Author 
Message 
TAGS:

Hide Tags

Director
Joined: 30 Sep 2017
Posts: 922
GMAT 1: 720 Q49 V40
GPA: 3.8

How many different 3digit integers have exactly two d
[#permalink]
Show Tags
Updated on: 21 Aug 2019, 12:22
Question Stats:
59% (02:12) correct 41% (02:04) wrong based on 158 sessions
HideShow timer Statistics
How many different 3digit integers have exactly two different digits? (A) 1000 (B) 648 (C) 504 (D) 352 (E) 243
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by chondro48 on 03 Aug 2019, 02:25.
Last edited by chondro48 on 21 Aug 2019, 12:22, edited 3 times in total.




Director
Joined: 30 Sep 2017
Posts: 922
GMAT 1: 720 Q49 V40
GPA: 3.8

How many different 3digit integers have exactly two d
[#permalink]
Show Tags
Updated on: 21 Aug 2019, 12:22
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)
Originally posted by chondro48 on 03 Aug 2019, 02:54.
Last edited by chondro48 on 21 Aug 2019, 12:22, edited 1 time in total.




Senior Manager
Joined: 10 Aug 2018
Posts: 280
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
03 Aug 2019, 02:42
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.
_________________
On the way to get into the Bschool and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL"



Director
Joined: 16 Jan 2019
Posts: 604
Location: India
Concentration: General Management
WE: Sales (Other)

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
03 Aug 2019, 02:51
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)



Manager
Joined: 28 Jan 2019
Posts: 75
Location: Peru

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
Updated on: 03 Aug 2019, 03:11
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, 03:01.
Last edited by Mizar18 on 03 Aug 2019, 03:11, edited 1 time in total.



Director
Joined: 30 Sep 2017
Posts: 922
GMAT 1: 720 Q49 V40
GPA: 3.8

How many different 3digit integers have exactly two d
[#permalink]
Show Tags
Updated on: 09 Sep 2019, 15:32
.
Originally posted by chondro48 on 03 Aug 2019, 03:04.
Last edited by chondro48 on 09 Sep 2019, 15:32, edited 4 times in total.



Senior Manager
Joined: 10 Aug 2018
Posts: 280
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
03 Aug 2019, 03:12
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
_________________
On the way to get into the Bschool and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL"



SVP
Joined: 24 Nov 2016
Posts: 1567
Location: United States

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
03 Aug 2019, 07:42
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).



Manager
Joined: 13 Apr 2019
Posts: 178
Location: India
Concentration: Marketing, Operations
Schools: Ross '22, Stern '22, Anderson '22, Darden '21, Johnson '22, Kelley '22, INSEAD Jan '20, IESE '22, HKUST '22, ISB '21, Rotman '22, NUS '22, CEIBS '22, NTU '21, Rutgers '22
GPA: 3.5
WE: General Management (Retail)

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
07 Aug 2019, 21:16
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



Manager
Joined: 10 Mar 2018
Posts: 77
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 680 Q44 V38
WE: Design (Retail)

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
08 Aug 2019, 00:31
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?
_________________



Intern
Joined: 02 Sep 2019
Posts: 9

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
09 Sep 2019, 06:46
What about negative 3 digit integers



Intern
Joined: 20 Jun 2013
Posts: 18
Location: India
WE: Consulting (Health Care)

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
09 Sep 2019, 09:37
AAB or ABA  \(9C_1*2C_1*9C_1\) = 168 BAA  \(9_C_1*9_C_1\) = 81
Total  243, Hence E.



Intern
Joined: 02 Sep 2019
Posts: 9

Re: How many different 3digit integers have exactly two d
[#permalink]
Show Tags
13 Sep 2019, 01:14
So are there 243+243 = 486 numbers, negative and Positive put together




Re: How many different 3digit integers have exactly two d
[#permalink]
13 Sep 2019, 01:14




