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CAT 2002 — QA Question 32

Basics of Mensuration/PrismEasy
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.

Neeraj has a rectangular field of size 20 × 40 sq.m. He has to mow the field with a mowing machine of width 1 m. If he mows the field from the extremes to the centre, then the number of rounds taken by him to mow half of the field will be

Answer & solution

  • A

    3.5

  • 3.8

  • C

    3

  • D

    4

Solution

The movement of the mower may be considered as shown in the figure.

Total area of the plot = 20 × 40 = 800 sq.m.

After 1st mowing, area left = (20 – 2) × (40 – 2) = 684 sq.m.

After 2nd mowing, area left = (20 – 4) × (40 – 4) = 576 sq.m.

After 3rd mowing, area left = (20 – 6) × (40 – 6) = 476 sq.m.

After 4th mowing, area left = (20 – 8) × (40 – 8) = 384 sq.m.

∴ Half the area is mowed between 3 to 4 rounds.

∵ 476 − 384 = 92 sq.m.

3+[(476-400)92]=3+(7692)=3.8

Hence, option (b).

CAT 2002 QA Q32: Neeraj has a rectangular field of size 20 × 40 sq.m. He has to mow the field with a mowing machine of wi — Solution | TheCATExam