Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

02 Jul 2012, 02:01

Expert's post

34

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

49% (03:06) correct
51% (02:06) wrong based on 850 sessions

HideShow timer Statistics

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

Diagnostic Test Question: 11 Page: 22 Difficulty: 650

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

02 Jul 2012, 02:02

31

This post received KUDOS

Expert's post

19

This post was BOOKMARKED

SOLUTION

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

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

Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700); A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9); C. all three are alike = 3 (777, 888, 999).

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

02 Jul 2012, 02:49

5

This post received KUDOS

2

This post was BOOKMARKED

Bunuel wrote:

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

Diagnostic Test Question: 11 Page: 22 Difficulty: 650

The first digit can be 7, 8 or 9, so three possibilities. If the first digit is repeated, we have \(2 * 9\) possibilities, because the numbers can be of the form \(aab\) or \(aba\), where \(b\neq a\). If the first digit is not repeated, the number is of the form \(abb\), for which there are 9 possibilities. This gives a total of 27 choices for a given first digit. Altogether, we will have \(3 * 27 = 81\) choices from which we have to eliminate one choice, 700 (because the numbers should be greater than 700). We are finally left with 80 choices.

Answer: C _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

06 Jul 2012, 02:40

2

This post received KUDOS

Expert's post

SOLUTION

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

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

Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700); A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9); C. all three are alike = 3 (777, 888, 999).

Re: Of the 3digit nos greater than 700, how many have 2 digits [#permalink]

Show Tags

15 Feb 2013, 23:41

2

This post received KUDOS

For 3 digit numbers greater than 700, the first digit has to be 7, 8, or 9. The last two digits can be anything except 00.

There can be three possible cases for such numbers:

Case 1- first two digits same. The last digit has to be different from the first two. As the first digit is constrained to be 7,8,or 9, total number of such numbers = 3*9 = 27

Case 2 - first and third digits same. By the same logic as above, total number of such numbers = 27

Case 3 - second and third digits same. Total number of such numbers = (3*9)-1 = 26 (we need to subtract one to remove the 00 case).

Therefore total = 27 + 27 + 26 = 80 numbers (option C)

We have assumed here that numbers where all three digits are the same are not allowed. _________________

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

12 Mar 2013, 21:42

2

This post received KUDOS

From 701 to 799 we will have: 711, 722.... 799( excluding 777 ) = 8; From 770 to 779 we have 9 numbers ( excluding 777 ). We will also have numbers such as 707, 717, 727.... 797, total 9 numbers ( excluding 777 ) Similarly from 800 to 899 we will have 9 numbers ( we will exclude 888 ) From 880 to 899 we will once again have 9 numbers We will also have numbers such as 808, 818.... 898, total 9 numbers ( excluding 888 ) Similarly for numbers greater than equal to 900 and till 999 we will have 27 such numbers. Total = 26(>700) + 27(>=800) + 27(>=900) = 80 such numbers.

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

02 Jul 2012, 05:33

1

This post received KUDOS

Hi,

To satify the given condition, required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same, number greater than 700; total numbers = 1*10*10 = 100 numbers with all digits different = 1*9*8 = 72 numbers when all three digits are same (777) = 1 req. = 100- 72 - 1 = 27 considering the numbers between 700 & 999 = 27*3=81 Answer is 80 ('cause 700 can't be included)

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

16 Dec 2013, 14:57

1

This post received KUDOS

Bunuel wrote:

SOLUTION

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

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

Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700); A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9); C. all three are alike = 3 (777, 888, 999).

So, 299-216-3=80.

Answer: C.

I just dont't understand why the "3*9*8" can anyone explain me? please

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

25 Jan 2014, 21:19

1

This post received KUDOS

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

Let the three digit number be represented as X Y Z.

There are 3 cases:

Case I. [ X=Y ] & Z is not equal to X & Y : XXZ or YYZ X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways After X is chosen, Y can be chosen in 1 way After X & Y are chosen, Z can be chosen in 9 ways Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1) [example numbers: 774,779,882,993 etc]

Case II. [ X=Z ] & Y is not equal to X & Z: XYXor ZYZ X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways After X is chosen, Z can be chosen in 1 way After X & Z are chosen, Z can be chosen in 9 ways Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2) [example numbers: 747,797,828,939 etc]

Case III. [ Y =Z ]& X is not equal to Y & Z :XYY or XZZ X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways After X is chosen, Y can be chosen in 9 ways After Y is chosen, Z can have 1 way Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3) [example numbers: 744,799,822,933 etc]

Therefore, total numbers of possible digits [sum of Case (1), (2) & (3) above] = 27 + 27 + 27 - 1 = 80 One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 700.

You are right about the range of the numbers. In the solution presented we are subtracting from total possible numbers (i.e. 299) the numbers which have all the 3 digits same and the numbers which have all the three digits distinct. In case of numbers with distinct digits between 701 and 999 both inclusive we can have numbers like 710, 720... etc. So zero can be there at the units place.

Alternatively in case of numbers with exactly two similar digits we can have numbers like 800,900 or 770, 880, 990 which have zero at their units place.

Hope it's clear . Let me know if you are having trouble at any point of the explanation.

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

02 Jul 2012, 06:34

There are 2 numbers that have the same two digits for each of the 10's (700-709, 710-719, 720-729, etc.), with the exception for where the tens digit is the same as the hundreds (770-779), in this scenario there are 9 digits that have the same two digits.

So for 700-799 inclusive there are (9 * 2) + 9 - 1 = 26 numbers that the same two digits. Subtract one cause 700 shouldn't be included. For 800 - 999 the calculation simply becomes 27 * 2 = 54

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

02 Jul 2012, 12:22

Total Number of 3 digit number greter than 700 = 299 In 700 series - The total number of number with distinct digit = 9*8 So from 700 till 999 we will have - 3*9*8 = 216 So total number of numbers with duplicate digit = 299-216 = 83 Need to Subtract 777,888 & 999 so answer is 80.

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

17 Dec 2013, 01:34

Expert's post

mandrake15 wrote:

Bunuel wrote:

SOLUTION

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

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

Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700); A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9); C. all three are alike = 3 (777, 888, 999).

So, 299-216-3=80.

Answer: C.

I just dont't understand why the "3*9*8" can anyone explain me? please

A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9);

Since given three-digit integers must be greater than 700, then the first digit can take three values: 7, 8, or 9. The second digit can take 9 values: 10 digits minus one digit we've already used for the first digit. Similarly, the third digit can take 8 values: 10 digits minus two digits we've already used for the first and second digits.

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

19 May 2014, 09:28

Bunuel, what an elegant solution as always! Please can you provide more such problems for practice? I often struggle with this type. Thanks! _________________

Please consider giving 'kudos' if you like my post and want to thank

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

21 May 2014, 02:25

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

Consider numbers from 701 to 799

Case 1: Numbers such as 707, 717..... 797 (Except 777)

\(1*9*1 = 9\) ---> (1)

Case 2: Numbers such as 770, 771..... 779 (Except 777)

\(1*1*9 = 9\) ---> (2)

Case 3: Numbers such as 711, 722...... 799 (Except 777)

\(1*8*1 = 8\) ---> (3) [NOTE: Did not consider 0 & 7 for the unit's and ten's digit]

Adding (1), (2) & (3)

\(9 + 9 + 8 = 26\)

This can be done for 801 to 899 and 901 to 999.

So, we get \(26 * 3 = 78\)

We also need to consider \(800\) and \(900\) (But NOT \(700\))

So, \(78 + 2 = 80\)

Can an expert evaluate the method. I understand that this method is long and could take time. But I want to be sure that I considered the cases correctly (In case, it comes to this during the exam!).

Re: Of the three-digit integers greater than 700, how many have [#permalink]

Show Tags

28 Mar 2015, 01:23

Bunuel wrote:

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90 (B) 82 (C) 80 (D) 45 (E) 36

Diagnostic Test Question: 11 Page: 22 Difficulty: 650

lets count the number for one range 700-799 and we will multiply it by 3 .

77_= 9 7_7= 9 7__= 9 so total 27 numbers are there starting with 7XX . total 81 such numbers will be there in 700-999 inclusive .

as the question asks for all such numbers which are greater than 700 so 81 -1 = 80 Answer D . _________________

Thanks, Lucky

_______________________________________________________ Kindly press the to appreciate my post !!

gmatclubot

Re: Of the three-digit integers greater than 700, how many have
[#permalink]
28 Mar 2015, 01:23

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

With the limited financing options available to NZ citizens (especially those comme moi who aren't planning to return to work in NZ), I've really had to...

Strategy, innovation, marketing, finance... The second module has been pretty engaging. Though, no lack of memorable times. There is no lack of high profile guest speakers. One of the...