McqkartGet appPractise

If (L)M represents number L in a base-M number system, identify the correct descending order of the following numbers when converted to the decimal system. Choose the correct answer from the options given below.

1.base 7
2.base 3
3.base 6
4.base 5
A1, 3, 2, 4
B2, 4, 1, 3
C4, 2, 3, 1
D3, 1, 4, 2 ✓ Correct
Correct answer: (D) 3, 1, 4, 2
Explanation

Converting each to decimal and ranking largest first gives Statement 3, Statement 1, Statement 4, Statement 2.

Statement 3, (212) in base 6, equals 2 times 36 plus 6 plus 2, which is 80, the largest.

Statement 1, (123) in base 7, equals 49 plus 14 plus 3, which is 66.

Statement 4, (201) in base 5, equals 50 plus 1, which is 51.

Statement 2, (1211) in base 3, equals 27 plus 18 plus 3 plus 1, which is 49, the smallest.

Each digit is multiplied by its base raised to the power of its position.

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.

Practise on Mcqkart →🎓 Book an expert →