Set S consists of all prime integers less than 10. If two numbers are chosen form set 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 Guru/ Experts

S = {2. 3, 5, 7}

2*3=6

2*5=10

2*7=14

3*5=15

3*7=21

5*7=35

How to proceed further?

Thanks

Nandish

## Set S consists of all prime integers less than 10

##### This topic has expert replies

- GMATGuruNY
- GMAT Instructor
**Posts:**15532**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1897 members**GMAT Score:**790

It is not possible for the two products -- that of the two chosen numbers and that of the two unchosen numbers -- to be equal.NandishSS wrote:Set S consists of all prime integers less than 10. If two numbers are chosen form set 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

Each of the two products has the same probability of being greater.

Thus, the probability that the product of the two chosen numbers is greater = 1/2.

The correct answer is C.

Alternate approach:

The four prime numbers less than 10 -- 2, 3, 5, 7 -- can be divided into pairs as follows:

chosen = 2*3, unchosen = 5*7

chosen = 2*5, unchosen = 3*7

chosen = 2*7, unchosen = 3*5

chosen = 5*7, unchosen = 2*3

chosen = 3*7, unchosen = 2*5

chosen = 3*5, unchosen = 2*7

Of the 6 possible cases, only the last 3 are such that the two chosen numbers have a greater product than the two unchosen numbers.

Thus:

The probability that the 2 chosen numbers have a greater product = 3/6 = 1/2.

Mitch Hunt

Private Tutor for the GMAT and GRE

[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3

Private Tutor for the GMAT and GRE

[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3