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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

This post received KUDOS

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.

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?

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

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01 Jul 2013, 23:35

Bunuel wrote:

moniralinda wrote:

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

(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 negative 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.

Hope it's clear.

GENIUS. Newbie here but I'm already tired of giving you kudos. What a legend.

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

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17 Aug 2014, 14:44

zz0vlb wrote:

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. (2) There is an even number of integers in the list.

(1): the greatest and smallest integer could be both negative or both positive --> insufficient (2): even number of integers does not point out the sign of the product --> insufficient

(1) + (2): all number are positive or negative and even number --> both the products are positive --> sufficient

C is the answer
_________________

......................................................................... +1 Kudos please, if you like my post

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

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04 Aug 2016, 21:45

Hi All,

I always find it extremely useful whenever I am able to rephrase the question and simplify what is being asked.

A certain list contains several different integers. Is the product of the integers in the list positive? - Lets list conditions wherein the product will be positive ( also do let me know if I have missed any thing else)

1. All the number are positive 2. All number negative and the even number of terms ( neg * neg = positive )--> 2 negatives make one positive. 3. Mixed set --> Again even number of negatives. We dont really have to bother about the number of positive terms

P.s: 0 is not a positive integer, so also look out for any information that says one of the terms is 0. In which case the product will NOT be positive.

Now lets look at the statements:

1. The product of the greatest and the smallest of the integers in the list is positive

This means that both the terms are of the same sign:

a) Both are negatives, this means that all the terms are negative. In this case we need to number of terms to be even. Refer to point number 2 in the question analysis. b) Both are positives, All terms positive.

Since we dont know the exact sign this statement is insufficient.

(2) There is an even number of integers in the list

Now since we dont know which category the set belongs to ( of the 3 listed above), we cant be sure. For example:

a) 3 negatives , 5 positives ( total 8, even number of terms ) --> product is negative b) 4 negatives, 4 positives ( total 8, even number of terms )-->product is positive

Hence insufficient.

Now combining 1 & 2:

a) Both are negatives, this means that all the terms are negative & Even number of terms --> product is even b) Both are positives, All terms positive & Even number of terms --> product is even

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

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07 Feb 2017, 05:49

To have a positive product, we must have an even number of negatives (0, 2, 4...) so that the negatives will cancel out in the multiplication.

REPHRASE: Are there an even number of negatives?

1) Max * Min is positive means Max and Min have the same sign. If they're both positive, then everything is positive and so is the product of all integers. However, if Max and Min are both negative, the product could be negative if we do NOT have an even number of negatives. Example {-3, -2, -1}. NOT SUFFICIENT.

2) By itself, this doesn't tell us whether there is an even number of negatives. Doesn't answer our rephrase.

Merge statements: (2) tells us that we have an even number of values. Since all the values have the same sign (1 says Max and Min have the same sign), either we have all positives or we have an even number of negatives. Either way, the product of all terms will be positive.