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# GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11

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GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11 [#permalink]  11 Jul 2009, 20:02
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I am having a problem in understanding the answer provided by GMAT REVIEW 11TH EDITION. QUESTION 11 (QUANT. DIAGNOSTIC TEST) IS ASKING:

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.

The explanation provided is that there are 3 pairs of digits that can be the same while the other digit is different. The 3 pairs are:

tens and ones
hundreds and tens
hundreds and ones (THIS IS THE ONE THAT I AM HAVING PROBLEM WITH). The only ones that I can think of are 707,808,909 and the book says there are at least 27 others (including the 3 I have given). Am I the only one not getting this?
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Re: GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11 [#permalink]  11 Jul 2009, 20:33
It is because you are assuming only 0 to be the tens digit, whereas it can be anything from 0-9 excluding the digit already repeated, ie 7/8/9

ie 9 for each of them so 27
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Re: GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11 [#permalink]  12 Jul 2009, 23:45
On my count, there are 54 numbers meeting these criteria.

First, there are numbers greater than 700 with matching digits in the hundreds and unit positions: 707, 808, 909 = 3.

Second, there are numbers with matching digits in the tens and units positions: 711, 722, 733, 744, 755, 766, 788, 799 = 8 x 3 = 24

Finally, there are numbers with matching digits in the hundreds and tens positions: 770, 771, 772, 773, 774, 775, 776, 778, 779 = 9 x 3 = 27

24+3+27 = 54.

Can you please provide the OA?
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Re: GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11 [#permalink]  14 Jul 2009, 08:49
ANS.. 54..
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Re: GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11 [#permalink]  14 Jul 2009, 11:20
carriedinterest wrote:
On my count, there are 54 numbers meeting these criteria.

First, there are numbers greater than 700 with matching digits in the hundreds and unit positions: 707, 808, 909 = 3.

Correct, but there are such numbers as 717, 727, etc., 9 of them in every hundred: 9 x 3 = 27

Quote:
Second, there are numbers with matching digits in the tens and units positions: 711, 722, 733, 744, 755, 766, 788, 799 = 8 x 3 = 24

Correct, but only for the 7th hundred, in 8th and 9th there are also numbers 800 and 900. Total: 8 + 9 + 9 = 26

Quote:
Finally, there are numbers with matching digits in the hundreds and tens positions: 770, 771, 772, 773, 774, 775, 776, 778, 779 = 9 x 3 = 27

Completely agree

27+26+27=80
Re: GMAT REVIEW BOOK DIAGNOSTIC QUANT QUESTION 11   [#permalink] 14 Jul 2009, 11:20
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