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A certain list consists of several different integers [#permalink]
 28 Apr 2010, 07:28
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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.
Last edited by Bunuel on 08 Aug 2012, 05:32, edited 1 time in total.
OA added.
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Re: Stuck with an easy number property....:( [#permalink]
24 May 2010, 11:00
Ithink both statement together is not sufficient, so what is the real answer here? why do care about the existence of 0 ?
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Re: Stuck with an easy number property....:( [#permalink]
24 May 2010, 11:43
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diemxua175 wrote: 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. Answer: C. Hope it's clear.
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Re: Stuck with an easy number property....:( [#permalink]
23 Feb 2011, 18:06
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
(i.e, lets say 6 even numbers)
- - - - + - = -
+ + - - + + = +
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Re: Stuck with an easy number property....:( [#permalink]
23 Feb 2011, 18:26
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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.
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Re: Stuck with an easy number property....:( [#permalink]
23 Feb 2011, 20:01
Ohh.... Genius...Thanks a lot! Now I understood how come all have the same sign...Thank u sooo much.
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Re: Stuck with an easy number property....:( [#permalink]
24 Feb 2011, 23:50
great question! Kudos are due
Completely missed it!
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Re: Product of integers - Gmatprep [#permalink]
04 Jan 2012, 02:09
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Hi Janealams, 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.
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Re: Product of integers - Gmatprep [#permalink]
04 Jan 2012, 02:55
arvindravulavaru wrote: Hi Janealams,
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!
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Re: Product of integers - Gmatprep [#permalink]
04 Jan 2012, 14:07
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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Re: Product of integers - Gmatprep [#permalink]
04 Jan 2012, 17:13
BDSunDevil wrote: Can you reconfirm the OA. I am getting E. The official answer is C. Its a gmatprep question. Statement 1 tells the product of the smallest and greatest numbers is positive which means they are both of the same sign, either positive or negative. If the signs of the the smallest and greatest number in a range same the numbers in between are of the same sign. e.g (-8,x,y,z,-1) we can say that x y and z are all negative. statement 2 say number of items are even ....> product of even number of positive values is positive, product of even number is negative values is positive. Statement 1 and 2 together r sufficient.
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Re: Product of integers - Gmatprep [#permalink]
13 Jan 2012, 06:46
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Re: A certain list consists of several different integers [#permalink]
04 May 2012, 19:37
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.
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Re: A certain list consists of several different integers [#permalink]
04 May 2012, 21:48
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pgmat wrote: 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. 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. Hope it's clear.
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Re: A certain list consists of several different integers [#permalink]
05 May 2012, 10:04
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.
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Re: Product of integers - Gmatprep [#permalink]
26 Jan 2013, 07:49
Janealams wrote: arvindravulavaru wrote: Hi Janealams,
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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Re: Product of integers - Gmatprep
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26 Jan 2013, 07:49
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