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A, B, R and S are four positive numbers. Does AS = BR? [#permalink]
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22 Sep 2016, 18:59
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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 xy 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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22 Sep 2016, 19:29
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 xy 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=6No 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
Last edited by rohit8865 on 22 Sep 2016, 22:10, 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, 20:44
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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 xy 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, 21:51
(1) \(\sqrt{A^2 + B^2} = \sqrt{R^2 + S^2}\) ==> \(A^2 + B^2 = R^2 + S^2\) ==> \(A^2  S^2 = R^2  B^2\) ==> (AS)(A+S)=(RB)(R+B)  Not sufficient. (2) In the xy plane, the line through (A, B) and (R, S) goes through the origin Slope of line between Origin and point (A,B) = \(\frac{(B0)}{(A0)}\)= \(\frac{B}{A}\)Slope of line between Origin and point (R,S) = \(\frac{(S0)}{(R0)}\)= \(\frac{S}{R}\)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, 05:08
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




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