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07 Feb 2021, 11:01
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D
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Difficulty:
75%
(hard)
Question Stats:
57% (02:09) correct
43%
(02:29)
wrong
based on 129
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How many even numbers are there with three digits such that if 5 is one of the digits in a number then 7 is the next digit in that number?
A. 180
B. 215
C. 360
D. 365
E. 420
Are You Up For the Challenge: 700 Level Questions
A. 180
B. 215
C. 360
D. 365
E. 420
Are You Up For the Challenge: 700 Level Questions
07 Feb 2021, 11:17
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Bunuel
Clearly there are two cases.
1) 5 is one of the digits.
As it is even number, the units digit cannot be 7, so the only possibility is 57e, where e is an even digit. => ways = 1*1*5=5
2) 5 is not there at all.
If abc is the number, a can be any number except 5 and 0, so 8 ways, while b can be any digit except 5, so 9 ways. Since it is even, c can be any of 5 even digits, so 5 ways. => ways = 8*9*5=360
Total = 5+360=365 ways.
D
