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A certain list consists 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 is an even number of integers in the list.
As I pointed out (1) is insuff coz we can take -4,-3,-2 as an example
(2) There are two cases
a)the number of negatives is odd AND the number of positives is odd
b)the number of negatives is even AND the number of positives is even
in b) the product of all integers in the list is positive
in a) the product of all integers in the list is negative
Also , consider the case of 0 belonging to the list, the product is 0, not positive as well as negative.
---> (2) insuff
(1) and (2)
(1) ensures that 0 doesn't belong to the list, that is to say
ALL integers in the list are positive or ALL of them are negative.
in the former, the stem statement is correct.
in the latter, all are negative but since the number of integers in the list is even---> their product is positive
C it is.
Himalaya: I noticed you re-choose C ...sorry for my ante-comment
A certain list consists 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 is an even number of integers in the list.
As I pointed out (1) is insuff coz we can take -4,-3,-2 as an example (2) There are two cases a)the number of negatives is odd AND the number of positives is odd b)the number of negatives is even AND the number of positives is even
in b) the product of all integers in the list is positive in a) the product of all integers in the list is negative Also , consider the case of 0 belonging to the list, the product is 0, not positive as well as negative. ---> (2) insuff
(1) and (2) (1) ensures that 0 doesn't belong to the list, that is to say ALL integers in the list are positive or ALL of them are negative. in the former, the stem statement is correct. in the latter, all are negative but since the number of integers in the list is even---> their product is positive
C it is.
Himalaya: I noticed you re-choose C ...sorry for my ante-comment
rigger> since the product of the smallest and the greatest is positive. These two numbers must be TOGETHER negative or TOGETHER positive.
That is to say
In the former case :a<b<c<d.......< x<0 -------> b,c,d,.......<0 or a,b,c,d......x<0
In the latter case : 0<a<b<c<d.......<x
(1) can have, for example, a -10 as the small number and a -1 as the greatest number. The product of those would be positive. Another example would be 1 as the small number and 10 as the greatest. The product for these would be also positive. The product will be positive with an even number of integers and be negative with an odd number of integers in the list. However, since we do not know how many integers are on the list, this statement is insufficient.
(2) tells us that there is an even number of integers in the list but gives no additional information. We need more information and hence, this statement is also insufficient.
TOGETHER these statements answer the question with a definitive yes. The product will be positive with an even number of integers - C.
Himalaya, can you explain how you came to your conclusion?
i am using example only:
from (i) suppose the set: {1,2,3,4,5,6,7}, the result is +ve. but if the set is: {-1, -2, -3, -4, -5, -6, -7}, the result is -ve. so not enough.
from (ii) suppose the set: {1,2,3,4,5,6}, the result is +ve. if the set is: {-1, -2, -3, -4, -5, -6}, the result is also +ve. if the set is: {-1, -2, 3, 4, 5, 6}, then the result is -ve. so still not enough...
from (i) and (ii) suppose the set must have elements either all +ve or all -ve and the number of elements are even. this is enough. if there are 6 elements, all elements must be either all +ve or all -ve because (i) says the product of gretest and smallest is +ve. so this is suff.
therefore, C is correct...
i initially picked A but immidiately (before lexique's post) rechoose C.
If you combine (1) and (2) or just take (1) alone, the product of the greatest and smallest should be positive. In your example above, c is obviously the greatest (and product negative). But, (1) rules out this combination.
1) smallest=-4, largest = -1 -->positive
smallest =1, largets=4 -->positive
not sufficient
2) integers in list even not sufficient
if we combine 1 and 2, it pretty much locks the range of number either all on the right side of the number line or all on the left side of the number line. Since the product of the larget and the smallest must be positive..
St1:
Set can be {-5,-4,-3,-2,-1}. Product of greatest and smallest integer in the list is positive but all elements are negative. Set can also be {1,2,3,4,5} and the product of the greatest and smallest element is positive but all elements are positive. Insufficient.
St2:
Insufficient. Set can be {-5,1,2,3} or {1,2,3,4}.
Using St1 and St2:
Insufficient. Set can be {-4,-3,-2,-1} or {1,2,3,4}
St1: Set can be {-5,-4,-3,-2,-1}. Product of greatest and smallest integer in the list is positive but all elements are negative. Set can also be {1,2,3,4,5} and the product of the greatest and smallest element is positive but all elements are positive. Insufficient.
St2: Insufficient. Set can be {-5,1,2,3} or {1,2,3,4}.
Using St1 and St2: Insufficient. Set can be {-4,-3,-2,-1} or {1,2,3,4}
Ans E
Question is: Is the product of all the integers in the list positive?
Using (1) and (2), you got:
Set can be {-4,-3,-2,-1} or {1,2,3,4}
just as a to keep in mind, in stmt 2, dont forget to consider the possibility of including zero in the list. Once you do that you no longer get a +ve result of the product of integers.
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