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CAT 2002 — QA Question 2

LCM & HCFEasy

There are three pieces of cake weighing 9/2 lbs, 27/4 lbs and 36/5 lbs. Pieces of the cake are equally divided and distributed in such a manner that every guest in the party gets one single piece of cake. Further the weight of the pieces of the cake is as heavy as possible. What is the largest number of guests to whom we can distribute the cake?

Answer & solution

  • A

    54

  • B

    72

  • C

    20

  • None of these

Solution

The largest possible piece of cake from the three given pieces [9/2, 27/4, 36/5] can be obtained by finding the H.C.F of the three fractions,

∴ H.C.F. [92,274,365]=H.C.F. of NumeratorL.C.M. of Denominator=920

∴ The weight of the piece of cake given to each guest 9/20 lbs.

∴ Number of Guests = (92920)+(274920)+(365920)= 10 + 15 + 16 = 41
Hence, option (d).

CAT 2002 QA Q2: There are three pieces of cake weighing 9/2 lbs, 27/4 lbs and 36/5 lbs. Pieces of the cake are equally divided — Solution | TheCATExam