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# Of the three digits greater than 700, how many have two digi

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Intern
Joined: 01 Feb 2016
Posts: 8
Re: Of the three digits greater than 700, how many have two digi  [#permalink]

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16 Jun 2016, 11:57
Repeating the explanation from above, the sequence of nos. should be XXY, XYX, YXX. As we need 3 digit nos. greater that 700, the 100th place in can be either of 7, 8 or 9 (3 ways to select 100th place digit)

Once 100th place if fixed, say units place is same as hundred place (XYX). this means that the tens place can be picked in 9 ways (all digits from 0-9 except the place in hundred place) and unit place can be picked in 1 way only (same as hundred place). So total ways for XYX is 3*9*1=27

We need to repeat this for XXY format. This would again generate 3*1*9 ways = 27

We need to repeat this now with YXX which will give 3.9.1 ways = 27. But we need to exclude 700 from this as we need nos greater than 700. This this combination will give 27-1=26 ways

Total ways = 27+27+26=80
Math Expert
Joined: 02 Sep 2009
Posts: 59721
Re: Of the three digits greater than 700, how many have two digi  [#permalink]

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04 Jul 2017, 07:36
gurpreet07 wrote:
Of the three digits 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

Is there a faster method to find out the answer, because i listed down all the numbers and it took me hardly 1.5 mins.
but what if there are more numbers ?

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/of-the-three- ... 35188.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/of-the-three- ... 35188.html
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Re: Of the three digits greater than 700, how many have two digi   [#permalink] 04 Jul 2017, 07:36

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