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How many integers between 200 and 400 contain at least one digit that

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Ravixxx
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How many integers between 200 and 400 contain at least one digit that [#permalink] New post   29 May 2020, 12:40
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How many integers between 200 and 400 contain at least one digit that is a 5?

(A) 28
(B) 32
(C) 38
(D) 45
(E) 52
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C
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How many integers between 200 and 400 contain at least one digit that [#permalink] New post   29 May 2020, 12:44
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Ravixxx wrote:
How many integers between 200 and 400 contain at least one digit that is a 5?

(A) 28
(B) 32
(C) 38
(D) 45
(E) 52

let's count number from 200 and 399 without using digit 5

- - - three places to be filled

Hundreds place can be filled in 2 ways (using digits 2 and 3)
Tens place can be filled in 9 ways (using digits 0 to 9 except 5)
Units place can be filled in 9 ways (using digits 0 to 9 except 5)

Total Numbers = 2*9*9 = 162

Total Numbers from 200 to 399 (inclusive) = 200

Remaining numbers with atleast one digit 5 = 200 - 162 = 38

Answer: Option C
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Re: How many integers between 200 and 400 contain at least one digit that [#permalink] New post   29 May 2020, 12:53
Ravixxx wrote:
How many integers between 200 and 400 contain at least one digit that is a 5?

(A) 28
(B) 32
(C) 38
(D) 45
(E) 52


This is a 3-digit no. between 200 and 400.
Thus, on hundredth place 2 or 3 can come.
If there is 5 on ten's place, then one's place can be filled in 9 ways, therefore integers = 2 * 9 = 18
If there is 5 on one's place, then ten's place can be filled in 9 ways, therefore integers = 2 * 9 = 18
If 5 is on both ten's place and one's place, then integers = 2 * 1 = 2

Total integers = 18 + 18 + 2 = 38
Hence, OA is C
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Re: How many integers between 200 and 400 contain at least one digit that [#permalink]
29 May 2020, 12:53
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