rakeshd347 wrote:How many odd three-digit integers greater than 800 are there such that all their digits are different?
A. 40
B. 60
C. 72
D. 81
E. 104
Alternate approach:
Good integers = total - bad.
Total:
Number of options for the hundreds place = 2. (8 or 9).
Number of options for the units place = 5. (1, 3, 5, 7, or 9).
Number of options for the tens place = 8. (Any digit 0-9 but the two already selected.)
To combine these options, we multiply:
2*5*8 = 80.
Bad:
Among the integers counted above, a bad integer occurs when both the hundreds digit and the units digit are 9.
P(the hundreds digit is 9) = 1/2. (Since 1 of the 2 options is 9.)
P(the units digit is 9) = 1/5. (Since 1 of the 5 options is 9.).
Thus:
P(both the hundreds digit and the units digit are 9) = 1/2 * 1/5 = 1/10, implying that 1/10 of the counted integers are BAD:
1/10 * 80 = 8.
Good:
Total - bad = 80-8 = 72.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
