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# x & y are consecutive positive integers. Also, x>y

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x & y are consecutive positive integers. Also, x>y [#permalink]  25 Jun 2008, 22:22
x & y are consecutive positive integers. Also, x>y and x^2-1> y^2 -4y+x-1

Which of the following represents all the possible values of y?

1. y>=0
2.y>0
3.y>1
4.y>7
5.y>8
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Re: M02 - Not happy with the OA! [#permalink]  25 Jun 2008, 22:50
iamcartic wrote:
x & y are consecutive positive integers. Also, x>y and x^2-1> y^2 -4y+x-1

Which of the following represents all the possible values of y?

1. y>=0
2.y>0
3.y>1
4.y>7
5.y>8

I got y > 0, B

although I wonder if I interpreted the equation correctly ---> x^2-1> y^2 -4y+x-1 is meant to be as (x^2) - 1 > (y^2) - 4y + x - 1 ?

x and y are consecutive positive integers, and x > y, so x = y + 1, also y has to be at least 1

substitute y + 1 for x

((y + 1)^2) - 1 > (y^2) - 4y + (y + 1) - 1

(y + 1)(y + 1) - 1 > (y^2) - 4y + y + 1 - 1

(y^2) + 2y + 1 - 1 > (y^2) - 4y + y + 1 - 1

(y^2) + 2y > (y^2) - 3y

5y > 0

and since y is a positive integer, y can be 1, 2, 3 ...

In choice C and y > 1 means y can not be 1, but y can be 1, so C can't be the answer.

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Re: M02 - Not happy with the OA! [#permalink]  25 Jun 2008, 22:59
So do you mean x can be a 0? --- then is 0 a positive integer?
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Re: M02 - Not happy with the OA! [#permalink]  25 Jun 2008, 23:00
no, x is greater than y, so x starts at 2
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Re: M02 - Not happy with the OA! [#permalink]  25 Jun 2008, 23:57
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Re: M02 - Not happy with the OA! [#permalink]  26 Jun 2008, 06:37
iamcartic wrote:
x & y are consecutive positive integers. Also, x>y and x^2-1> y^2 -4y+x-1

Which of the following represents all the possible values of y?

1. y>=0
2.y>0
3.y>1
4.y>7
5.y>8

This a poorly constructed question, at least if it has been transcribed accurately. None of the answers can possibly be correct. The correct answer here is "y >= 1 and y is an integer" (or, equivalently, "y > 0 and y is an integer"). All of the answer choices allow y to be a non-integer, so allow many impossible values for y.

What is the source?
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Re: M02 - Not happy with the OA! [#permalink]  26 Jun 2008, 06:44
Thatz from M03 - Gmatclub tests!!
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Re: M02 - Not happy with the OA! [#permalink]  26 Jun 2008, 23:29
IanStewart wrote:
iamcartic wrote:
x & y are consecutive positive integers. Also, x>y and x^2-1> y^2 -4y+x-1

Which of the following represents all the possible values of y?

1. y>=0
2.y>0
3.y>1
4.y>7
5.y>8

This a poorly constructed question, at least if it has been transcribed accurately. None of the answers can possibly be correct. The correct answer here is "y >= 1 and y is an integer" (or, equivalently, "y > 0 and y is an integer"). All of the answer choices allow y to be a non-integer, so allow many impossible values for y.

What is the source?

could you explain why you think it's a poorly constructed question? I don't see any problem with it. y>0 includes all positive integers which is within the premises.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 06:53
sanjay_gmat wrote:
could you explain why you think it's a poorly constructed question? I don't see any problem with it. y>0 includes all positive integers which is within the premises.

Yes, but that's not what the question asks. If the question asks 'Which of the following includes all of the possible values of y?", then there are two correct answers: A and B. And of course, if that's what the question meant, you could choose A without reading any other part of the question; if any other answer choice includes all of the possible values of y, then clearly A must as well, since the range of values in each other answer choice is included in the range of values in answer choice A.

Of course, the question does not use the word include. The question asks: "Which of the following represents all the possible values of y?" I take that to mean: "which of the following defines the set of values of y that could satisfy the given conditions." In other words, I expect the question to be asking "Which of the following represents all of the possible values of y, and no impossible values of y?" The inequality y>0 allows y to be equal to Pi or root(2). These are not possible values of y.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 07:02
It is written since the beginning of the question that you work on the sets of integers.

Therefore y>0 is perfectly correct.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 07:35
Oski wrote:
It is written since the beginning of the question that you work on the sets of integers.

Therefore y>0 is perfectly correct.

exactly, y is integer. end of story.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 08:19
No. By that logic, I could equally well say that A is the correct answer, because it includes all the integer solutions for y, and I know y can't be zero: the question tells me that. You can't assume facts from the question when choosing your answer; if you could, this type of question would be pointless.

You will never find a real GMAT question that expects you to assume a certain fact from the question holds a priori when choosing your answer, unless the question explicitly directs you as such.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 13:59
IanStewart wrote:
No. By that logic, I could equally well say that A is the correct answer, because it includes all the integer solutions for y, and I know y can't be zero: the question tells me that. You can't assume facts from the question when choosing your answer; if you could, this type of question would be pointless.

You will never find a real GMAT question that expects you to assume a certain fact from the question holds a priori when choosing your answer, unless the question explicitly directs you as such.

A can't be the answer, since y is a positive integer and 0 is not a positive integer. The question stem very specifically says that x and y are positive integers. So, if one of the answer choices says that "y > n", that means y = n+1, n+2, n+3 and so on.

You can't assume facts from the question when choosing your answer; if you could, this type of question would be pointless.

I will take the information given in the question to get to an answer. To me, this question is a genuine question, with no faults whatsoever.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 15:04
sanjay_gmat wrote:
A can't be the answer, since y is a positive integer and 0 is not a positive integer. The question stem very specifically says that x and y are positive integers. So, if one of the answer choices says that "y > n", that means y = n+1, n+2, n+3 and so on.

I'm not especially interested in continuing this discussion, but if you see the inequality "y > 0", that only means that y is to the right of 0 on the number line. If "y > 0" is the solution set to an inequality, that means that y can take on any value greater than 0.

"y > 0 and y is an integer" is what you arrive at by combining information from the question with information provided in the answer choice. It is not what the answer choice says. If I can combine the information "y is an integer" from the question with an answer choice, why should I not be permitted to combine the information "y is positive" from the question with the answer choice "y >= 0" here? If I can ignore the requirement that y is an integer when considering the answers, why shouldn't I also be allowed to ignore the requirement that y is positive?

The purpose of these questions is to translate the information in the question into something which is logically equivalent. You cannot be selective about which information is important to translate and which not. Regardless, this discussion is immaterial to anyone taking the GMAT, because you will never see a question worded in this way on the test. If you think that's untrue, try to find an example.
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 15:17
iamcartic wrote:
x & y are consecutive positive integers. Also, x>y and x^2-1> y^2 -4y+x-1

Which of the following represents all the possible values of y?

1. y>=0
2.y>0
3.y>1
4.y>7
5.y>8

x^2-1 > y^2-4y+x-1
x = y+1
y^2+2y+1-1 > y^2-4y+y+1-1
5y > 0 -> y > 0 -> B
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Re: M02 - Not happy with the OA! [#permalink]  27 Jun 2008, 19:17
iamcartic wrote:
x & y are consecutive positive integers. Also, x>y and x^2-1> y^2 -4y+x-1

Which of the following represents all the possible values of y?

1. y>=0
2.y>0
3.y>1
4.y>7
5.y>8

x^2 - 1 > y^2-4y+x-1
x^2 - x > y^2 - 4y
x (x -1 ) > y (y - 4)
x (y) > y (y - 4) ......... since x and y are consecutive integers x-1 = y.
x > (y - 4)
x > (y - 4)

any +ve value for y fits to the above eq. so B.
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Re: M02 - Not happy with the OA!   [#permalink] 27 Jun 2008, 19:17
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