    0

  • D

    None of these

Solution

Area (∆) = |x1y11x2y22x3y33|

where x1 = y1 = a, x2 = a + 1, y2 = a, x3 = a and y3 = a + 2

∴ Area (∆) = 12|aa1a+1a1aa+121|

∴ Area (∆) = 12{a[a(1) - (a + 2)(1)] - a[(a + 1)(1) - a(1)] + 1[(a + 1)(a + 2) - a2]} = 12 {- 2a - a + 3a + 2} = 1

Hence, option (b).

CAT 2002 QA Q30: The area of the triangle with the vertices (a, a), (a + 1, a) and (a, a + 2) is — Solution | TheCATExam