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Director

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If x and y are selected from 2, 3, 4, 5, and 6, what is the [#permalink ]
21 Mar 2006, 23:24

If x and y are selected from 2, 3, 4, 5, and 6, what is the probability that x*y is divisible by 4?

Director

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isn't it 2/5?

5C2 total possible number of picks... = 10

Favourable picks 4

Intern

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is it 1/2.

5/5C2

Thanks

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Director

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Gmate wrote:

is it 1/2. 5/5C2 Thanks

Oh yeah, 5 favourable outcomes.... 1/2

Director

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can you guys elaborate on this one? Is there a quick way or did you guys just calclated all the outcomes? thanks

Senior Manager

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total outcome 10
favorable outcome 5
5/10 = 1/2

SVP

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I think we get 6 favorable outcomes.
(2,4) (3,4) (4,4) (5,4) (6,4) (2,6)

Director

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vivek123 wrote:

I think we get 6 favorable outcomes. (2,4) (3,4) (4,4) (5,4) (6,4) (2,6)

Nope you can not count 4 and 4, because you have to choose from 2 3 4 5 and 6... there are no two 4s

Director

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joemama142000 wrote:

can you guys elaborate on this one? Is there a quick way or did you guys just calclated all the outcomes? thanks

We calculated total outcomes by using the combination formula....

n!/(k!(n!-k!))

n! - denotes the total number of choices we have = 5

k! - denotes the number of choices we are arranging = 2

In this example n!=1*2*3*4*5

k!=1*2

And yes, the favourable outcomes are calculated by hand

but it does not take long... max 1 minute...

Manager

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vivek123 wrote:

I think we get 6 favorable outcomes. (2,4) (3,4) (4,4) (5,4) (6,4) (2,6)

in that case (2,2) and (6,6) would work too but it would be over 5^2 = 25

I guess Sima is right

GMAT Club Legend

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x*y must be a multiple a 4: 4,8,12,16,20,24,28
(x,y) sets
(2,4)
(2,6)
(3,4)
(4,5)
(4,6)
We don't have to consider (4,2) (6,2) (4,3) (5,4) amd (6,4) as we're not interested in placing but groupings.
# of ways ot pick any 2 numbers = 5C2 = 10
P = 5/10 = 1/2

Director

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I got the favourable outcomes as
2 2
2 4
2 6
3 4
4 2
4 3
4 4
4 5
4 6
5 4
6 2
6 4
Total outcomes = 25 (x can be any of the 5 nos and y can be any of the 5 nos.)
Probability = 12/25

Director

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remgeo wrote:

I got the favourable outcomes as 2 2 2 4 2 6 3 4 4 2 4 3 4 4 4 5 4 6 5 4 6 2 6 4 Total outcomes = 25 (x can be any of the 5 nos and y can be any of the 5 nos.) Probability = 12/25

I had the same result, because no where it is written that once you picked a number, there is one less for the next selection.

So my answer is 12/25.

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