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Of the 3-digit positive integers greater than 600, how many

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Of the 3-digit positive integers greater than 600, how many  [#permalink]

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New post Updated on: 08 Aug 2019, 16:00
4
5
00:00
A
B
C
D
E

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?

A. 144
B. 108
C. 107
D. 90
E. 72

Source: modified from OG Diagnostic Test

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 3-digit positive integers greater than 600, how many  [#permalink]

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New post Updated on: 02 Sep 2019, 17:13
6
The three-digit 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

:thumbup: 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 3-digit positive integers greater than 600, how many  [#permalink]

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New post 08 Aug 2019, 15:31
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Hi chondro48

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

(C) is the answer
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Re: Of the 3-digit positive integers greater than 600, how many  [#permalink]

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New post 08 Aug 2019, 15:45
:cry: :cry: :cry: 108.
Why I am missing these traps?
Nice question chondro48

Posted from my mobile device
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Re: Of the 3-digit positive integers greater than 600, how many  [#permalink]

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New post 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

36+36+35 = 107

C is the answer!
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Re: Of the 3-digit positive integers greater than 600, how many  [#permalink]

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New post 08 Aug 2019, 15:55
Prasannathawait wrote:
:cry: :cry: :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  [#permalink]

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New post 08 Aug 2019, 15:56
chondro48 wrote:
Hi snoep,

Kindly :thumbup: either the question or my explanation. I haven give you :thumbup: already. Thanks :)

Posted from my mobile device


yep , +1 for you :thumbup:

also +1 for your explanation as well
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Re: Of the 3-digit positive integers greater than 600, how many  [#permalink]

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New post 08 Aug 2019, 19:48
2
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 3-digit positive integers greater than 600, how many  [#permalink]

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New post 09 Aug 2019, 02:51
:cry: 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: :cry: :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  [#permalink]

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New post 02 Sep 2019, 05:25
Prasannathawait wrote:
:cry: :cry: :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  [#permalink]

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New post 02 Sep 2019, 05:26
lnm87 wrote:
Prasannathawait wrote:
:cry: :cry: :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).


Prasannathawait

Refer above.

Hope it helps.
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Re: Of the 3-digit positive integers greater than 600, how many   [#permalink] 02 Sep 2019, 05:26
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