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Manager  G
Joined: 03 Oct 2012
Posts: 159
Location: India
Concentration: Entrepreneurship, Strategy
WE: Brand Management (Pharmaceuticals and Biotech)
Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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9 00:00

Difficulty:   85% (hard)

Question Stats: 44% (02:02) correct 56% (02:40) wrong based on 89 sessions

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Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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1
JackMasterNone wrote:
Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests

Three-digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.

We need to calculate B. B = Total - A - C

The number of three-digit numbers which are greater than 500 is 499 (from 501 to 999, inclusive).
A. all digits are distinct = 5*9*8 = 360 (first digit can have only five values 5, 6, 7, 8, or 9);
C. all three are alike = 5 (555, 666, 777, 888, 999).

So, 499 - 360 - 5 = 134.

Similar questions:
https://gmatclub.com/forum/of-the-three ... 28853.html
https://gmatclub.com/forum/of-the-three ... 27390.html
https://gmatclub.com/forum/of-the-three ... 35188.html

Hope it helps.
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Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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i did it in a different way
so whatever the number will be , it will be (multiple of 5) -1
because in each series we will have 600, 700, 800,900 but not 1000,
only 134 is that kind of number

did it in 30 seconds

Hit kudos if u like it
Intern  B
Joined: 22 Jun 2019
Posts: 2
Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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lifeforhuskar wrote:
i did it in a different way
so whatever the number will be , it will be (multiple of 5) -1
because in each series we will have 600, 700, 800,900 but not 1000,
only 134 is that kind of number

did it in 30 seconds

Hit kudos if u like it

This won't work if all options were in the form 5n -1

Posted from my mobile device
VP  P
Joined: 07 Dec 2014
Posts: 1222
Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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Bombsante wrote:
Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests

three ways:
xxy
xyx
yxx
3(5*9*1)=135
135-1 (for 500)=134
A
Manager  G
Joined: 28 Jan 2017
Posts: 136
WE: Consulting (Computer Software)
Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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Bunuel wrote:
JackMasterNone wrote:
Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests

Three-digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.

We need to calculate B. B = Total - A - C

The number of three-digit numbers which are greater than 500 is 499 (from 501 to 999, inclusive).
A. all digits are distinct = 5*9*8 = 360 (first digit can have only five values 5, 6, 7, 8, or 9);
C. all three are alike = 5 (555, 666, 777, 888, 999).

So, 499 - 360 - 5 = 134.

Similar questions:
https://gmatclub.com/forum/of-the-three ... 28853.html
https://gmatclub.com/forum/of-the-three ... 27390.html
https://gmatclub.com/forum/of-the-three ... 35188.html

Hope it helps.

hi, Is there any way which doesn't subtract unfavorable cases and directly count favorable cases? I know the above one is the best efficient but want to know other possibility as well.
SVP  P
Joined: 03 Jun 2019
Posts: 1689
Location: India
Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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Bombsante wrote:
Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests

Asked: Of the three digit numbers greater than 500, how many have exactly one digit repeating?

Numbers can be of form = {abb, bab, bba}

Form abb;
a = {6,7,8,9} = 4 ways
b = {0,1,2,3,4,5,6,7,8,9} except digit a = 9 ways
Total numbers = 4*9 = 36 numbers
Let us take a = 5
b = {1,2,3,4,6,7,8,9} = 8 ways
Total numbers = 36 + 8 = 44 numbers

Form bab;
b = {5,6,7,8,9} = 5 ways
a = {0,1,2,3,4,5,6,7,8,9} except digit b = 9 ways
Total numbers = 5*9 = 45 numbers

Form bba;
b = {5,6,7,8,9} = 5 ways
a = {0,1,2,3,4,5,6,7,8,9} except digit b = 9 ways
Total numbers = 5*9 = 45 numbers

Adding all cases = 44 + 45 + 45 = 134 numbers

IMO A
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SVP  P
Joined: 03 Jun 2019
Posts: 1689
Location: India
Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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1
nkhl.goyal wrote:
Bunuel wrote:
JackMasterNone wrote:
Of the three digit numbers greater than 500, how many have exactly one digit repeating?

a) 134
b) 135
c) 136
d) 142
e) 148

Source: Expert's global practice tests

Three-digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.

We need to calculate B. B = Total - A - C

The number of three-digit numbers which are greater than 500 is 499 (from 501 to 999, inclusive).
A. all digits are distinct = 5*9*8 = 360 (first digit can have only five values 5, 6, 7, 8, or 9);
C. all three are alike = 5 (555, 666, 777, 888, 999).

So, 499 - 360 - 5 = 134.

Similar questions:
https://gmatclub.com/forum/of-the-three ... 28853.html
https://gmatclub.com/forum/of-the-three ... 27390.html
https://gmatclub.com/forum/of-the-three ... 35188.html

Hope it helps.

hi, Is there any way which doesn't subtract unfavorable cases and directly count favorable cases? I know the above one is the best efficient but want to know other possibility as well.

nkhl.goyal
Please see my solution and suggest any changes.
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Manager  G
Joined: 28 Jan 2017
Posts: 136
WE: Consulting (Computer Software)
Re: Of the three digit numbers greater than 500, how many have exactly one  [#permalink]

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hi, Is there any way which doesn't subtract unfavorable cases and directly count favorable cases? I know the above one is the best efficient but want to know other possibility as well.[/quote]

nkhl.goyal
Please see my solution and suggest any changes.[/quote]

Yes, I was looking the same.

For 1st part :
Form abb;
a = {6,7,8,9} = 4 ways
b = {0,1,2,3,4,5,6,7,8,9} except digit a = 9 ways
Total numbers = 4*9 = 36 numbers
Let us take a = 5
b = {1,2,3,4,6,7,8,9} = 8 ways
Total numbers = 36 + 8 = 44 numbers

You can directly do this. a = {5, 6,7,8,9} = 5 ways, b same as yours.
Total numbers = 5*9 = 45, but here 500 is included so remove that. So, total 45-1 = 44 Re: Of the three digit numbers greater than 500, how many have exactly one   [#permalink] 09 Sep 2019, 05:15
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