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Re: OA=AB [#permalink]
K=21 so A

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Re: OA=AB [#permalink]
if you could not find out roots of equation then what to do??
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Re: OA=AB [#permalink]
KarunMendiratta wrote:
Carcass wrote:
Attachment:
GRE OA=AB.jpg


OA=AB


Quantity A
Quantity B
k
18



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


OA = \(\sqrt{(18 - 0)^2 + (3 - 0)^2}\)

AB = \(\sqrt{(18 - 15)^2 + (3 - k)^2}\)

Since, OA = AB
\(\sqrt{(18 - 0)^2 + (3 - 0)^2} = \sqrt{(18 - 15)^2 + (3 - k)^2}\)

Squaring both sides;
\(18^2 + 3^2 = 3^2 + (3 - k)^2\)
\(18^2 = (3 - k)^2\)

On comparison;
either \((3 - k) = 18\) or \((3 - k) = -18\)

i.e. \(k = -15\) or \(21\)

Since, \(k\) is in Ist Quadrant \(k > 0\)

Hence, option A


Cant we say that distance is always positive and neglect the negative value of K?
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Re: OA=AB [#permalink]
1
Distance is always positive but what if point B was in 3rd quadrant? K will be -ve. but the distance will be +ve always.

Here B is in first quad hence -ve value is not considered.

Please ask if the doubt remains.

kumarneupane4344 wrote:
KarunMendiratta wrote:
Carcass wrote:
Attachment:
GRE OA=AB.jpg


OA=AB


Quantity A
Quantity B
k
18



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


OA = \(\sqrt{(18 - 0)^2 + (3 - 0)^2}\)

AB = \(\sqrt{(18 - 15)^2 + (3 - k)^2}\)

Since, OA = AB
\(\sqrt{(18 - 0)^2 + (3 - 0)^2} = \sqrt{(18 - 15)^2 + (3 - k)^2}\)

Squaring both sides;
\(18^2 + 3^2 = 3^2 + (3 - k)^2\)
\(18^2 = (3 - k)^2\)

On comparison;
either \((3 - k) = 18\) or \((3 - k) = -18\)

i.e. \(k = -15\) or \(21\)

Since, \(k\) is in Ist Quadrant \(k > 0\)

Hence, option A


Cant we say that distance is always positive and neglect the negative value of K?
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Re: OA=AB [#permalink]
hello expert, i am having little trouble with high difficulty level question, any suggestion!!!
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Re: OA=AB [#permalink]
Sir,

I would suggest you first learn all the basics than try solving medium question from this forum UNTIMED. Then you can go for hard ones. Also in specific, where do you think you are lacking? in time management, concepts, ... ?

void wrote:
hello expert, i am having little trouble with high difficulty level question, any suggestion!!!
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Re: OA=AB [#permalink]
rx10 wrote:
Sir,

I would suggest you first learn all the basics than try solving medium question from this forum UNTIMED. Then you can go for hard ones. Also in specific, where do you think you are lacking? in time management, concepts, ... ?

void wrote:
hello expert, i am having little trouble with high difficulty level question, any suggestion!!!



YES, Absolutely
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Re: OA=AB [#permalink]
rx10 wrote:
Sir,

I would suggest you first learn all the basics than try solving medium question from this forum UNTIMED. Then you can go for hard ones. Also in specific, where do you think you are lacking? in time management, concepts, ... ?

void wrote:
hello expert, i am having little trouble with high difficulty level question, any suggestion!!!


thank you for replying, i think concept are little dusty ...please link comprehensive guide for quants.
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Re: OA=AB [#permalink]
2
Here it is : https://gre.myprepclub.com/forum/gre-quant ... 22642.html

Feel free to ask anything. :)

void wrote:
rx10 wrote:
Sir,

I would suggest you first learn all the basics than try solving medium question from this forum UNTIMED. Then you can go for hard ones. Also in specific, where do you think you are lacking? in time management, concepts, ... ?

void wrote:
hello expert, i am having little trouble with high difficulty level question, any suggestion!!!


thank you for replying, i think concept are little dusty ...please link comprehensive guide for quants.
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Re: OA=AB [#permalink]
1
Expert Reply
rx10

The rock 👍👍

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Re: OA=AB [#permalink]
1
We do not have to calculate exact length.
Difference of y values of O and A is 3,
Difference of x values of O and A is 18,

Difference of x values of A and B is 3,
So difference of y values of A and B should be 18, and y value of A is 3 , so y values of B is 21.

21 > 18 so answer is A)
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Re: OA=AB [#permalink]
We won't have to venture into the distance/length formula if we know a key concept about the slopes of perpendicular lines.

The concept is - if two straight lines, with slopes m1 and m2 respectively, are perpendicular to each other, then m1*m2 = -1

The slope of OA, m1= 3-0/18-0 = 1/6
So the slope of OB, m2 will be: 1/6*m2 = -1; So, m2 = -6

Now we just have to plug in the value of m2 in the formula of slope for line AB to get the value of k.
3-k/18-15 = -6;
k = 21
So A is the answer.

It wouldn't take a minute to solve if you can use this concept.
I hope this helps! :D
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Re: OA=AB [#permalink]
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Re: OA=AB [#permalink]
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