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Of the 3-digit positive integers greater than 600, how many
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Updated on: 08 Aug 2019, 16:00
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A
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C
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Difficulty:
95% (hard)
Question Stats:
38% (02:08) correct 63% (02:39) wrong based on 112 sessions
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Of the 3-digit positive integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
We can translate three-digit positive integers greater than 600 that have exactly two digits that are equal to each other to this:
All 3 digit integers > 600 - all 3 different digit integers > 600 - all 3 same digit integers > 600 = all 3 digit integers that have exactly two digits that are equal to each other > 600
All 3 digit integers > 600 =4*10*10 - 1 (since 600 is not included) = 399 all 3 different digit integers > 600 = 4*9*8 = 288 all 3 same digit integers > 600 = 666, 777, 888 and 999 = 4
3 digit integers that have exactly two digits that are equal to each other > 600 = 399 - 288 - 4 = 107
Re: Of the 3-digit positive integers greater than 600, how many
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08 Aug 2019, 15:47
1
its a nice one
combination 1 Digits from 660, 661, 662...669 = 10 , subtract 1 to not account 666 = total 9 as these combinations could be also with digit 7 , 8, and 9 = 9*4 = 36
combination 2 Digits from 606, 616, 626, 636,.....696 -> 10 , subtract 1 to not account 666 = total 9 as these combinations could be also with digit 7 , 8, and 9 = 9*4 = 36
combination 3 Digits from 600, 611, 622, 633,.....699 -> 10 , subtract 1 to not account 666 = total 9. Note number is greater than 600 as given in the question. So 9-1 = total 8 as these combinations could be also with digit 7 , 8, and 9 = 9*3 = 27 27 + 8 = total 35
Re: Of the 3-digit positive integers greater than 600, how many
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08 Aug 2019, 19:48
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Clearly, the format of the numbers should by XXY - 4.9 = 36 YXX - 4.9 = 36 XYX - 4.9 = 36
Total = 36*3 = 108 Now, Sanity Check = There is 600 also included in the above count ,So remove it as mentioned in the problem. So Total Number = 108 -1 = 107
Re: Of the 3-digit positive integers greater than 600, how many
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09 Aug 2019, 02:51
That is naive of me after this much prep. Thanks for reminding me that I have to watch out for these traps and that I should avoid making the same mistakes again.
chondro48 wrote:
Prasannathawait wrote:
:cry: 108. Why I am missing these traps? Nice question chondro48
Posted from my mobile device
I intentionally wrote the multiple choices with a trap in mind.
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Re: Of the 3-digit positive integers greater than 600, how many
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02 Sep 2019, 05:25
Prasannathawait wrote:
:cry: 108. Why I am missing these traps? Nice question chondro48
Posted from my mobile device
Looks longer method but if pattern of 9 digits for each case and for each digit barring 600 is realized then its smooth as it can be. No need to make a table.
Refer snapshot.
26 + 27*3 = 107.
Answer (C).
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Re: Of the 3-digit positive integers greater than 600, how many
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02 Sep 2019, 05:26
lnm87 wrote:
Prasannathawait wrote:
:cry: 108. Why I am missing these traps? Nice question chondro48
Posted from my mobile device
Looks longer method but if pattern of 9 digits for each case and for each digit barring 600 is realized then its smooth as it can be. No need to make a table.
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38% (02:08) correct 
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