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Of the 3digit positive integers greater than 600, how many
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Updated on: 08 Aug 2019, 16:00
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Of the 3digit 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? A. 144 B. 108 C. 107 D. 90 E. 72 Source: modified from OG Diagnostic Test
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Originally posted by chondro48 on 08 Aug 2019, 13:54.
Last edited by chondro48 on 08 Aug 2019, 16:00, edited 6 times in total.




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Of the 3digit positive integers greater than 600, how many
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Updated on: 02 Sep 2019, 17:13
The threedigit positive integers greater than 600 that have exactly two digits that are equal to each other can mean: AAB, ABA, ABB. As hundreds digit, A can only be of 4 digits, that are 6,7,8, or 9. AAB = 4*1*9 =36 (e.g. 660) ABA = 4*9*1 =36 (e.g. 606) ABB = 4*9*1 =36 (e.g. 600) Sum of all is 108. However, don't forget to subtract 1 from 108 (as ABB =600 should NOT be included). Final answer is (C)  107 and subscribe if you like the explanation
Originally posted by chondro48 on 08 Aug 2019, 14:11.
Last edited by chondro48 on 02 Sep 2019, 17:13, edited 10 times in total.




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Re: Of the 3digit positive integers greater than 600, how many
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08 Aug 2019, 15:31
Hi chondro48We can translate threedigit 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 (C) is the answer



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Re: Of the 3digit positive integers greater than 600, how many
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08 Aug 2019, 15:45
108. Why I am missing these traps? Nice question chondro48 Posted from my mobile device
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Re: Of the 3digit positive integers greater than 600, how many
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08 Aug 2019, 15:47
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 91 = total 8 as these combinations could be also with digit 7 , 8, and 9 = 9*3 = 27 27 + 8 = total 35
36+36+35 = 107
C is the answer!



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Re: Of the 3digit positive integers greater than 600, how many
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08 Aug 2019, 15:55
Prasannathawait wrote: :cry: 108. Why I am missing these traps? Nice question chondro48 Posted from my mobile deviceI intentionally wrote the multiple choices with a trap in mind.



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Re: Of the 3digit positive integers greater than 600, how many
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08 Aug 2019, 15:56
chondro48 wrote: Hi snoep, Kindly either the question or my explanation. I haven give you already. Thanks Posted from my mobile deviceyep , +1 for you also +1 for your explanation as well



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Re: Of the 3digit positive integers greater than 600, how many
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08 Aug 2019, 19:48
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



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Re: Of the 3digit 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 deviceI intentionally wrote the multiple choices with a trap in mind.
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Re: Of the 3digit 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 deviceLooks 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 3digit 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 deviceLooks 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). PrasannathawaitRefer above. Hope it helps.
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Re: Of the 3digit positive integers greater than 600, how many
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