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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

For how many positive two-digit integers is the ones digit greater than twice the tens digit?

Answer Choices

Right! (Applause.)

Explanation

The correct answer is (A). If the tens digit is 1, there are 7 positive two-digit integers with the ones digit greater than twice the tens digit: 13 comma 14 comma 15 comma 16 comma 17 comma 18 and 19. If the tens digit is 2, there are 5 positive two-digit integers with the ones digit greater than twice the tens digit: 25, 26, 27, 28 and 29. If the tens digit is 3, there are 3 positive two-digit integers with the ones digit greater than twice the tens digit: 37, 38 and 39. If the tens digit is 4, there is 1 positive two-digit integer with the ones digit greater than twice the tens digit: . If the tens digit is equal to or greater than 5, then the ones digits, which cannot be greater than 9, is not greater than twice the tens digit. Therefore, there is a total of 7 + 5 + 3 + 1 = 16 positive two-digit integers for which the ones digit is greater than twice the tens digit.

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