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OA=AB

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Carcass
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OA=AB [#permalink] New post   19 May 2021, 01:26
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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.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: OA=AB [#permalink] New post   19 May 2021, 12:32
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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
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Re: OA=AB [#permalink] New post   19 May 2021, 02:11
B

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Re: OA=AB [#permalink] New post   19 May 2021, 02:14
K=21 so A

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Re: OA=AB [#permalink] New post   19 May 2021, 10:15
if you could not find out roots of equation then what to do??
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Re: OA=AB [#permalink] New post   01 Jun 2021, 19:53
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] New post   02 Jun 2021, 02:37
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] New post   03 Jun 2021, 08:05
hello expert, i am having little trouble with high difficulty level question, any suggestion!!!
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Re: OA=AB [#permalink] New post   03 Jun 2021, 08:16
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] New post   03 Jun 2021, 08:22
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] New post   03 Jun 2021, 09:00
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] New post   03 Jun 2021, 09:07
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] New post   03 Jun 2021, 09:11
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rx10

The rock 👍👍

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Re: OA=AB [#permalink] New post   03 Jun 2021, 10:03
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] New post   03 Jun 2021, 12:46
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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