Statement (1) tells you that the greatest and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

A bit elaborate approach

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

Hi Raz

I can pretty much follow the logic....my issue is the statement 1 which to me means what the product of the greatest and the smallest integer is positive - a fact which to my mind has no bearing on other integers

am I missing something here?....I am pretty decent in quant so really unsure why am I not able to interpret statement 1 as others are able to

raz1024 wrote:Statement (1) tells you that the greatest and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

gmatmillenium wrote:Hi Raz

I can pretty much follow the logic....my issue is the statement 1 which to me means what the product of the greatest and the smallest integer is positive - a fact which to my mind has no bearing on other integers

am I missing something here?....I am pretty decent in quant so really unsure why am I not able to interpret statement 1 as others are able to

raz1024 wrote:Statement (1) tells you that the and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

The issue with statement 1 is that it doesn't tell us how many integers we have:

If our list of integers is {-2, -1}, the product of the smallest and greatest is (-2)(-1) = 2, and the product all the integers is also (-2)(-1) = 2.
If our list of integers is {-3, -2, -1}, the product of the smallest and greatest is (-3)(-1) = 3, but the product of all the integers is (-3)(-2)(-1) = -6.

So we can't tell whether the product of all the integers is positive or negative, and the statement is INSUFFICIENT.

Some advice for number property questions:

Make the question less abstract. Try different kinds of actual numbers so that you can more clearly see what's going on.

Mitch

Let us say the product of greatest and smallest integers is positive and you also know that there are even # (let us say 4) of integers...

in this case how can we determine the sign of the product of all integers....the intermediate terms in the list can be say one positive and one negative in which case the product of all integers is -ve whereas if both intermediate terms are positive or both negative then the the product of all integers is +ve...

GMATGuruNY wrote:

gmatmillenium wrote:Hi Raz

I can pretty much follow the logic....my issue is the statement 1 which to me means what the product of the greatest and the smallest integer is positive - a fact which to my mind has no bearing on other integers

am I missing something here?....I am pretty decent in quant so really unsure why am I not able to interpret statement 1 as others are able to

raz1024 wrote:Statement (1) tells you that the and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

The issue with statement 1 is that it doesn't tell us how many integers we have:

If our list of integers is {-2, -1}, the product of the smallest and greatest is (-2)(-1) = 2, and the product all the integers is also (-2)(-1) = 2.
If our list of integers is {-3, -2, -1}, the product of the smallest and greatest is (-3)(-1) = 3, but the product of all the integers is (-3)(-2)(-1) = -6.

So we can't tell whether the product of all the integers is positive or negative, and the statement is INSUFFICIENT.

Some advice for number property questions:

Make the question less abstract. Try different kinds of actual numbers so that you can more clearly see what's going on.

gmatmillenium wrote:Mitch

Let us say the product of greatest and smallest integers is positive and you also know that there are even # (let us say 4) of integers...

in this case how can we determine the sign of the product of all integers....the intermediate terms in the list can be say one positive and one negative in which case the product of all integers is -ve whereas if both intermediate terms are positive or both negative then the the product of all integers is +ve...

GMATGuruNY wrote:

gmatmillenium wrote:Hi Raz

I can pretty much follow the logic....my issue is the statement 1 which to me means what the product of the greatest and the smallest integer is positive - a fact which to my mind has no bearing on other integers

am I missing something here?....I am pretty decent in quant so really unsure why am I not able to interpret statement 1 as others are able to

raz1024 wrote:Statement (1) tells you that the and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

The issue with statement 1 is that it doesn't tell us how many integers we have:

If our list of integers is {-2, -1}, the product of the smallest and greatest is (-2)(-1) = 2, and the product all the integers is also (-2)(-1) = 2.
If our list of integers is {-3, -2, -1}, the product of the smallest and greatest is (-3)(-1) = 3, but the product of all the integers is (-3)(-2)(-1) = -6.

So we can't tell whether the product of all the integers is positive or negative, and the statement is INSUFFICIENT.

Some advice for number property questions:

Make the question less abstract. Try different kinds of actual numbers so that you can more clearly see what's going on.

For the product of the smallest and greatest to be positive, both will have to be negative, or both will have to be positive:

{-3, -2} works because (-3)(-2) = 6

{2, 3} works because 2*3 = 6.

But if the smallest is negative and the greatest is positive, the product of the smallest and greatest will be negative:

{-3, 2} won't satisfy statement 1 because (-3)(2) = -6.

Does this help?

Mitch

I now know what i been missing sight of - all integers will bear the same sign as that of the smallest or largest integers in this case.....(cant believe it took me so long to figure).....and incase you thought am a complete non starter in quant, I been scoring 51 regularly in practice tests (just not sure how the wiring went wrong here)

GMATGuruNY wrote:

gmatmillenium wrote:Mitch

Let us say the product of greatest and smallest integers is positive and you also know that there are even # (let us say 4) of integers...

in this case how can we determine the sign of the product of all integers....the intermediate terms in the list can be say one positive and one negative in which case the product of all integers is -ve whereas if both intermediate terms are positive or both negative then the the product of all integers is +ve...

GMATGuruNY wrote:

gmatmillenium wrote:Hi Raz

I can pretty much follow the logic....my issue is the statement 1 which to me means what the product of the greatest and the smallest integer is positive - a fact which to my mind has no bearing on other integers

am I missing something here?....I am pretty decent in quant so really unsure why am I not able to interpret statement 1 as others are able to

raz1024 wrote:Statement (1) tells you that the and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

The issue with statement 1 is that it doesn't tell us how many integers we have:

If our list of integers is {-2, -1}, the product of the smallest and greatest is (-2)(-1) = 2, and the product all the integers is also (-2)(-1) = 2.
If our list of integers is {-3, -2, -1}, the product of the smallest and greatest is (-3)(-1) = 3, but the product of all the integers is (-3)(-2)(-1) = -6.

So we can't tell whether the product of all the integers is positive or negative, and the statement is INSUFFICIENT.

Some advice for number property questions:

Make the question less abstract. Try different kinds of actual numbers so that you can more clearly see what's going on.

For the product of the smallest and greatest to be positive, both will have to be negative, or both will have to be positives:

-3, -2 works because (-3)(-2) = 6

2, 3, works because 2*3 = 6.

But if the smallest is negative and the greatest is positive, the product of the smallest and greatest will be negative:

-3, 2 won't work because (-3)(2) = -6.

Does this help?

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