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# Set S consists of all prime numbers less than 10. If two num

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Intern
Joined: 18 Nov 2011
Posts: 34
Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
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Set S consists of all prime numbers less than 10. If two num  [#permalink]

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Updated on: 11 Jan 2013, 13:35
2
6
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:01) correct 36% (02:06) wrong based on 154 sessions

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Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5

Originally posted by hitman5532 on 11 Jan 2013, 12:45.
Last edited by Bunuel on 11 Jan 2013, 13:35, edited 1 time in total.
RENAMED THE TOPIC.
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11 Jan 2013, 13:00
2
Prime integers below 10: 2, 3, 5, 7

Total outcomes: Number of ways you can choose 2 from 4 = $$4C2= 6 pairs$$
No. of ways for Event: Pairs that will have products greater than product of pairs not selected i.e. (3,5), (3,7), (5,7) $$= 3 pairs$$

Probability = number of ways/Total outcomes $$= 3/6 = 1/2$$

Hence choice(C) is correct.
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Re: Set S consists of all prime numbers less than 10. If two num  [#permalink]

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11 Jan 2013, 13:37
2
hitman5532 wrote:
Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5

S={2, 3, 5, 7}

The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.
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GMAT Date: 06-18-2013
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Re: Set S consists of all prime numbers less than 10. If two num  [#permalink]

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11 Jan 2013, 14:51
Bunuel wrote:
hitman5532 wrote:
Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5

S={2, 3, 5, 7}

The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.

Sorry about that, failed to remember that after reading the rules a while back.

This question was nice and simple when I don't make a stupid mistake and put 9 in with the set (doh!)
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Re: Set S consists of all prime numbers less than 10. If two num  [#permalink]

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07 Aug 2017, 18:13
2
Primes in action -> 2,3,5,7

Cases ->
2,3 => (NO)
2,5 => (NO)
2,7 => (NO)
3,5 => (YES)
3,7 => (YES)
5,7 => (YES)

Total cases -> 6
Favourable cases -> 3

P(E) => 3/6 => 1/2

Hence C.
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Re: Set S consists of all prime numbers less than 10. If two num  [#permalink]

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12 Apr 2019, 05:20
Bunuel

Should we assume that the choice is without replacement if it's not directly mentioned in the prompt (something like "2 unique" or "2 different" numbers)? If we could pick the same number twice it would be 1/2 + 1/4 = 3/4, right? (since only 7*7 will be have a greater product than the remaining possibilities)
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Re: Set S consists of all prime numbers less than 10. If two num  [#permalink]

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14 Apr 2019, 08:31
hitman5532 wrote:
Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5

Hi, how can we know that (3,5) is the same as choosing (5,3) for example?
Re: Set S consists of all prime numbers less than 10. If two num   [#permalink] 14 Apr 2019, 08:31
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