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CAT 2005 — QA Question 8

Number TheoryEasy
Passage / Data

Answer the next 2 questions based on the information given below.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at  a speed of 10 km/hr, reaches B and comes back to A at the same speed.

If R = 3065-29653064+2964 then

Answer & solution

  • A

    0 < R ≤ 0.1

  • B

    0.1 < R ≤ 0.5

  • C

    0.5 < R ≤ 1.0

  • R > 1.0

Solution

R = 3065-29653064+2964

∵ an – bn = (a – b)(an – 1 + an – 2b + an – 3b2 + ... + bn – 1)

∴ R = (30-29)[3064+(3063×29)+...+2964]3064+2964

∵ 3064 + 3063 × 29 + ... + 2964 > 3064 + 2964

∴ R > 1

Hence, option (d).

CAT 2005 QA Q8: If R = 30 65 - 29 65 30 64 + 29 64 then — Solution | TheCATExam