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Probability of sum of 2 distinct pos. divisors of 64 is <

Expert replies
by gmattesttaker2 » Sun May 04, 2014 11:09 pm
Hello,

Can you please assist with this problem:

If two distinct positive divisors of 64 are randomly selected, what is the probability that their sum will be less than 32?


OA: [spoiler]10/21[/spoiler]


Positive divisors of 64 are 1, 2, 4, 8, 16, 32, 64

The following pairs have a sum which is less than 32:

1,2
1,4
1,8
1,16

2,4
2,8
2,16

4,8
4,16


So probability of selecting two distinct positive divisors whose sum is less than 32 is:

P(Selecting a 1 and 2 or 4 or 8 or 16) = 1/7 x 4/6 = 4/42
+
P(Selecting a 2 and 4 or 8 or 16) = 1/7 x 3/6 = 3/42
+
P(Selecting a 4 and 8 or 16) = 1/7 x 2/6 = 2/42

= 4/42 + 3/42 + 2/42
= 9/42
= 3/14

Can you please tell me where I am going wrong? Thanks for your help.

Best Regards,
Sri
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Source: — Problem Solving |

by [email protected] » Sun May 04, 2014 11:26 pm
Hi Sri,

You've deduced everything correctly, but you've made a small logic mistake with your calculations.

Picking 2 terms with a sum that is less than 32, you're ultimately saying "don't pick 32 or 64, any other 2 numbers will do."

So, with 7 numbers to choose from, the math is….

(5/7)(4/6) = 20/42 = 10/21

Your calculations assume that there's only one way to pick the "first number", which is NOT the case.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by gmattesttaker2 » Mon May 05, 2014 6:06 pm
[email protected] wrote:Hi Sri,

You've deduced everything correctly, but you've made a small logic mistake with your calculations.

Picking 2 terms with a sum that is less than 32, you're ultimately saying "don't pick 32 or 64, any other 2 numbers will do."

So, with 7 numbers to choose from, the math is….

(5/7)(4/6) = 20/42 = 10/21

Your calculations assume that there's only one way to pick the "first number", which is NOT the case.

GMAT assassins aren't born, they're made,
Rich
Hello Rich,

Thanks a lot for the explanation.

Best Regards,
Sri
Join the discussion