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How many integers from 600 to 899, inclusive, contain 7 or 8 in digit?

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Bunuel
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How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink] New post   07 Dec 2021, 08:15
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How many integers from 600 to 899, inclusive, contain 7 or 8 in digit?

(A) 220

(B) 236

(C) 238

(D) 240

(E) 242


Are You Up For the Challenge: 700 Level Questions
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B
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Nidzo
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Re: How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink] New post   08 Dec 2021, 01:09
Numbers between 700 and 899:

All numbers between 700 and 899 will include either a 7 or an 8.

\(899 - 700 + 1 = 200\)

Numbers between 600 and 699:

Numbers which will have 7 or 8 as a unit's digit: each number will appear 10 times as a unit's digit \(10*2 = 20\)

Numbers which will have 7 or 8 as a ten's digit but which don't have 7 or 8 as a unit's digit: Each number will again appear 10 times \(10*2 = 20\), but as 7 and 8 has been counted for as a unit's digit already one needs to subtract the numbers which will have either 7 or 8 as both a tens and units digit, this occurs 4 times \(20 - 4 = 16\)

Total numbers between 600 and 899 which include the numbers 7 or 8:

\(200 + 20 + 16 = 236\)

Answer B
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tanghoathien
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Re: How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink] New post   06 Jan 2022, 06:43
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Total number of integers from 600 to 899 = 899 - 600 +1 = 300

Number of integers that don't contain 7 or 8 in digit = 1 x 8 x 8 = 64

Number of integers contain 7 or 8 in digit = 300 - 64 = 236

The answer is B
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Sabbir266
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Re: How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink] New post   06 Jan 2022, 12:45
tanghoathien wrote:
Total number of integers from 600 to 899 = 899 - 600 +1 = 300

Number of integers that don't contain 7 or 8 in digit = 1 x 8 x 8 = 64

Number of integers contain 7 or 8 in digit = 300 - 64 = 236

The answer is B


Brother, how did you get 1×8×8 =64?

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Re: How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink] New post   06 Jan 2022, 23:01
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Bunuel wrote:
How many integers from 600 to 899, inclusive, contain 7 or 8 in digit?

(A) 220

(B) 236

(C) 238

(D) 240

(E) 242


Are You Up For the Challenge: 700 Level Questions



From 600 to 899, we have 300 integers (600 - 699, 700 - 799 and 800 - 899)
The hundreds place can be taken by 6/7/8.
Tens and units place by any one of the 10 digits 0-9.

All 200 numbers of 700 and 800 series will have 7 or 8 in them.
There are many integers in the 600 series too that will have 7 and 8 in them including lots of overlap such as 678 and 687.
Easier way to calculate is to find the integers that do not have 7 or 8 in them.
How can we make a 3 digit number of 600 series without 7 and 8.

6 __ __

There are 8 ways for tens place (no 7, no 8) and 8 ways for units place (no 7, no 8). Hence, 8*8 = 64 integers out of these 100 will not have a 7 or an 8. Hence 36 numbers will have 7 and/or 8.

Total 200 + 36 = 236 numbers out of these 300 will have a 7 or an 8.

Answer (B)
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Re: How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink] New post   06 Jan 2022, 23:30
Thanks a lot, brother.

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Re: How many integers from 600 to 899, inclusive, contain 7 or 8 in digit? [#permalink]
06 Jan 2022, 23:30
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