If (L)M represents the number L in a base-M number system, which of the following are equivalent to (19) base 16? Choose the correct answer from the options given below.

1.base 2

2.base 3

3.base 4

4.base 5

5.base 10

A1, 3, 5 only ✓ Correct

B2, 4 only

C1, 2, 4 only

D1, 2, 3, 4, 5

Correct answer: (A) 1, 3, 5 only

Explanation

The target value is (19) in base 16, which equals 1 times 16 plus 9, that is 25 in decimal.

Statement 1, (11001) in base 2, is 16+8+1 = 25, so it matches.

Statement 2, (201) in base 3, is 18+0+1 = 19, which does not match.

Statement 3, (121) in base 4, is 16+8+1 = 25, so it matches.

Statement 4, (101) in base 5, is 25+0+1 = 26, which does not match.

Statement 5, (25) in base 10, is already 25, so Statements 1, 3 and 5 are the equivalents.

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