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CAT 2003 Slot 1 — QA Question 19

MiscellaneousEasy

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

Answer & solution

Correct answer: 91

  • A

    31

  • B

    63

  • C

    75

  • 91

Solution

Of the four given options 63 and 75 are multiples of 3. Their remainder cannot be 1.

∴ The last digit cannot be 1. Thus, 63 and 75 are eliminated.

For the options 31 and 91, the remainder is 1. Thus, the last digit is 1.

31 = (11111)2 = (1011)3 = (111)5

91 = (1011011)2 = (10101)3 = (331)5

91 has 1 as the first digit in only 2 of the notations.

Hence, option (d).

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CAT 2003 Slot 1 QA Q19: A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notatio — Solution | TheCATExam