Source: Revised GRE PDF 2nd Ed. Section 6; #15 (p. 90)


How many different two-digit positive integers

How many different two-digit positive integers are there in which the tens digit is greater than 6 and the units digit is less than 4 ? 7, 9, 10, 12, 24

3 Explanations


Purva Deepak Juvekar

I'm still confused: the question asks for different two-digit positive integers. Suppose I take 7 for the tens digit and 3 for the units digit. Can't I treat 73 and 37 as different integers, in which case the answer would be 24?

Sep 5, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Purva :)

73 and 37 are different integers. However, 37 doesn't meet the requirements of the prompt. The tens digits of 37 is 3, which is less than 6. Since the tens digit must be greater than 6, 37 is not part of the count :)

Hope this helps!

Sep 5, 2016 • Reply


Khyati Dalal

This question says....different two-digit positive integers. 0 is not the positive number. then why do we count it?

Apr 11, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Khyati :)

Happy to help! We consider 0 as a possible value for the units digit or one's place of the two digit number. The units digit must be less than 4, so the possible values of the units digit are: 0, 1, 2, 3. For example, 70 is a two-digit number that meets the requirements in the question and has a units digit of 0. :)

Hope this clears up your doubts!

Apr 15, 2016 • Reply

Keith Beard

Just adding clarification that 70 is a positive two digit integer and the question would have said "positive integers" for the units if it didn't want 0 to be a possibility.

Sep 15, 2017 • Reply

Sam Kinsman, Magoosh Tutor

Yes, that's right!

Sep 20, 2017 • Reply


Gravatar Chris Lele, Magoosh Tutor

Sep 27, 2012 • Comment

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