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If x and y are consecutive odd integers such that x < y, what is the

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If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 03 Dec 2011, 12:30
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If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative.
(2) The sum x + y is the square of an integer

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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 03 Dec 2011, 12:51
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The question states that x and y are consecutive odd integers such that x < y.
We are asked to find the value of 'x+y'.
Let's look at the given statements.

Statement 1 says that the product of x and y is negative.
If the odd integers x and y are both positive, their product will be positive. (E.g. 3 and 5, 19 and 21, etc)
Similarly, if x and y are both negative, their product will still be positive. (-1 and -3, -13 and -15, etc)
Hence, the only possible numbers which satisfy the given condition are 1 and -1 i.e. one negative and other positive number. Here x = -1 and y = 1 since x < y.
1 and -1 are consecutive odd integers such that their product is -1 which is negative.
Hence we can find the sum of these 2 odd integers as -1 +1 = 0.
Hence this statement by itself is sufficient.

Statement 2 says that the sum x + y is the square of an integer.
Let's consider a few examples which satisfy this condition.
Let x = 1 and y = 3. Their sum = 1+3 = 4 (which is the square of 2 or -2)
If x = 7 and y = 9, then their sum 7+9 = 16 is the square of 4 or -4.
We see that there can be a number of possible combinations of numbers which satisfy this condition.
Hence, this statement by itself is insufficient.

As statement 1 is sufficient and statement 2 is not, the correct answer is option A.

Hope this helps :)
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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 03 Dec 2011, 13:22
sudish wrote:
The question states that x and y are consecutive odd integers such that x < y.
We are asked to find the value of 'x+y'.
Let's look at the given statements.

Statement 1 says that the product of x and y is negative.
If the odd integers x and y are both positive, their product will be positive. (E.g. 3 and 5, 19 and 21, etc)
Similarly, if x and y are both negative, their product will still be positive. (-1 and -3, -13 and -15, etc)
Hence, the only possible numbers which satisfy the given condition are 1 and -1 i.e. one negative and other positive number. Here x = -1 and y = 1 since x < y.
1 and -1 are consecutive odd integers such that their product is -1 which is negative.
Hence we can find the sum of these 2 odd integers as -1 +1 = 0.
Hence this statement by itself is sufficient.

Statement 2 says that the sum x + y is the square of an integer.
Let's consider a few examples which satisfy this condition.
Let x = 1 and y = 3. Their sum = 1+3 = 4 (which is the square of 2 or -2)
If x = 7 and y = 9, then their sum 7+9 = 16 is the square of 4 or -4.
We see that there can be a number of possible combinations of numbers which satisfy this condition.
Hence, this statement by itself is insufficient.

As statement 1 is sufficient and statement 2 is not, the correct answer is option A.

Hope this helps :)


Thanks buddy !!
i had problem with statement A: i knew either x or y is negative. I'm so dumb, i was taking x=-13 and y= 15 as negative odd integers without realizing that that are NOT consecutive.
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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 02 Apr 2015, 03:52
Bunuel wrote:
If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative.

(2) The sum x + y is the square of an integer.


Kudos for a correct solution.


x is odd; y=x+2; y+x=2(x+1)--->?

1. this mean x is negative since x<y. Also x and y are consecutive odd numbers.
X=-1 and y=1
y+x=0...Sufficient

2. x and y could be -1 and 1, 1 and 3, 7 and 9 etc.
Not Sufficient

Answer: A
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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 02 Apr 2015, 10:18
x & y are consecutive integers; x<y; x+y=?

1. x*y=-ve; one of the number is negative and another is positive;and both are odd; so we have only one combination x=-1,y=1; therefore x+y=0. Sufficient
2. x+y=square of an integer; so x+y can be anything, so not sufficient.

Hence Answer is A

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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 02 Apr 2015, 14:35
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Bunuel wrote:
If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative.

(2) The sum x + y is the square of an integer.


Kudos for a correct solution.



two consecutive odd integers x and y can be (2n+1) and (2n+3) respectively.

Now given (1) the product is negative. The only way for a product of two integers to be negative is if one of them is negative while the other isn't.
Given the consecutive nature, only -1,1 satisfies for x and y.

Therefore Option (1) is sufficient alone.

Now given (2) Sum of x and y is the square of an integer. So x and y can be 1,3 as well as 7,9. Their respective sums (4 and 16) are squares of 2 and 4.
SO insufficient for a conclusive answer.

Therefore, Option 1 alone is sufficient to answer.
Answer:A
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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 06 Apr 2015, 05:17
Bunuel wrote:
If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative.

(2) The sum x + y is the square of an integer.


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
oddconsecutives_explanation(1).png
oddconsecutives_explanation(1).png [ 32.24 KiB | Viewed 3355 times ]

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Re: If x and y are consecutive odd integers such that x < y, what is the  [#permalink]

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New post 06 Aug 2018, 08:08
Top Contributor
shrive555 wrote:
If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative.
(2) The sum x + y is the square of an integer


Target question: What is the value of y + x?

Given: x and y are consecutive odd integers such that x < y

Statement 1: The product of xy is negative
In order for the product xy to be NEGATIVE, it must be the case that one value is POSITIVE and one value of NEGATIVE.
Since x and y are CONSECUTIVE ODD integers, it must be the case that x = -1 and y = 1
This is the ONLY way to satisfy statement 1.
If x = -1 and y = 1, then x + y = (-1) + 1 = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum x + y is the square of an integer.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 3. Notice that x + y = 1 + 3 = 4, and 4 IS the square of an integer (4 = 2²) In this case, the answer to the target question is x + y = 4
Case b: x = 7 and y = 9. Notice that x + y = 7 + 9 = 16, and 16 IS the square of an integer (16 = 4²) In this case, the answer to the target question is x + y = 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Re: If x and y are consecutive odd integers such that x < y, what is the &nbs [#permalink] 06 Aug 2018, 08:08
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