Of the three digit greater than 700....

Expert replies

nchaswal: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Fri Apr 17, 2015 8:16 pmFollowed by: 2 members; Thanked: 6 times; GMAT Score:740

by nchaswal » Tue May 10, 2016 12:40 pm

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

a) 90
b) 82
c) 80
d) 36
e) 45

It is GMAT. So what?

Like this post

Source: Beat The GMAT — Problem Solving | Tue May 10, 2016 12:40 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 10, 2016 12:45 pm

Of the 3-digit integers greater than 700, how many have 2 digits that are equal to each other and the remaining digit different from the other 2 ?

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

Integers with exactly 2 digits the same = Total integers - Integers with all 3 digits the same - Integers with all 3 digits different.

Total integers:
To count consecutive integers, use the following formula:
Number of integers = biggest - smallest + 1.
Thus:
Total = 999 - 701 + 1 = 299.

Integers with all 3 digits the same:
777, 888, 999.
Number of options = 3.

Integers with all 3 digits different:
Number of options for the hundreds digit = 3. (7, 8, or 9)
Number of options for the tens digit = 9. (Any digit 0-9 other than the digit already used.)
Number of options for the units digit = 8. (Any digit 0-9 other than the two digits already used.)
To combine these options, we multiply:
3*9*8 = 216.

Thus:
Integers with exactly 2 digits the same = 299-3-216 = 80.

The correct answer is C.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Fri May 13, 2016 9:00 pm

nchaswal 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) 36
e) 45

Here's an alternate method.

The three digit integers greater than 700 are the integers from 701 - 999 inclusive.

Start with the integers that begin with 7.

Any integer that ends in 7 except 777 will work.

So we have 707, 717, 727 ... 797 for a total of 9.

Also integers except 777 that have 7 as the second number will work. 770, 771, 772, 773 ... 779. For a total of 9.

Then other than 777 any integer with the second two digits the same will work.

711, 722, 733 ... 799, for a total of 8.

So we have 9 + 9 + 8 = 26.

This pattern holds for the integers from 801 to 899, 9 + 9 + 8 = 26, and for the integers from 901 to 999, 9 + 9 + 8 = 26.

So, so far we have 3 x 26 = 78 integers that fit.

(If you were tempted to go with 78 as the answer, you would be saved by the fact that 78 is not one of the answer choices.)

800 and 900 work too.

So 78 + 2 = 80.

The correct answer is C.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review