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How many positive five-digit integers contain the digit grou

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How many positive five-digit integers contain the digit grou [#permalink] New post 15 Sep 2017, 07:37
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Question Stats:

45% (01:42) correct 54% (02:12) wrong based on 33 sessions



How many times does the digit grouping “57” (in that order) appear in all of the five-digit positive integers? For instance, “57” appears once in 12,357, twice in 57,057, and does not appear in 24,675.

(A) 279

(B) 3,000

(C) 3,500

(D) 3,700

(E) 4,000
[Reveal] Spoiler: OA

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Last edited by Carcass on 08 Jul 2018, 11:34, edited 1 time in total.
Edited by Carcass
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Re: How many positive five-digit integers contain the digit grou [#permalink] New post 18 Sep 2017, 00:59
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Is there a solution faster than mine?

My idea is to think that these numbers can be of three kinds, given that they are 5-digit: YXX57, YX57X or Y57XX, plus the numbers 57XXX. Then, digit Y can be each integer between 1 and 9, thus it can take nine values, whereas the X digit can take any value between 0 and 9, meaning ten values. For one of the first three numbers the possibilities are 9*10*10 = 900, thus for the three number we have a total of 2700 numbers. The numbers 57XXX instead are 10*10*10 = 1000. Summing 2700 and 1000 we get 3700, thus answer D!
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Re: How many positive five-digit integers contain the digit grou [#permalink] New post 18 Sep 2017, 06:13
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Correct answer. However, in such questions, the shortcut is not too short. It works till some point.

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Re: How many positive five-digit integers contain the digit grou [#permalink] New post 08 Jul 2018, 02:34
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This question is wrong worded and Manhattan has issued the errata. Check here https://www.manhattanprep.com/gre/errat ... a-5lb-2ed/
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Kudos [?]: 3372 [0], given: 12174

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Re: How many positive five-digit integers contain the digit grou [#permalink] New post 08 Jul 2018, 11:34
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Thank you so much.

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Re: How many positive five-digit integers contain the digit grou [#permalink] New post 11 Jun 2020, 07:51
With the corrected question in mind, would the correct solution strategy be as follows? There are 3700 five digit numbers in which 57 appears at least once, but the grouping is only counted once in each such case and we still need to count the groupings which appear a second time in a single number. So in the case of 5757X we would count an additional 10 groupings, in the case of 57X57 we would count an additional 10 groupings, and in the case of Y5757 we would count an additional 9 groupings. Therefore, the answer is 3700 + 10 + 10 + 9 = 3729.
Re: How many positive five-digit integers contain the digit grou   [#permalink] 11 Jun 2020, 07:51
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