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# M10-14

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Intern
Joined: 14 Aug 2017
Posts: 13

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30 Aug 2018, 20:42
Hi Bunuel,

Does this 'Not necessarily different' terminology given in the question implies that the number is not repeated?
Because when I first attempted this question i got 1/2 i.e . (1/4)*(3/3) + (3/4)*(1/3) = (1/2)

But now when I saw your solution, I came to know that the numbers should not be reduced and should be kept same.
I just wanted to get it confirmed with you that everytime in future if I see this term 'Not necessarily different' should I consider that the number is not repeated?
Math Expert
Joined: 02 Sep 2009
Posts: 55631

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30 Aug 2018, 21:00
1
varmashreekanth wrote:
Hi Bunuel,

Does this 'Not necessarily different' terminology given in the question implies that the number is not repeated?
Because when I first attempted this question i got 1/2 i.e . (1/4)*(3/3) + (3/4)*(1/3) = (1/2)

But now when I saw your solution, I came to know that the numbers should not be reduced and should be kept same.
I just wanted to get it confirmed with you that everytime in future if I see this term 'Not necessarily different' should I consider that the number is not repeated?

If a number is selected from set S at random and then another number, not necessarily different, is selected from set S at random, ...

The highlighted part in the question means that from S={2,3,5,7} we can choose any number more than once. So, we can choose the following two numbers:
(2,2)
(2,3)
(3,2)
(2,5)
(5,2)
(2,7)
(7,2)

(3,3)
(3,5)
(5,3)
(3,7)
(7,3)
(5,5)
(5,7)
(7,5)
(7,7)
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Intern
Joined: 14 Aug 2017
Posts: 13

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30 Aug 2018, 22:07
Thanks a lot Bunuel. Now I understood the scenario.
Intern
Joined: 26 Aug 2017
Posts: 10

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23 Sep 2018, 14:28
susheelh wrote:
Hello Bunuel

I think this is a high-quality question and I agree with the solution. I have the same conceptual gap as Demba below. Can you please help?

Usually, for questions like these, I find the total possibilities first and then the favourable outcomes. To do this, its necessary to know if the order of outcome matters.

Clearly, in this question order matters. (2,3) is different from (3,2). How do we understand after reading the question that order matters? Is it because the question says 'not necessarily different' which implies repetition is allowed?

I was comparing this solution with this one - https://gmatclub.com/forum/m20-184246.html#p1859217. In this solution that I pasted, Order does not matter. So, we wanted to know how to decide after reading a question if order matters or no.

I hope I was able to communicate what I intend to say.

Thanking you in advance!

Demba wrote:
I struggle to know when order matters. Why is the answer not simply 1/4*3/4?

Why is picking 2 then 3 or 5 or 7 different from picking picking 3 or 5 or 7 then 2?

Bumping
Intern
Joined: 18 Dec 2015
Posts: 2

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17 Dec 2018, 22:26
rsamant wrote:
I quickly listed out the set of numbers (2,2) (2,3) (2,5) (2,7) (3,3) (3,5) (3,7) (5,5) (5,7) and (7,7) and then I counted the only odd pair which left me with a probability of 3/10. Why is this method incorrect?

If you do it that way without order, you have to consider that combination {2,3} is more likely than combination {2,2} (twice as likely). If you don't consider this you'd get 3/10 which is not correct.
Intern
Joined: 21 Sep 2013
Posts: 20

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28 Feb 2019, 03:16
I think this is a poor-quality question and I agree with explanation. Would the question be framed better if it read as follows:-

Set S consists only of all prime #s less than 10 , instead of Set S consists of all prime #s less than 10 -- this can be misread to mean all integers less than including the prime #s or even worse all integers less than 10 including negative integer.

Just a thought, would be happy if somebody can comment on the same.
Re M10-14   [#permalink] 28 Feb 2019, 03:16

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# M10-14

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