Data Sufficiency

A set consists of of several different integers. Is the product of all the integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive

(2) There are an even number of integers in the list

Statement 1: Smallest & greatest number product is Positive. So both these numbers are either Positive or Negative. (-10,-5,...,-1) or (3,6,... 10) But as we don't know the number of elements in the set, we cannot be sure if the product of all numbers will be Positive or Negative - Insufficient

Statement 2: A set contains even number of elements, can have product of all numbers either +/-.

Combining both the statements:
The set of integers are either all positive and even or Negative and even. The product will always be positive. Sufficient

Ans (C)

Let's say the set has 4 numbers:

Combining statements (1) and (2):

scenerio1:

2, -3, 4, 5 -- the product of these four numbers is a negative

scenario 2:

-2, 3, 4, -5 -- the product of these four numbers is positive

Both scenarios satisfy statement (1) and statement (2), but the answer could still go both ways.

I'm probably misinterpreting the question.

(1) The product of the greatest and smallest of the integers in the list is positive

-1 -2 -3

1 2 3

Insuf

(2) There are an even number of integers in the list

-1 3

2 3

INSUF

1+2)

first statement tells us the numbers are either POSITIVE or NEGATIVE

Second statement tell us the ones in the middle can be PAIRS

1 2 3 4 = +

-1 -2 -3 - 4 = +

Choose C

logitech,

How did you derive from statement (2) that the integers in the middle can be pairs?

Emawk wrote:logitech,

How did you derive from statement (2) that the integers in the middle can be pairs?

(2) There are an even number of integers in the list

Since there are even numbers in the set

EVEN - (the first + the last) = ANOTHER EVEN number

So Even Number can be paired. In other words they are divisible by 2

logitech wrote:

Emawk wrote:logitech,

How did you derive from statement (2) that the integers in the middle can be pairs?

(2) There are an even number of integers in the list

Since there are even numbers in the set

EVEN - (the first + the last) = ANOTHER EVEN number

So Even Number can be paired. In other words they are divisible by 2

So statement (2) isn't saying n = even?

Im confused also.

Statement 1 tells us that the product of the highest and lowest is Positive
so lets say our numbers are :

1 2 3 4 1 and 4 have the same sign, either both - or both + to give us a postive product

Statement 2 says there are an even # of numbers in the set.
So 1 2 3 4 still works here.
Why cant it be -2 +3 ? or +3 , -2? There are still an even # of numbers here

logitec, would you be able to clarify statement (2) more?

Emawk the conclusion from statement A is that All the numbers in the seris are either positive or Negative. ( From Product of Smallest and largest number is a positive number)

statement B : number of elements in set is even.

If we combine both the statements:
1. Seris contains all Positive or Negative ( so a set cannot contain have (-3,2 or 4,-6 etc)
Eg: -7,-4,-3,-2 ( All negative nos)
1,2,4,5,7,8 ( All positive nos)
2. Even number of integers

As all the numbers are either:
A. Positive and the set has even number of integers - Product will be positive
B. Negative nos and the set has even nos of integers - Product will be positive.

Hence (C) as the product will always be positive

Can someone shed some more light on this problem?

Are we supposed to assume that the list is in ascending order?

How else is C possible?

Please help!!

Cheers,
Pd

From statement 1,the product of small and large number is positive.

The possible scenarios are like below,

S1={-1,-2,-3}, +ve

S2={1,2,3},+ve


If it contain both positive and negative integers,statement 1 will not be valid.

Ex:S={-1,2,3},the product is -ve

So Set should contain either all positive or all negative integers.

If the set of integers is as S2,it it sufficient. But for S1 since the number of integers are unknown,statement 1 is insufficient.


From statement 2,there are even number of integers in a set.So the possible scenarios,

S1={-1,2,3,4}=-ve

S2={1,2,3,4}=+ve


Since both scenarios are there statement 2 is insufficient.

Combining both,the conditions are,

1.The sets should contain either all positive integers or all negative integers.
2.There should be even number of intergers.

So the possible scenarios are,

S1={-1,-2,-3,-4}

S2={1,2,3,4}

since there are even number of integers,the product of all integers will be positive for both S1 and S2 and sufficient.

Hence answer is C

[The reply below is copied from this thread]

To have a positive product, we must have an even number of negatives (0, 2, 4...) so that the negatives will cancel out in the multiplication.

REPHRASE: Are there an even number of negatives?

1) Max * Min is positive means Max and Min have the same sign. If they're both positive, then everything is positive and so is the product of all integers. However, if Max and Min are both negative, the product could be negative if we do NOT have an even number of negatives. Example {-3, -2, -1}. NOT SUFFICIENT.

2) By itself, this doesn't tell us whether there is an even number of negatives. Doesn't answer our rephrase.

Merge statements: (2) tells us that we have an even number of values. Since all the values have the same sign (1 says Max and Min have the same sign), either we have all positives or we have an even number of negatives. Either way, the product of all terms will be positive.

The answer is C

If the explanations above don't make sense to you, watch the step-by-step video solution. This is GMATPrep question 1106.

You can practice similar questions by using the Drill Engine to generate timed drills and setting topic='Number Properties' and difficulty='500-600 & 600-700'

Best of luck,
-Patrick

SHOULD WE ASSUME THAT THE LIST OF NUMBERS IS IN ORDER? Otherwise, it doesn't make sense to choose C. Please some EXPERT help

Thouraya wrote:SHOULD WE ASSUME THAT THE LIST OF NUMBERS IS IN ORDER? Otherwise, it doesn't make sense to choose C. Please some EXPERT help

Hi!

It doesn't matter if the list is in order. "Greatest" means the biggest number in the list and "smallest" means the smallest number in the list, regardless of how you arrange the terms. For example, in the sets:

{1, 2, 3, 4, 92}

and

{2, 4, 92, 3, 1}

the product of the greatest and smallest numbers is still 92*1 = 92.

I hope that clears up your confusion - if not, let me know exactly why you think ordering the list matters.