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Digits, Numbers

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Digits, Numbers

by vinay1983 » Tue Aug 27, 2013 5:11 am
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 two?

A. 90
B. 82
C. 80
D. 45
E. 36

The explanation in the OG is waaaayy lengthy to comprehend.How about this question appearing frequently on the GMAT?

OA: C
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by Brent@GMATPrepNow » Tue Aug 27, 2013 5:48 am
vinay1983 wrote: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 two?

A. 90
B. 82
C. 80
D. 45
E. 36
One approach is to list the numbers and look for a pattern.

Let's first focus on the numbers from 800 to 899 inclusive.
We have 3 cases to consider: 8XX, 8X8, and 88X

8XX
800
811
822
.
.
.
899
Since we cannot include 888 in this list, there are 9 numbers in the form 8XX

8X8
808
818
828
.
.
.
898
Since we cannot include 888 in this list, there are 9 numbers in the form 8X8

88X
880
881
882
.
.
.
889
Since we cannot include 888 in this list, there are 9 numbers in the form 88X

So, there are 27 (9+9+9) numbers from 800 to 899 inclusive that meet the given criteria.

Using the same logic, we can see that there are 27 numbers from 900 to 999 inclusive that meet the given criteria.

And there are 27 numbers from 700 to 799 inclusive that meet the given criteria. HOWEVER, the question says that we're looking at numbers greater than 700, so the number 700 does not meet the criteria. So, there are actually 26 numbers from 701 to 799 inclusive that meet the given criteria.

So, our answer is 27+27+26 = [spoiler]80 = C[/spoiler]

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sun Apr 05, 2015 6:56 am, edited 1 time in total.
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by ganeshrkamath » Tue Aug 27, 2013 6:31 am
vinay1983 wrote: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 two?

A. 90
B. 82
C. 80
D. 45
E. 36

The explanation in the OG is waaaayy lengthy to comprehend.How about this question appearing frequently on the GMAT?

OA: C
First digit different, rest two same:
7xx => 8 (x cannot be 0 or 7)
8xx => 9 (x cannot be 8)
9xx => 9 (x cannot be 8)

Second digit different, rest two same:
7x7 => 9 (x cannot be 7)
8x8 => 9
9x9 => 9

Third digit different, rest two same:
77x => 9
88x => 9
99x => 9

Total = (8+9+9) + 9*3 + 9*3 = 26 + 27 + 27 = 80

Choose C

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by [email protected] » Tue Aug 27, 2013 11:36 am
Hi vinay1983,

You won't see too many questions on test day that are this work-intensive, but the truth is that the work isn't THAT hard and it wouldn't take THAT long to answer this question. Certain Quant questions will require 3 minutes of your clock to solve (and that's if you KNOW what you're doing). If you don't see an immediate pattern, formula, number property, etc. when attempting these types of questions, then you're going to have to "brute force" your way through it. If you're not willing to do the work, then take a quick guess and move past the question.

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by GMATGuruNY » Tue Aug 27, 2013 7:27 pm
vinay1983 wrote: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 two?

A. 90
B. 82
C. 80
D. 45
E. 36
An alternate approach:

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.
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