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# If the operation % is defined by x % y = px^2 + qy^2 (p and q are cons

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
If the operation % is defined by x % y = px^2 + qy^2 (p and q are cons  [#permalink]

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04 Jul 2018, 23:47
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Difficulty:

55% (hard)

Question Stats:

40% (01:27) correct 60% (01:01) wrong based on 12 sessions

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[GMAT math practice question]

If the operation $$%$$ is defined by $$x % y = px^2 + qy^2$$ ($$p$$ and $$q$$ are constants), what is the value of $$2 % 4?$$

(1) 1 % 2 = 5
(2) 1 % 1 = 2

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Status: Learning stage Joined: 01 Oct 2017 Posts: 951 WE: Supply Chain Management (Energy and Utilities) If the operation % is defined by x % y = px^2 + qy^2 (p and q are cons [#permalink] ### Show Tags 05 Jul 2018, 00:28 MathRevolution wrote: [GMAT math practice question] If the operation $$%$$ is defined by $$x % y = px^2 + qy^2$$ ($$p$$ and $$q$$ are constants), what is the value of $$2 % 4?$$ (1) 1 % 2 = 5 (2) 1 % 1 = 2 Given, x % y = $$px^2 + qy^2$$ Question stem:-2 % 4=4p+16q=? Statement-1:- 1 % 2 = 5 Or, p+4q=5 or, 4(p+4q)=20 Or. 4p+16q=20 Sufficient. Statement-2:- 1 % 1 = 2 Or, p+q=2 2 variables and one equation, we can't find p & q. hence insufficient. Ans. A _________________ Regards, PKN Rise above the storm, you will find the sunshine Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the operation % is defined by x % y = px^2 + qy^2 (p and q are cons [#permalink] ### Show Tags 08 Jul 2018, 03:15 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. 2 % 4 = $$4p + 16q = 4 ( p + 4q ) = 4( p* 1^2 + q*2^2 )$$ = 4(1%2) Thus, condition 1) is sufficient. Condition 2) Now, 1%1 = $$p + q = 2.$$ If p = 1 and q = 1, then 2 % 4 = $$1*2^2 + 1*4^2 = 20.$$ If p = 3 and q = -1, then 2 % 4 =$$3*2^2 + (-1)*4^2 = 12 – 16 = -4.$$ Since we don’t have a unique solution, condition 2) is not sufficient. Therefore, A is the answer. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If the operation % is defined by x % y = px^2 + qy^2 (p and q are cons &nbs [#permalink] 08 Jul 2018, 03:15
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