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XAT 2014 — QA & DI Question 18

Simple EquationsEasy

Two numbers, 297B and 792B, belong to base B number system. If the first number is a factor of the second number then the value of B is:

Answer & solution

Correct answer: 19

  • A

    11

  • B

    12

  • C

    15

  • D

    17

  • 19

Solution

Solving by options,

By option(1), we get,

297B = 112 × 2 + 11 × 9 + 7 = 348

792B = 112 × 7 + 11 × 9 + 2 = 948

Since 348, is not a factor of 948, option(1) is eliminated.

By option(2), we get,

297B = 122 × 2 + 12 × 9 + 7 = 403

792B = 122 × 7 + 12 × 9 + 2 = 1118

Since 403, is not a factor of 1118, option(2) is eliminated.

By option(3), we get,

297B = 152 × 2 + 15 × 9 + 7 = 592

792B = 152 × 7 + 15 × 9 + 2 = 1712

Since 592, is not a factor of 1712, option(3) is eliminated.

By option(4), we get,

297B = 172 × 2 + 17 × 9 + 7 = 738

792B = 172 × 7 + 17 × 9 + 2 = 2178

Since 738, is not a factor of 2178, option(4) is eliminated.

By option(5), we get,

297B = 192 × 2 + 19 × 9 + 7 = 900

792B = 192 × 7 + 19 × 9 + 2 = 2700

Since 900, is a factor of 2700,

Hence, option (e).

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XAT 2014 QA & DI Q18: Two numbers, 297 B and 792 B , belong to base B number system. If the first number is a factor of the second n — Solution | TheCATExam