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Ithink both statement together is not sufficient, so what is the real answer here? why do care about the existence of 0 ?

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

(1) The product of the greatest and smallest of the integers in the list is positive. Two cases: A. all integers in the list are positive: in this case product of all integers would be positive; OR B. all integers in the list are negative: now, if there is even number of integers, then product of all integers would be positive BUT if there is odd number of integers, then product of all integers would be negative.

Not sufficient.

(2) There is an even number of integers in the list. Clearly insufficient. {-2, 2} - answer NO; {2,4} - answer YES.

(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.

Re: Stuck with an easy number property....:( [#permalink]

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23 Feb 2011, 17:06

Dear Bunuel:

I am sorry still i am not clear.

Can you explain how are you sure From ST 1 that all are either - or +? We just know smallest and largest number's multiplication is positive. if we combine ST 1 & 2, it may be

Can you explain how are you sure From ST 1 that all are either - or +? We just know smallest and largest number's multiplication is positive. if we combine ST 1 & 2, it may be

(i.e, lets say 6 even numbers)

- - - - + - = - + + - - + + = +

(1) says: The product of the greatest and smallest of the integers in the list is positive.

Product of two multiple to be positive they must have the same sign:

So either: smallest * greatest = negative * negative and in this case as both the smallest and the greatest are negative then ALL integers in the list are negative OR smallest * greatest = positive * positive and in this case as both the smallest and the greatest are positive then ALL integers in the list are positive.

1. The above DS question is a Yes/No type Question. 2. Question Stem: Products of all integers in a list positive? => [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set 3. Statement I: The product of Greatest and smallest integer in the List is +ve => Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES => Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES => Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO Hence Statement I is Not Sufficient. 4. Statement 2: There is an even number of Integers in the list => We know from number properties that -ve no multiplied even number of times is +ve and +ve no multiplied even number of times is +ve Ex: -2 * -2 * -3*-7 = +ve and 2 * 7 * 9 *10 = +ve This statement provides only information about the Integers in the Set and this cant be helpful in determining the Question stem. So NO - In Sufficient. 5. Now Taking I and II together. => We know that from I - All numbers in set are either +ve or -ve and from II that there are even number of Integers. Hence we can use the above information to get the value if the product of all Integers is +ve or not.

Stem rephrase: There are even number of negative numbers or all are positive.

1. Not sufficient information on the middle numbers, insufficient 2. Even numbers does not mean even negatives or all positives, insufficient

Together, no overlapping information, so insufficient. E
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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Re: A certain list consists of several different integers [#permalink]

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04 May 2012, 18:37

Quote:

(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.

Hi, I have one question here. Statement 2 says, there are even number of integers in the list. How can we assume all are negative or positive? What if, (-,-,-,+). This will result in negative.

I think answer should be E. Could you please explain. Thanks.

(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.

Hi, I have one question here. Statement 2 says, there are even number of integers in the list. How can we assume all are negative or positive? What if, (-,-,-,+). This will result in negative.

I think answer should be E. Could you please explain. Thanks.

Answer to the question is C, not E.

(1)+(2): From statement (1) we have that either all integers are negative or all integers are positive (check this: a-certain-list-consists-of-several-different-integers-126040.html#p878206). Statement (2) says that there are even number of elements in the set. So in either of cases the product will be positive.

Re: A certain list consists of several different integers [#permalink]

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05 May 2012, 09:04

1

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Statement 2 is insufficient, because it says there are even number of items.

But from the first statement the numbers are either on the negative side of the number line or positive side of the number line. only then multiplying the larger and smaller will lead to a positive number.

Ignoring the positive side, because odd number of items or even number of items will lead to a positive outcome.

But for the negative side of the number line to become postive there should be an even number of multiples.
_________________

1. The above DS question is a Yes/No type Question. 2. Question Stem: Products of all integers in a list positive? => [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set 3. Statement I: The product of Greatest and smallest integer in the List is +ve => Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES => Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES => Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO Hence Statement I is Not Sufficient. 4. Statement 2: There is an even number of Integers in the list => We know from number properties that -ve no multiplied even number of times is +ve and +ve no multiplied even number of times is +ve Ex: -2 * -2 * -3*-7 = +ve and 2 * 7 * 9 *10 = +ve This statement provides only information about the Integers in the Set and this cant be helpful in determining the Question stem. So NO - In Sufficient. 5. Now Taking I and II together. => We know that from I - All numbers in set are either +ve or -ve and from II that there are even number of Integers. Hence we can use the above information to get the value if the product of all Integers is +ve or not.

Do let me know, if you need further explanation.

Thanks, Arvind.

Thanks Arvind for your explanation. One point I was missing that if the smallest and the greatest integers have same signs mean the numbers in between have the same sign too. Thanks again much appreciated!

i missed the same.. tricky stuffs u c
_________________

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1. The above DS question is a Yes/No type Question. 2. Question Stem: Products of all integers in a list positive? => [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set 3. Statement I: The product of Greatest and smallest integer in the List is +ve => Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES => Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES => Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO Hence Statement I is Not Sufficient.

Thanks, Arvind.

Isn't this case incorrect as the stem says the product of the largest and smallest integer is positive? Is there an example where the list of largest and smallest is positive and the product of the integers can be negative? _________________

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1. The above DS question is a Yes/No type Question. 2. Question Stem: Products of all integers in a list positive? => [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set 3. Statement I: The product of Greatest and smallest integer in the List is +ve => Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES => Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES => Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO Hence Statement I is Not Sufficient.

Thanks, Arvind.

Isn't this case incorrect as the stem says the product of the largest and smallest integer is positive? Is there an example where the list of largest and smallest is positive and the product of the integers can be negative?

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