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14 Aug 2019, 01:03
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
57% (02:30) correct
43%
(02:35)
wrong
based on 225
sessions
History
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How many odd numbers from 700 to 999, inclusive, have distinct non-zero digits?
A. 88
B. 89
C. 90
D. 91
E. 92
A. 88
B. 89
C. 90
D. 91
E. 92
How many odd numbers are there from the integers 700 to 999 (inclusive)? If every digit of such an odd number must be non-zero and different.
14 Aug 2019, 01:55
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odd numbers from 700 to 799, inclusive, have distinct non-zero digits= 1*7*4=28 (unit digit can be 1, 3 ,5 or 9)
odd numbers from 800 to 899, inclusive, have distinct non-zero digits= 1*7*5=35 (unit digit can be 1, 3 ,5, 7 or 9)
odd numbers from 900 to 999, inclusive, have distinct non-zero digits= 1*7*4=28 (unit digit can be 1, 3 ,5 or 7)
Total numbers= 28+35+28= 91
odd numbers from 800 to 899, inclusive, have distinct non-zero digits= 1*7*5=35 (unit digit can be 1, 3 ,5, 7 or 9)
odd numbers from 900 to 999, inclusive, have distinct non-zero digits= 1*7*4=28 (unit digit can be 1, 3 ,5 or 7)
Total numbers= 28+35+28= 91
Bunuel
Archit3110
Major Poster
14 Aug 2019, 11:43
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Bunuel
total odd ; unit place ; 1,3,5,7,9
distinct no are to be identified
so from 700 to 799 ; 1*7*4 ; 28
800 to 899 ; 1*7*5 ; 35
900 to 999; 1*7*4 ; 28
total 28+28+35; 91
IMO D
