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How many different 3digit integers have exactly two d
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Updated on: 03 Aug 2019, 03:56
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How many different 3digit integers have exactly two different digits? (A) 1000 (B) 648 (C) 504 (D) 352 (E) 243 Give +1 kudo if you like this question
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Originally posted by chondro48 on 03 Aug 2019, 03:25.
Last edited by chondro48 on 03 Aug 2019, 03:56, edited 2 times in total.




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Re: How many different 3digit integers have exactly two d
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03 Aug 2019, 03:54
Prasannathawait wrote: IMO the answer has to be 162. 9x9x2=162
First digit can be any among the 9 digits Second cannot be 1 digit that is in first place, hence 9 possible options. Third has to be one of the two digits of first or second otherwise 3 unique digits will be there. Hi, you seems to miss the point that exactly two different digits can mean: AAB, ABA, ABB. I believe you missed out the third part. Have you carefully taken into account that? AAB = 9*1*9 =81 ABA = 9*9*1 =81 ABB = 9*9*1 =81 Sum of all is 243 (E) Hit +1 kudo if you like my solutionPosted from my mobile device




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Re: How many different 3digit integers have exactly two d
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03 Aug 2019, 03:42
IMO the answer has to be 162. 9x9x2=162First digit can be any among the 9 digits Second cannot be 1 digit that is in first place, hence 9 possible options. Third has to be one of the two digits of first or second otherwise 3 unique digits will be there.
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On the way to conquer the GMAT and I will not leave it until I win. WHATEVER IT TAKES. Target 720+ " I CAN AND I WILL"Your suggestions will be appreciated: https://gmatclub.com/forum/youroneadvicecouldhelpmepoorgmatscores299072.html1) Gmat prep: 620 Q48, V27 2) Gmat prep: 610 Q47, V28 3) Gmat prep: 620 Q47, V28 4) Gmat prep: 660 Q47, V34 5) Gmat prep: 560 Q37, V29 6) Gmat prep: 540 Q39, V26 7) Veritas Cat: 620 Q46, V30 8) Veritas Cat: 630 Q45, V32



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Re: How many different 3digit integers have exactly two d
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03 Aug 2019, 03:51
Number of 3digit integers that have exactly two different digits = Total number of 3 digit integers \(\) Number of 3 digit integers with 0 different digits (All digits are same) \(\) Number of 3 digit integers with 3 different digits (All digits are different)
Total number of 3 digit integers = 999100+1 = 900
Number of 3 digit integers with 0 different digits (All digits are same) = 9*1*1 = 9 (These are 111, 222, 333 ..... 999)
Number of 3 digit integers with 3 different digits (All digits are different) = 9*9*8 = 648 (First digit can be 19, second digit can be 09 except the one used for first digit, third digit can be 09 except the digits used for first and second digits)
So, Number of 3digit integers that have exactly two different digits = 9009648 = 243
Answer is (E)



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How many different 3digit integers have exactly two d
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Updated on: 03 Aug 2019, 04:11
We can translate different 3digit integers have exactly two different digits as this:
All 3 digit integers  all 3 different digit integers  all 3 same digit integers = all 3 digit integers with two different digits, so:
All 3 digit integers = 9 * 10 * 10 all 3 different digit integers = 9 * 9 * 8 all 3 same digit integers = 111, 222, 333... = 9
all 3 digit integers with two different digits = 900  648  9 = 243
(E) is our answer
Originally posted by Mizar18 on 03 Aug 2019, 04:01.
Last edited by Mizar18 on 03 Aug 2019, 04:11, edited 1 time in total.



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How many different 3digit integers have exactly two d
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Updated on: 03 Aug 2019, 08:57
Anyone, try this question with timer, leave out good explanation, and kindly leave +1 kudo if this question is quite good.
Originally posted by chondro48 on 03 Aug 2019, 04:04.
Last edited by chondro48 on 03 Aug 2019, 08:57, edited 3 times in total.



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Re: How many different 3digit integers have exactly two d
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03 Aug 2019, 04:12
I missed the question completely. chondro48 wrote: Prasannathawait wrote: IMO the answer has to be 162. 9x9x2=162
First digit can be any among the 9 digits Second cannot be 1 digit that is in first place, hence 9 possible options. Third has to be one of the two digits of first or second otherwise 3 unique digits will be there. Hi, you seems to miss the point that exactly two different digits can mean: AAB, ABA, ABB. I believe you missed out the third part. Have you carefully taken into account that? AAB = 9*1*9 =81 ABA = 9*9*1 =81 ABB = 9*9*1 =81 Sum of all is 243 (E) Hit +1 kudo if you like my solutionPosted from my mobile device
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On the way to conquer the GMAT and I will not leave it until I win. WHATEVER IT TAKES. Target 720+ " I CAN AND I WILL"Your suggestions will be appreciated: https://gmatclub.com/forum/youroneadvicecouldhelpmepoorgmatscores299072.html1) Gmat prep: 620 Q48, V27 2) Gmat prep: 610 Q47, V28 3) Gmat prep: 620 Q47, V28 4) Gmat prep: 660 Q47, V34 5) Gmat prep: 560 Q37, V29 6) Gmat prep: 540 Q39, V26 7) Veritas Cat: 620 Q46, V30 8) Veritas Cat: 630 Q45, V32



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Re: How many different 3digit integers have exactly two d
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03 Aug 2019, 08:42
chondro48 wrote: exc4libur, try this question and leave +1 kudo if this question is quite good. [method 1] threedigit numbers with 2 different digits has 3 cases: XXY: hundreds ≠ 0 so 9 choices • tens = hundreds = 1 choice • units ≠ other digits = 101 = 9 choices … 9*1*9=81 XYX: hundreds ≠ 0 so 9 choices • units = hundreds = 1 choice • tens ≠ other digits = 101 = 9 choices … 9*1*9=81 YXX: hundreds ≠ 0 so 9 choices • tens ≠ hundreds = 9 choices • units = hundreds = 1 choice … 9*9*1=81 total: 81+81+81=243 [method 2] 3d numbers  3d triplets  3d's with different digits = 3d numbers with 2 different digits: 3d numbers = 9*10*10 = 900 or (range between 999100 inclusive is 999100+1=900) 3d triplets = 9*1*1 (9 because hundreds ≠ 0) = 9 3d's with different digits = 9*9*8= 81*8 = 648 total: 9009648=243 Answer (E).



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Re: How many different 3digit integers have exactly two d
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07 Aug 2019, 22:16
chondro48 wrote: How many different 3digit integers have exactly two different digits?
(A) 1000 (B) 648 (C) 504 (D) 352 (E) 243
Give +1 kudo if you like this question Approach: Total  unfavourable cases with zero Total: 10C2*2C1*3 Cases which start with zero: 1) 1 zero and 2 any other number (first digit can't be zero, everything else is acceptable): 9 2) 2 zero and 1 any other number (other number has to be in hundredth place, everything else is not acceptable): 9*2 Therefore answer: 10C2*2C1*3  (9 +9*2) 243



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Re: How many different 3digit integers have exactly two d
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08 Aug 2019, 01:31
chondro48 wrote: Prasannathawait wrote: IMO the answer has to be 162. 9x9x2=162
First digit can be any among the 9 digits Second cannot be 1 digit that is in first place, hence 9 possible options. Third has to be one of the two digits of first or second otherwise 3 unique digits will be there. Hi, you seems to miss the point that exactly two different digits can mean: AAB, ABA, ABB. I believe you missed out the third part. Have you carefully taken into account that? AAB = 9*1*9 =81 ABA = 9*9*1 =81 ABB = 9*9*1 =81 Sum of all is 243 (E) Hit +1 kudo if you like my solutionPosted from my mobile deviceHi, I solved the same way, but I took one additional case apart from the three cases (AAB, ABA, ABB) and that is BAA. For example; AAB= 223 ABA= 232 ABB= 233 BAA= 322 Can you please explain where did I go wrong?
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Re: How many different 3digit integers have exactly two d
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