Bunuel wrote:
For how many of the integers from 10 to 99 is at least one of the two digits a 4 ?
A. 9
B. 10
C. 18
D. 19
E. 20
PS21197
Number of 2-digit integers with at least one 4 = (
total number of 2-digit integers) - (
number of 2-digit integers that have ZERO 4's)
total number of 2-digit integersWe want to count the number of integers from 10 to 99 inclusive
A nice rule says:
the number of integers from x to y inclusive equals y - x + 1So the number of integers from 10 to 99 inclusive = 99 - 10 + 1 =
90number of 2-digit integers that have ZERO 4'sLet's build some 2-digit integers that have ZERO 4's
The tens digit can be 1, 2, 3, 5, 6, 7, 8, or 9 (8 options)
The units digit can be 0, 1, 2, 3, 5, 6, 7, 8, or 9 (9 options)
So, the total number of 2-digit integers that have ZERO 4's = (8)(9) =
72We get:
Number of 2-digit integers with at least one 4 =
90 -
72 =
18Answer: C
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
