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Director  Joined: 17 Sep 2005
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If a and b are positive numbers, what are the coordinates of  [#permalink]

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If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b)
(2) The coordinates of D are (1-a, b)

Originally posted by b14kumar on 09 Sep 2007, 15:56.
Last edited by Bunuel on 27 Jul 2014, 15:57, edited 1 time in total.
Edited the question and added the OA.
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sandranjeim wrote:
If a and b are positive numbers, what are the coordinates pf the midpoint of line segment CD in the xy plane?

1) C (a, 1 - b)

2) D (1 - a, b)

OA = C

Coordinates of the midpoint $$M (x_m,y_m)$$ of the line segment AB, ($$A (x_1,y_1)$$ and $$B (x_2,y_2)$$) are $$x_m=\frac{x_1+x_2}{2}$$ and $$y_m=\frac{y_1+y_2}{2}$$

(1) C (a, 1 - b). Not sufficient.

(2) D (1 - a, b). Not sufficient.

(1)+(2) $$M (x_m,y_m)=M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=M(\frac{a+1-a}{2},\frac{1-b+b}{2})=M(\frac{1}{2},\frac{1}{2})$$. Sufficient.

sandranjeim wrote:
So we find the coordinates of the midpoint in terms of a and b right?

Thanks

If it were so, then answer would be E. In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc.
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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b14kumar wrote:
If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in xy plane?

1. The coordinates of C are (a,1-b)
2. The coordinates of D are (1-a,b)

- Brajesh

to find the mid point u just take the mean of x1 and x2 and mean of y1 and y2, that leaves us with mid point coordinates of x=1/2 y=1/2
to have it we need to use both statements
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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St1 and St2 by themselves are insufficient.

Using both, the midpoint is ((a+1-a/2), (1-b+b)/2) -> (1/2, 1/2). Sufficient.

Ans C
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It is necessary to add values of X and Y than divide by 2

Ans: C
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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C indeed

To find the mid point , you need co-ordinates of C and D

The forumulae to calculate Mid POint, given 2 points

(X1, Y1) and ( X2, Y2) = (X1+X2)/2 , (Y1+y2)/2
Intern  Joined: 11 Apr 2010
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If a and b are positive numbers, what are the coordinates of  [#permalink]

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If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b)
(2) The coordinates of D are (1-a, b)
Manager  Joined: 07 May 2008
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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It's pretty straightforward, knowing the coordinates of C and D the midpoint of line segment CD can be found out. Option C.

Do you any specific doubt in this question?

PS: Would be good if you can use the spoiler option for the OA thanks

Originally posted by sh00nya on 17 Apr 2010, 04:25.
Last edited by sh00nya on 17 Apr 2010, 04:34, edited 1 time in total.
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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So we find the coordinates of the midpoint in terms of a and b right?

Thanks
Manager  Joined: 07 May 2008
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Yes you find the coordinates of the midpoint but if you look closely your answer will be a definite value and not in terms of a and b.
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coordinates of the midpoint will be (1/2,1/2). both statements will be required to find out the answer.
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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Point to be noted

"In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc. "

Thanks Bunuel!
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Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b)
(2) The coordinates of D are (1-a, b)

There are 2 variables (x,y) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer.
Looking at the conditions together,
midpoint=(a+1-a/2, 1-b+b/2)=(1/2,1/2)
This is unique and sufficient,

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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In order to find the midpoint of a line segment, both the end points of a line are needed. What further solves the question is the victory over laziness before one selects E due to presence of variables from the two statements; they get cancelled and the midpoint is (0.5,0.5)

Also, I applied a learning from a previous question. Positive numbers and Positive Integers are different. While we tend to know the difference, remembering the same every time we see integers and numbers pop up on the screen is important. Be careful folks!
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Bunuel wrote:
In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc.

I know what you mean (solving in terms of a variable is rarely sufficient), but we have to be careful--this is not always true. If the question being asked is a yes/no question ("is x positive?" or "is y less than 0?"), then the statements could be sufficient even if we can get multiple values for x or y, so long as they always result in the same answer to the question being asked (either "always yes", or "always no").

There are some cases on DS where both solving in terms of a variable, and getting multiple numerical values, can be sufficient.

For example, if the question asks, "is x > 5?" and statement #1 leads me to the conclusion that x = 10, 15, or 20, then I can conclude "sufficient," even though I found multiple solutions for x, because the answer to the question being asked is always yes.

This can also be true when solving in terms of a variable. If the question asked "is x positive?" and I am able to solve for x as $$(y^2+1)$$, then I know that regardless of the value of y, x must be positive. Hence it would be sufficient.
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Originally posted by mcelroytutoring on 04 Aug 2016, 16:48.
Last edited by mcelroytutoring on 05 Aug 2016, 07:37, edited 1 time in total.
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mcelroytutoring wrote:
Bunuel wrote:
In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc.

I know what you mean (solving in terms of a variable is rarely sufficient), but we have to be careful--this is not always true. If the question being asked is a yes/no question ("is x positive?" or "is y less than 0?"), then the statements could be sufficient even if we can get multiple values for x or y, so long as they always result in the same answer to the question being asked (either "always yes", or "always no").

There are some cases on DS where both solving in terms of a variable, and getting multiple numerical values, can be sufficient.

For example, if the question asks, "is x > 5?" and statement #1 leads me to the conclusion that x = 10, 15, or 20, then I can conclude "sufficient," even though I found multiple solutions for x, because the answer to the question being asked is always yes.

This can also be true when solving in terms of a variable. If the question asked "is x positive?" and I am able to solve for x as $$(y^2+1)$$, then I know that regardless of the value of y, x must be positive. Hence it would be sufficient.

Yes. This is a value question so I think it's clear what I meant: When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.
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_________________ Re: If a and b are positive numbers, what are the coordinates of   [#permalink] 27 Oct 2018, 07:31
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