Data Sufficiency

I computed the answer to be E, but its not.

example:

[1,2,3,4]

1. 1 * 4 = positive. CHECK
2. even number of integers. CHECK

product of all integers positive? YES

but

[1,2,-3,4]

1. 1 * 4 = positive. CHECK
2. even number of integers. CHECK

product of all integers positive? NO

Therefore, E

Why is it C?

Thanks. I really hope I am not misreading something

1 - insufficient. We just know that the list is comprised of
all positive or all negative numbers. With negative numbers,
the product of all integers in the list can be either positive or
negative depending on the number of elements (even or odd)

2 - insufficient. Just knowing that there are an even number of
elements in the list does not help as the numbers can be positive
or negative

Combining 1 and 2, we have 2 cases -- either all numbers are positive
or all numbers are negative. In the all-positive case, it is fairly
straightforward to see that the product is positive.

In the all-negative case, since we have even number of elements, we
can say that the product of all integers = positive

Hence C

In your example, [1,2,-3,4],

1. 1 * 4 = positive. CHECK <-- this should be -3 * 4 = -12

The question mentions a list of integers and wants to find out if the product of all the ones on the list is positive.

Statement I says that the product of the smallest and the greatest integer on the list is positive..

Now consider the following lists:

-15, - 11, -8, -7, -3, 0, 2, 9

Here the product of -15 and 9 is negative

Hence we know that either the smallest and greatest integer are both positive (Note + * + = +); or both are negative (- * - = -)

But even in this scenario we cant predict if the product of all the integers on the list is positive or negative

In a list -15, -14 , - 3, and -1 the product of all is positive but in the list - 15, -13, -12, - 8, -4 the product is negative. Hence Statement I is insufficient

Statement II:

There are even number of integers on the list. All we know is that there are even number of integers. But we cant predict the product

In case of -3, -2, 1, 4, 5, 6 - the product is negative

In case of -20, -19, -13, -14 - the product is positive.

Hence Statement II alone is insufficient


If we combine both we can say that the product for sure will be positive. Hence C

Hi maxim730,

The error you made is this:
in the example, you gave a list of numbers [1,2,-3,4]
then you wrote 1 * 4 = positive
The above is not consistent with statement 1, which states that the product of the smallest
and the greatest number is positive. so you cannot use the above example coz it gives you -12[-3,1,2,4]

C is sufficient. here's why:
combining 1 and 2, you get only 2 possibilities:
1. greatest and smallest are positive making the product positive
1,5,7,9

2. greatest and smallest are negative, still yielding a positive product

-10,-1
-7,-6,-4,-1
-100,-78,-50,-30,-24,-10 .....etc

Why are we ignoring 0 in our example? 0 is also integer.
Combining 1 andd 2, and take 0 as case.. it can be positive or negative.

Please help.

anky666 wrote:Why are we ignoring 0 in our example? 0 is also integer.
Combining 1 andd 2, and take 0 as case.. it can be positive or negative.

Please help.

We cant have 0 here.

The first statement states the product is POSITIVE

therefore there cant be 0.

e.g
[0,2,3,47]

product of 0*7 = 0 [0 is neither positive nor negative]

[-13,-4, -3, -1,0]

product of -13*0 = 0 [0 is neither positive nor negative]


therefore,

The integers in the SET are either greater than 0 or less than 0 but never equal to 0

Hope this helps.