How many two-digit numbers have digits summing to 9?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

How many two-digit numbers have digits summing to 9?

Explanation:
Counting two-digit numbers whose digits sum to 9 means setting the tens digit to t (with t between 1 and 9) and the ones digit to u (with u between 0 and 9), and enforcing t + u = 9. For every choice of t from 1 to 9, you get u = 9 − t, which is a valid digit between 0 and 8. This gives exactly nine pairs: (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1), (9,0). The corresponding two-digit numbers are 18, 27, 36, 45, 54, 63, 72, 81, 90. Therefore, there are 9 such numbers.

Counting two-digit numbers whose digits sum to 9 means setting the tens digit to t (with t between 1 and 9) and the ones digit to u (with u between 0 and 9), and enforcing t + u = 9. For every choice of t from 1 to 9, you get u = 9 − t, which is a valid digit between 0 and 8. This gives exactly nine pairs: (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1), (9,0). The corresponding two-digit numbers are 18, 27, 36, 45, 54, 63, 72, 81, 90. Therefore, there are 9 such numbers.

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