TheCATExam
Sign in

CAT 2002 — QA Question 47

Number TheoryEasy

In a book store, the words of the glowsign board "MODERN BOOK STORES" are individually flashed after 5/2, 17/4 and 41/8 seconds respectively. Each word is put off after a second. What is the least time after which full name of the book store can be read? 

Answer & solution

Correct answer: 73.5 seconds

  • 73.5 seconds

  • B

    79.4 seconds

  • C

    68.2 seconds

  • D

    None of these

Solution

The words MODERN, BOOK and STORES appear after 5/2, 17/4 and 41/8 seconds respectively and are put off after 1 second.

So, if all the words flashed together at t = 0 seconds, then

MODERN will flash after (5/2 + 1) = 7/2 seconds

BOOK will flash after (17/4 + 1) = 21/4 seconds

STORES will flash after (41/8 + 1) = 49/8 seconds.

So, all the words will flash together again after LCM(7/2, 21/4, 49/8) seconds.

∴ L.C.M. (72,214,498)=L.C.M. of NumeratorsH.C.F. of Denominators=1472= 73.5 seconds

Hence, option (a).

Related Number Theory questions

See all Number Theory questions →
CAT 2002 QA Q47: In a book store, the words of the glowsign board "MODERN BOOK STORES" are individually flashed after 5/2, 17/4 — Solution | TheCATExam