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

and subscribe if you like the explanation

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
_________________

108.
Why I am missing these traps?
Nice question chondro48

Posted from my mobile device
_________________

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!

I intentionally wrote the multiple choices with a trap in mind.

yep , +1 for you

also +1 for your explanation as well

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

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.



_________________

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.
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________