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y1 , y2 , y3 .... are all distinct integers and represent [#permalink]
15 Mar 2007, 23:55

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E

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct
100% (01:46) wrong based on 5 sessions

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

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
_________________

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.
_________________

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

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

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.
_________________

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.