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# A certain list consists of several different integers. Is

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A certain list consists of several different integers. Is [#permalink]

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12 Oct 2008, 22:04
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A certain list consists of several different integers. Is the product of all the integers in the list positive?
a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list
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13 Oct 2008, 05:11
C.

Stmt1 suggests that all the items are either positive or negative.

Stmt2 is not sufficient as one of the numbers can be 0.

Stmt1 and 2 together are sufficient.
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13 Oct 2008, 05:18
a. Could be either 6,-1,-2,4 or 6,-1,-2,-3,4
Not Sufficient

a. Could be either -2,-1,-2,4 or -1,-2,-3,-4
Not Sufficient

Together

Could be 6,-1,-2,-3,3,4 or 6,-1,-2,-3,-4,4

So Not Sufficient
I would go with E
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13 Oct 2008, 15:48
i will go with C as well..

basically we need to know if 0 is not in the middle..
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13 Oct 2008, 19:02
I'm confused with this

If highest and lowest number is positive and there's even numbers of integers:
set 1 (-2,1,2,-3)= positive
set 2 (-2, 1, -2, -3)= negative

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13 Oct 2008, 22:59
I'm confused with this

If highest and lowest number is positive and there's even numbers of integers:
set 1 (-2,1,2,-3)= positive
set 2 (-2, 1, -2, -3)= negative

In your set1, highest number is 2 and lowest number is -3 and these do not satisfy the condition.
In your set2, highest number is 1 and lowest number is -3 and these do not satisfy the condition.
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14 Oct 2008, 00:08
A certain list consists of several different integers. Is the product of all the integers in the list positive?
a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list

when the product of two integers is positive, it means that both integers are of the same sign.

So from A we understand that the largest and smallest integer are both of same sign. This means all the integers are either positive or negative. There is NO ZERO.

If all are positive then the product is positive, but if all are negative then we need to know the number of integers in the list. Because when we multiply even number of -ve numbers we get positive product and when we multiply odd number od -ve numbers the product is -ve.

So A alone not sufficient.

From B we know that there are even number of numbers. Not sufficient because we are not informed anything about the sign of the numbers. What if there is a 0 in between ?? Then the product wont be positive !! it will be 0

So B alone not sufficient.

Combined, sufficient ! From A we know that all numbers have same sign and there is no zero & from B we know that there are even number of numbers. SO the product is positive.

C.
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14 Oct 2008, 01:46
amitdgr wrote:
A certain list consists of several different integers. Is the product of all the integers in the list positive?
a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list

when the product of two integers is positive, it means that both integers are of the same sign.

So from A we understand that the largest and smallest integer are both of same sign. This means all the integers are either positive or negative. There is NO ZERO.

If all are positive then the product is positive, but if all are negative then we need to know the number of integers in the list. Because when we multiply even number of -ve numbers we get positive product and when we multiply odd number od -ve numbers the product is -ve.

So A alone not sufficient.

From B we know that there are even number of numbers. Not sufficient because we are not informed anything about the sign of the numbers. What if there is a 0 in between ?? Then the product wont be positive !! it will be 0

So B alone not sufficient.

Combined, sufficient ! From A we know that all numbers have same sign and there is no zero & from B we know that there are even number of numbers. SO the product is positive.

C.

Amit,

I find a logical flaw in your explanation. Product of greatest and smallest is postive it means both are of same sign but doesn't assure you all are of same sign. It gives you indication of all other integers signs. As the set is made of all integers, we can assume there is no ZERO.

So by stmt 1 - not sufficient - it doesnt give no. of integers in a set - but it gives you hint. suppose both smallest and greatest are positive integers then product is positive and all other digits lie between these 2. same is the case with negative integers. So it could be either positive or negative integers
by stmt 2 - not sufficient - it doesen't give you sign

combine both : it gives you even no of digits and either all positives or all negative digits - so by combining either way you get the product positive so Ans is C . I hope this helps. pls correct me where i m wrong.

OA ??
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14 Oct 2008, 02:03
rakeshmrana wrote:
amitdgr wrote:
A certain list consists of several different integers. Is the product of all the integers in the list positive?
a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list

when the product of two integers is positive, it means that both integers are of the same sign.

So from A we understand that the largest and smallest integer are both of same sign. This means all the integers are either positive or negative. There is NO ZERO.

If all are positive then the product is positive, but if all are negative then we need to know the number of integers in the list. Because when we multiply even number of -ve numbers we get positive product and when we multiply odd number od -ve numbers the product is -ve.

So A alone not sufficient.

From B we know that there are even number of numbers. Not sufficient because we are not informed anything about the sign of the numbers. What if there is a 0 in between ?? Then the product wont be positive !! it will be 0

So B alone not sufficient.

Combined, sufficient ! From A we know that all numbers have same sign and there is no zero & from B we know that there are even number of numbers. SO the product is positive.

C.

Amit,

I find a logical flaw in your explanation. Product of greatest and smallest is postive it means both are of same sign but doesn't assure you all are of same sign. It gives you indication of all other integers signs. As the set is made of all integers, we can assume there is no ZERO.

So by stmt 1 - not sufficient - it doesnt give no. of integers in a set - but it gives you hint. suppose both smallest and greatest are positive integers then product is positive and all other digits lie between these 2. same is the case with negative integers. So it could be either positive or negative integers
by stmt 2 - not sufficient - it doesen't give you sign

combine both : it gives you even no of digits and either all positives or all negative digits - so by combining either way you get the product positive so Ans is C . I hope this helps. pls correct me where i m wrong.

OA ??

ZERO is an even integer. So when a set is made of integers, it means that it can include zero, positive and negative number.

Consider this set { -5,-3,0,3,100} , this is a set of integers. So is { 0,2,4,5,10}

In our example we have statement 1 mentioning that the largest and smallest integer give out a positive product.

So the largest and smallest number have to be the same signed integers. This means, we have a set of integers that contains integers that are either left of zero or right of zero.
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14 Oct 2008, 06:47
based on the question is has to be an E

OA???
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14 Oct 2008, 21:57
I agree with amit's logic. Answer should be C. OA??
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14 Oct 2008, 22:22
I think the answer is c.
Statement 1 states that the mulplication of the greatest and smallest integer is +ve. It just means that these 2 integers should be of the same sign. ie; positive*positive or negative*negative. It does not mention the number of digits. If odd, then the whole product is negative otherwise positive or 0 if it is included.

Hence statement 1 is not sufficient

Statement 2 states that there is an even number of integers in the list. This means that it could be 3 negative numbers and one positive number or one negative and one positive or 2 negative and 2 positive. So it still could go both ways.

COmbining these 2 means that there are even number of positive or negative numbers.

Hence C.
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14 Oct 2008, 22:26
A certain list consists of several different integers. Is the product of all the integers in the list positive?

a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list

Intresting!!!!!!!!!!

C. There are even number of integers and they all are either -ve or +ve. in either case, 0 is not there.
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14 Oct 2008, 22:30
A certain list consists of several different integers. Is the product of all the integers in the list positive?
a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list

from a

all the numbers have the sam sign, however depending on their number that their product would be +ve or -ve....insuff

from 2

not suff

both

C
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23 Oct 2008, 10:40
LiveStronger wrote:
a. Could be either 6,-1,-2,4 or 6,-1,-2,-3,4
Not Sufficient

b. Could be either -2,-1,-2,4 or -1,-2,-3,-4
Not Sufficient

Together

Could be 6,-1,-2,-3,3,4 or 6,-1,-2,-3,-4,4

So Not Sufficient
I would go with E

Found my mistake and a terrible one too , yep the answer has to be C
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23 Oct 2008, 16:17
rakeshmrana wrote:
amitdgr wrote:
A certain list consists of several different integers. Is the product of all the integers in the list positive?
a. The product of the greatest and the smallest of the integers in the list is positive
b. There is an even number of integers in the list

when the product of two integers is positive, it means that both integers are of the same sign.

So from A we understand that the largest and smallest integer are both of same sign. This means all the integers are either positive or negative. There is NO ZERO.

If all are positive then the product is positive, but if all are negative then we need to know the number of integers in the list. Because when we multiply even number of -ve numbers we get positive product and when we multiply odd number od -ve numbers the product is -ve.

So A alone not sufficient.

From B we know that there are even number of numbers. Not sufficient because we are not informed anything about the sign of the numbers. What if there is a 0 in between ?? Then the product wont be positive !! it will be 0

So B alone not sufficient.

Combined, sufficient ! From A we know that all numbers have same sign and there is no zero & from B we know that there are even number of numbers. SO the product is positive.

C.

Amit,

I find a logical flaw in your explanation. Product of greatest and smallest is postive it means both are of same sign but doesn't assure you all are of same sign. [.......]
OA ??

yes, it does assure you. If smallest and largest are of the same sign, then everything in between is the same sign as well.
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23 Oct 2008, 16:55
LiveStronger wrote:
a. Could be either 6,-1,-2,4 or 6,-1,-2,-3,4
Not Sufficient

a. Could be either -2,-1,-2,4 or -1,-2,-3,-4
Not Sufficient

Together

Could be 6,-1,-2,-3,3,4 or 6,-1,-2,-3,-4,4

So Not Sufficient
I would go with E

In examples for A, we have to consider "the products of the greatest integer and the smallest one is positive". In your example, 6, -1, -2, 4 does not meet the requirement because 6*-2 = -12 (not positive).

IMO C
Re: even integers   [#permalink] 23 Oct 2008, 16:55
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