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CAT 2002 — QA Question 47

Number TheoryEasy
Passage / Data

Answer the following question based on the information given below.

There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets.

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

  • 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).

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