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There are n cards numbered consecutively, from 1 to n. Two cards are

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Joined: 02 Sep 2009
Posts: 54496
There are n cards numbered consecutively, from 1 to n. Two cards are  [#permalink]

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New post 16 Jul 2017, 23:36
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (01:08) correct 50% (01:40) wrong based on 69 sessions

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Joined: 22 Aug 2016
Posts: 81
Location: India
Concentration: Operations, Finance
GMAT 1: 650 Q49 V29
GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Other (Education)
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Re: There are n cards numbered consecutively, from 1 to n. Two cards are  [#permalink]

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New post 17 Jul 2017, 00:28
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1
Bunuel wrote:
There are n cards numbered consecutively, from 1 to n. Two cards are drawn. What is the probability that the number on the first card is less than the number on the second card?

(1) The two cards are drawn in succession, with replacement.
(2) n = 10.



(1) The first statement is not sufficient since we don't know the total number of cards: Insufficient
(2) We don't know if this is a case of with or without replacement; Insufficient

If we combine both statements, we know there are 10 cards that are drawn in succession with replacements.
The cases like (1,1), (2,2)---(10,10)(10 such possibilities) are not our favorable events. We need the number in the first to be less than scond.
First let us see how many cases are possible. This is a case of permutation since order matters. We are arranging 2 cards from 10 cards which can be done in 10P2 ways.
10P2 = 90. 10P2 doesn't include cases like (1,1), (2,2) etc.
So my total number ways are 90+10 =100. (10 here corresponds to the list of numbers from (1,1) to (10,10))

Out of the 90 possibilities, in half one number will be less than other, Other half will have that number greater than other.

So my number of possible events are 45.
Required probability is 45/100

Hence C
GMAT Club Bot
Re: There are n cards numbered consecutively, from 1 to n. Two cards are   [#permalink] 17 Jul 2017, 00:28
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There are n cards numbered consecutively, from 1 to n. Two cards are

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