Of the three digit numbers greater than 500, how many have exactly one : Problem Solving (PS)

Trev50

Joined: 22 Jun 2019

Last visit: 13 Dec 2019

Posts: 2

Given Kudos: 4

Posts: 2

Kudos: 0

29 Jul 2019, 08:42

Kudos

Bookmarks

lifeforhuskar

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

gracie

Joined: 07 Dec 2014

Last visit: 11 Oct 2020

Posts: 1,047

Own Kudos:

1,740

[3]

Given Kudos: 27

Posts: 1,047

Kudos: 1,740

[3]

29 Jul 2019, 09:24

1

Kudos

2

Bookmarks

Bombsante

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

800Dreamer

Joined: 28 Jan 2017

Last visit: 04 Feb 2024

Posts: 198

Own Kudos:

180

Given Kudos: 186

GMAT 1: 720 Q50 V36 Verified score

WE:Consulting (Computer Software)

Products:

GMAT 1: 720 Q50 V36 Verified score

Posts: 198

Kudos: 180

09 Aug 2019, 00:11

Kudos

Bookmarks

Bunuel

JackMasterNone

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.

Answer: A.

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.

Kinshook

GMAT Club Legend

Joined: 03 Jun 2019

Last visit: 23 Jan 2025

Posts: 5,508

Own Kudos:

4,784

Given Kudos: 161

Location: India

Schools: HBS '22 CBS '22 Wharton '22

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '22 CBS '22 Wharton '22

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,508

Kudos: 4,784

09 Sep 2019, 04:29

Kudos

Bookmarks

Bombsante

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

Kinshook

GMAT Club Legend

Joined: 03 Jun 2019

Last visit: 23 Jan 2025

Posts: 5,508

Own Kudos:

4,784

[1]

Given Kudos: 161

Location: India

Schools: HBS '22 CBS '22 Wharton '22

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '22 CBS '22 Wharton '22

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,508

Kudos: 4,784

[1]

09 Sep 2019, 04:38

1

Kudos

Bookmarks

nkhl.goyal

Bunuel

JackMasterNone

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.

Answer: A.

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.

800Dreamer

Joined: 28 Jan 2017

Last visit: 04 Feb 2024

Posts: 198

Own Kudos:

180

Given Kudos: 186

GMAT 1: 720 Q50 V36 Verified score

WE:Consulting (Computer Software)

Products:

GMAT 1: 720 Q50 V36 Verified score

Posts: 198

Kudos: 180

09 Sep 2019, 05:15

Kudos

Bookmarks

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

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Last visit: 27 Sep 2022

Posts: 10,107

Own Kudos:

18,015

Given Kudos: 4

GMAT 1: 760 Q51 V42 Verified score

GPA: 3.82

Expert reply

GMAT 1: 760 Q51 V42 Verified score

Posts: 10,107

Kudos: 18,015

26 Sep 2020, 07:18

Kudos

Bookmarks

Three digit numbers greater than 500: [501 to 999]: Total numbers are: 999 - 501 + 1 = 499

For the first position available options are: [5,6,7,8,9] and for the second and third position, we have 9 and 8 options.

Overall numbers with three distinct digits: 5 * 9 * 8 = 360

Overall numbers with all three digits same: 5[555, 666, 777, 888, 999]

=> Three digit numbers with exactly one digit repeating: 499 - 360 - 5 = 134

Answer A

GmatPoint

Joined: 02 Jan 2022

Last visit: 13 Oct 2022

Posts: 254

Own Kudos:

121

Given Kudos: 3

GMAT 1: 760 Q50 V42 Verified score

Posts: 254

Kudos: 121

03 Oct 2022, 23:34

Kudos

Bookmarks

Let a three-digit number abc.
Now, since only one digit is repeating, either a-b is the same, or a-c is the same, or b-c is the same.

Consider the case of a-c: For a the present limits, in a three digit number a-b-a, a can take 5 values(5-9) and b can take 9 values(0-9, except a).

Thus, total values = 9*5 = 45

Consider the case for a-b: For a the present limits, in a three digit number a-a-b, a can take 5 values(5-9) and b can take 9 values(0-9, except a).

Thus, total values = 9*5 = 45

Consider the case for b-c: For a the present limits, in a three digit number a-b-b, a can take 5 values(5-9) and b can take 9 values(0-9, except a).

Also, since 500 is excluded, total values = 9*5-1 = 45-1 = 44

Thus, the total number with exactly one digit repeating is 45+45+44 = 134

Thus, the correct option is A.

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

Prep Toolkit

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

My Rewards