DS: Number properties

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 109
Joined: Sun Oct 21, 2012 5:10 am
Followed by:1 members

DS: Number properties

by psm12se » Sat Nov 30, 2013 7:02 am
Set S consists of more than two integers. Are all the numbers in set S negative?

(1) The product of any three integers in the list is negative
(2) The product of the smallest and largest integers in the list is a prime number.

I marked the answer as B but the OA is C

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 30, 2013 7:41 am
psm12se wrote:Set S consists of more than two integers. Are all the numbers in set S negative?

(1) The product of any three integers in the list is negative
(2) The product of the smallest and largest integers in the list is a prime number.
Target question: Are all the numbers in set S negative?

Statement 1: The product of any three integers in the list is negative
There are only 2 scenarios in which the product of 3 integers is negative.
scenario #1: all 3 integers are negative
scenario #2: 2 integers are positive, and 1 integer is negative

So, here are two possible cases that satisfy statement 1:
Case a: set S = {-3, -2, -1}, in which case all of the numbers in set S are negative
Case b: set S = {-1, 1, 3}, in which case not all of the numbers in set S are negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The product of the smallest and largest integers in the list is a prime number.
Here are two possible cases that satisfy statement 2:
Case a: set S = {-3, -2, -1}, in which case all of the numbers in set S are negative
Case b: set S = {1, 2, 3}, in which case not all of the numbers in set S are negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Earlier, we learned that, if the product of 3 integers is negative, then there are 2 possible scenarios:
- scenario #1: all 3 integers are negative
- scenario #2: 2 integers are positive, and 1 integer is negative

Statement 2 tells us that the product of the smallest and largest integers in the list is a prime number. In other word, the product of the smallest and largest integers is POSITIVE.
This allows us to eliminate scenario #2, because under this scenario, the smallest integer in set S would be negative and the largest would be positive, so the product would be NEGATIVE (and prime numbers, by definition, are positive)

This leaves us with scenario #1.
From here, we can conclude that, if the product of any three integers is ALWAYS negative, then ALL of the integers in the set must be negative.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

Master | Next Rank: 500 Posts
Posts: 109
Joined: Sun Oct 21, 2012 5:10 am
Followed by:1 members

by psm12se » Sat Nov 30, 2013 8:05 am
Thanks Brent for the reply.

Yes, question has been copied here correctly and OA is C

Here is my analysis:

Statement A
possible lists are (-1, -2, -3) and (-1, 1, 3)

Not Sufficient

Statement B
Possible lists are (-1, -2, -3) and (1, 2, 3)

Combining both the statements should give us the answer,

I am confused about the prime numbers. Is it possible to have a -ve prime number in which case answer would be E

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 30, 2013 8:09 am
psm12se wrote: I am confused about the prime numbers. Is it possible to have a -ve prime number in which case answer would be E
Prime numbers, by definition, are positive.

Here's how the OG defines prime numbers: A prime number is a positive integer that has exactly two different positive divisors, 1 and itself.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Sun Dec 01, 2013 10:40 pm
psm12se wrote:Set S consists of more than two integers. Are all the numbers in set S negative?

(1) The product of any three integers in the list is negative
(2) The product of the smallest and largest integers in the list is a prime number.

I marked the answer as B but the OA is C
Here's another way:

From S1, we have at most two positive integers (if we had three +'s, we'd have + * + * + = +). If we have 0 positives, we have a set of three negative integers. If we have two positives, we have one negative. Since we already have two possible outcomes (all negative or only one negative), INSUFFICIENT.

From S2, we either have (1) * (prime) = prime or (-1) * (-prime) = prime. Since our range (smallest to largest) goes from either pos -> pos or neg -> neg, either ALL our #'s are positive or ALL our #'s are negative. INSUFFICIENT.

Together, we know from S1 that we have at most two positive integers, but we know from the stem that we have more than two integers. Hence we must have at least one negative, and from S2 we know that ALL our integers are negative.