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y1 , y2 , y3 .... are all distinct integers and represent

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GMAThopeful
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y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   16 Mar 2007, 00:55
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y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers. P is a non negative number such that
P = (x - y1 ) (x - y2 ) (x - y3 ) .... upto infinity, where x is an integer.

Which of the following value can x take so that p has the least value?
I. 0 II. 1 III. -1


Answer Choices :

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) any of I, II or III



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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   16 Mar 2007, 14:53
Direct (E) :)

All values of x provide P = 0 :).... There is no maximum or minimum but only equaled values of P to 0 :)
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Amardeep Sharma
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   16 Mar 2007, 23:20
I agree... infact for any integer its true, whenever Yn=X...

regards,

Amardeep
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   17 Mar 2007, 00:52
Yup.. E is the answer..
I got it wrong though :(
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   04 May 2010, 20:36
Hey,
I was going through this problem. Somehow, i could not understand the explanation provided. Please, help me through this.
Bibha :-)
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   05 May 2010, 04:07
GMAThopeful wrote:
y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers. P is a non negative number such that
P = (x - y1 ) (x - y2 ) (x - y3 ) .... upto infinity, where x is an integer.

Which of the following value can x take so that p has the least value?
I. 0 II. 1 III. -1


Answer Choices :

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) any of I, II or III



IMO E
here's my explanation-

questions say "y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers"
so one is a negative integer, one is positive and third zero
Now the least value of P will be zero because it goes upto infinity. Put in the values of y1, y2, y3 to make p=0


All three satisfies the condition.
Correct me if i am wrong
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   05 May 2010, 11:03
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GMAThopeful wrote:
y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers. P is a non negative number such that
P = (x - y1 ) (x - y2 ) (x - y3 ) .... upto infinity, where x is an integer.

Which of the following value can x take so that p has the least value?
I. 0 II. 1 III. -1


Answer Choices :

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) any of I, II or III



Its E.

since y1,y2 ...yn are disticnt integers they will be equal to 0,-1 and 1 at some point or the other and at that point

x = 0 will give (0-0) so P=0
x=1 will be 0 when y = -1
x =-1 will be 0 at y = 1

so no matter what value of x we take the value of P will be 0.
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   05 May 2010, 11:31
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It's E but it is not mandatory that the value of P = 0 in all the cases.

Let's see how: say y1, y2, y3,... = -4, -2, 0, 2, 4

I. x=0 >>> P = (0+4)(0+2)(0+0)(0-2)(0-4)... = 0
II. 1 >>> P = (1+4)(1+2)(1+0)(1-2)(1-4)... = Non-zero
III. -1 >>> P = (-1+4)(-1+2)(-1+0)(-1-2)(-1-4)... = Non-zero

Hope this helps.

hardnstrong wrote:
GMAThopeful wrote:
y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers. P is a non negative number such that
P = (x - y1 ) (x - y2 ) (x - y3 ) .... upto infinity, where x is an integer.

Which of the following value can x take so that p has the least value?
I. 0 II. 1 III. -1


Answer Choices :

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) any of I, II or III



IMO E
here's my explanation-

questions say "y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers"
so one is a negative integer, one is positive and third zero
Now the least value of P will be zero because it goes upto infinity. Put in the values of y1, y2, y3 to make p=0


All three satisfies the condition.
Correct me if i am wrong
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   07 May 2010, 05:44
ykaiim wrote:
It's E but it is not mandatory that the value of P = 0 in all the cases.

Let's see how: say y1, y2, y3,... = -4, -2, 0, 2, 4

I. x=0 >>> P = (0+4)(0+2)(0+0)(0-2)(0-4)... = 0
II. 1 >>> P = (1+4)(1+2)(1+0)(1-2)(1-4)... = Non-zero
III. -1 >>> P = (-1+4)(-1+2)(-1+0)(-1-2)(-1-4)... = Non-zero

Hope this helps.

hardnstrong wrote:
GMAThopeful wrote:
y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers. P is a non negative number such that
P = (x - y1 ) (x - y2 ) (x - y3 ) .... upto infinity, where x is an integer.

Which of the following value can x take so that p has the least value?
I. 0 II. 1 III. -1


Answer Choices :

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) any of I, II or III



IMO E
here's my explanation-

questions say "y1 , y2 , y3 .... are all distinct integers and represent the entire set of integers"
so one is a negative integer, one is positive and third zero
Now the least value of P will be zero because it goes upto infinity. Put in the values of y1, y2, y3 to make p=0


All three satisfies the condition.
Correct me if i am wrong



Question is asking for the least value of P , which can be 0 only(which is possible in this case) as P is a non negative number
if you find value of P as zero in one case and non zero in otherwise. that way you contradicts the correct answer that all three values satifies. Here we have to prove if all three conditions could satisfy it or not. Not necessarily true in all cases
You example shows that only one value satisfies. Hence changes the answer

Hope this helps
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   07 May 2010, 06:45
Agree. To become the least value, P is to be 0 or -ve.

I just took a sample to prove that it is not neccessary to have P = 0 as the only option. Since, the series is infinitly long so you can take as many values in the series.
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   08 May 2010, 23:34
great explanations !
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink] y1 , y2 , y3 .... are all distinct integers and represent   09 May 2010, 00:56
A few more things. It is not mentioned that:

1. Order is not mentioned that y1, y2, y3... can be concesutive numbers. So, this series can be >>> (-2, 0, 2, 4...), (-2, -1, 0, 1, 2...), (-5, -4, 0, 2, 10...)
2. P is non-negative, which means it can be 0 or a +ve number and moreover a limit on value of P is not mentioned.

So, my cases are correct.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: y1 , y2 , y3 .... are all distinct integers and represent [#permalink]
09 May 2010, 00:56
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