XAT 2014 — QA & DI Question 18
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
- A
11
- B
12
- C
15
- D
17
19
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).