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How many positive five-digit integers contain the digit grou

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Joined: 18 Apr 2015
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Kudos [?]: 1049 [0], given: 4698

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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:

53% (01:27) correct 46% (01:57) wrong based on 13 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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Joined: 18 Apr 2015
Posts: 5202
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Kudos [?]: 1049 [0], given: 4698

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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] 08 Jul 2018, 11:34
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