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# A, B, R and S are four positive numbers. Does AS = BR?

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A, B, R and S are four positive numbers. Does AS = BR?  [#permalink]

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22 Sep 2016, 19:59
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A, B, R and S are four positive numbers. Does AS = BR?

Statement #1: $$\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}$$
Statement #2: In the x-y plane, the line through (A, B) and (R, S) goes through the origin

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A, B, R and S are four positive numbers. Does AS = BR?  [#permalink]

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Updated on: 22 Sep 2016, 23:10
agrakul wrote:
A, B, R and S are four positive numbers. Does AS = BR?

Statement #1: $$\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}$$
Statement #2: In the x-y plane, the line through (A, B) and (R, S) goes through the origin

(1) Let A=B=R=S=\sqrt{50}---------Yes
Let A=B=\sqrt{50}
R=8 and S=6--------------------------No
insuff

(2) as we are making lines with unique points (A, B) and (R, S) , having same slope
both distance AS and BR must be equal.....suff..

Ans B

Originally posted by rohit8865 on 22 Sep 2016, 20:29.
Last edited by rohit8865 on 22 Sep 2016, 23:10, edited 1 time in total.
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Re: A, B, R and S are four positive numbers. Does AS = BR?  [#permalink]

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22 Sep 2016, 21:44
1
1
agrakul wrote:
A, B, R and S are four positive numbers. Does AS = BR?

Statement #1: $$\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}$$
Statement #2: In the x-y plane, the line through (A, B) and (R, S) goes through the origin

Hi,
Statement I is clearly insuff..
Let me concentrate on statement II..
Few points..
Since numbers are positive, all four numbers are in I quadrant..
Since they lie on the same line and line passes thru origin, the equation of line is y=mx....
So A=mB and R = mS..
But m or the slope is equal as they lie on same line..
So A/B = R/S..
Or AS= BR...

B
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A, B, R and S are four positive numbers. Does AS = BR?  [#permalink]

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22 Sep 2016, 22:51
1
(1) $$\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}$$

==> $$A^2 + B^2 = R^2 + S^2$$ ==> $$A^2 - S^2 = R^2 - B^2$$ ==> (A-S)(A+S)=(R-B)(R+B) -- Not sufficient.

(2) In the x-y plane, the line through (A, B) and (R, S) goes through the origin

Slope of line between Origin and point (A,B) =$$\frac{(B-0)}{(A-0)}$$= $$\frac{B}{A}$$

Slope of line between Origin and point (R,S) = $$\frac{(S-0)}{(R-0)}$$= $$\frac{S}{R}$$

As the line passes through (A, B) and (R, S) slope will always be same.

$$\frac{B}{A}$$ = $$\frac{S}{R}$$

$$BR = SA$$ --Sufficient.

Ans B.
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Re: A, B, R and S are four positive numbers. Does AS = BR?  [#permalink]

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23 Feb 2017, 06:08
Prompt analysis
A, B, R and S are positive numbers.

Superset
The answer will be either yes or no

Translation
To find the answer, we need:
1# exact value of the four numbers
2# 4 equations to find all 4 numbers
3# any relation or property that will lead us to find the answer

Statement analysis

St 1: cannot be said anything as we don't know anything about A, B, R and S individually
St 2: the equation of line passing through (A,B) and origin will be Ay =Bx. Putting (R,S) in the equation we get AS =BR. Answer

Option B
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Re: A, B, R and S are four positive numbers. Does AS = BR?  [#permalink]

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08 May 2018, 12:24
chetan2u wrote:
agrakul wrote:
A, B, R and S are four positive numbers. Does AS = BR?

Statement #1: $$\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}$$
Statement #2: In the x-y plane, the line through (A, B) and (R, S) goes through the origin

Hi,
Statement I is clearly insuff..
Let me concentrate on statement II..
Few points..
Since numbers are positive, all four numbers are in I quadrant..
Since they lie on the same line and line passes thru origin, the equation of line is y=mx....
So A=mB and R = mS..
But m or the slope is equal as they lie on same line..
So A/B = R/S..
Or AS= BR...

B

Thank you Chetan for the detailed explanation , I chose B , as the two lines are crossing through the origin , then I thought slopes of both the line will be equal. After going through your explanation , it makes sense .
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Re: A, B, R and S are four positive numbers. Does AS = BR? &nbs [#permalink] 08 May 2018, 12:24
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# A, B, R and S are four positive numbers. Does AS = BR?

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