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Bunuel
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A list contains several different integers. Is the product of all the 06 Dec 2016, 07:12
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

78% (01:21) correct 22% (01:21) wrong based on 63 sessions

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

(1) There are an odd number of integers in the list.
(2) The product of the greatest and smallest numbers in the list is less than zero.
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E
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A list contains several different integers. Is the product of all the 06 Dec 2016, 08:38
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Bunuel
A list contains several different integers. Is the product of all the integers in the list positive?

(1) There are an odd number of integers in the list.
(2) The product of the greatest and smallest numbers in the list is less than zero.
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(1) Since we dont know the sign of integers in that list, we dont know the sign of the product. Insufficient.

(2) The product of the greatest and smallest numbers is negative, so these two numbers have different signs. Hence the greatest number is positive and the smallest number is negative.

However, we dont know the other numbers in that list. Insufficient.

Combine (1) and (2)

If that list contains 3 different integers -2, -1, 3, then the product of all the integers is \((-2)\times (-1) \times 3 = 6\) is positive.
If that list contains 3 different integers -2, 1, 3, then the product of all the integers is \((-2)\times 1 \times 3 = -6\) is negative.

Hence, insufficient.

The answer is E.
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A list contains several different integers. Is the product of all the 06 Dec 2016, 11:22
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Bunuel
A list contains several different integers. Is the product of all the integers in the list positive?

(1) There are an odd number of integers in the list.
(2) The product of the greatest and smallest numbers in the list is less than zero.
Show more

FROM STATEMENT - I ( INSUFFICIENT )

Let there be 3 numbers , -1, -2 & 5 , So product will be Positive
Let there be 3 numbers , -1, 2 & 5 , So product will be Negative

So, From this statement we can not get a unique solution..


FROM STATEMENT - II ( INSUFFICIENT )

Let the greatest no be -1 & least no be -2 , so Product will not be Positive & less than 0
Let the greatest no be 2 & least no be -1 , so Product will be Negative & less than 0

So, From this statement we can not get a unique solution..

FROM STATEMENT - I & II ( INSUFFICIENT )

Let there be 3 numbers , -1, -2 & 5 , So product will be Negative and less than 0
Let there be 3 numbers , -1, -2 & -5 , So product will not be Negative and less than 0

Thus, Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed, answer will be (E)
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A list contains several different integers. Is the product of all the 06 Dec 2016, 18:25
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Bunuel
A list contains several different integers. Is the product of all the integers in the list positive?

(1) There are an odd number of integers in the list.
(2) The product of the greatest and smallest numbers in the list is less than zero.

FROM STATEMENT - I ( INSUFFICIENT )

Let there be 3 numbers , -1, -2 & 5 , So product will be Positive
Let there be 3 numbers , -1, 2 & 5 , So product will be Negative

So, From this statement we can not get a unique solution..


FROM STATEMENT - II ( INSUFFICIENT )

Let the greatest no be -1 & least no be -2 , so Product will not be Positive & less than 0
Let the greatest no be 2 & least no be -1 , so Product will be Negative & less than 0

So, From this statement we can not get a unique solution..

FROM STATEMENT - I & II ( INSUFFICIENT )

Let there be 3 numbers , -1, -2 & 5 , So product will be Negative and less than 0
Let there be 3 numbers ,-1, -2 & -5 , So product will not be Negative and less than 0

Thus, Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed, answer will be (E)

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The highlighted doesn't satisfy (II) since (-1)(-5)=5>0
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A list contains several different integers. Is the product of all the 07 Dec 2016, 09:13
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Bunuel
If a list contains several distinct integers, is the product of the integers in the list positive?

(1) There are an odd number of integers in the list.
(2) The product of the greatest and smallest numbers in the list is less than zero.
Show more


product in the list could be +ve , -ve or 0

from 1

no idea about signs .. insuff

from 2

the least number in the list is -ve and the largest is positive ... insuff

both

the -ve integer could be the only negative in the list , or the list could contain zero or the product of the set members could be +ve ( yes and no)

E
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A list contains several different integers. Is the product of all the 16 Jul 2023, 07:54
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Bunuel
A list contains several different integers. Is the product of all the integers in the list positive?

(1) There are an odd number of integers in the list.
(2) The product of the greatest and smallest numbers in the list is less than zero.
Show more

A list contains different integers, and we need to answer the question:

Is their product > 0 ?

A product of integers is positive if and only if their list contains an even number of negative numbers AND doesn’t contain zero. [If there are no negative numbers in the list, then the number of negative numbers is zero, which is an even number.]

Statement One Alone:

=> There are an odd number of integers in the list.

We don’t know whether the list contains an even number of negative numbers, and we don’t know whether the list contains zero.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> The product of the greatest and smallest numbers in the list is less than zero.

In other words, there are both negative and positive numbers in the list.

Again, we don’t know whether the list contains an even number of negative numbers, and we don’t know whether the list contains zero.

Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

We still don’t know whether the list contains an even number of negative numbers, and we still don’t know whether the list contains zero.

The two statements together are not sufficient.

Answer: E
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