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# The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42
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The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)  [#permalink]

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27 Nov 2019, 04:31
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Difficulty:

35% (medium)

Question Stats:

73% (02:39) correct 27% (01:50) wrong based on 22 sessions

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[GMAT math practice question]

The expansion of $$(203x^2 - 199x - 3)(72y^2 + 27y + 1)$$ is a1x^2y^2 + a2x^2y + a3x^2 +…..+ a7y^2 + a8y + a9. What is a1 + a2 + a3 +…..+ a7 + a8 + a9?

A. $$100$$

B. $$122$$

C. $$125$$

D. $$200$$

E. $$228$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 19 Oct 2018 Posts: 1171 Location: India Re: The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1) [#permalink] ### Show Tags 27 Nov 2019, 13:09 $$(203x^2 - 199x - 3)(72y^2 + 27y + 1)$$ = a1x^2y^2 + a2x^2y + a3x^2 +…..+ a7y^2 + a8y + a9 Put x=1 and y=1 (203-199-3)(72+27+1)=$$a1 + a2 + a3 +…..+ a7 + a8 + a9$$ 1*100= $$a1 + a2 + a3 +…..+ a7 + a8 + a9$$ 100= $$a1 + a2 + a3 +…..+ a7 + a8 + a9$$ MathRevolution wrote: [GMAT math practice question] The expansion of $$(203x^2 - 199x - 3)(72y^2 + 27y + 1)$$ is a1x^2y^2 + a2x^2y + a3x^2 +…..+ a7y^2 + a8y + a9. What is a1 + a2 + a3 +…..+ a7 + a8 + a9? A. $$100$$ B. $$122$$ C. $$125$$ D. $$200$$ E. $$228$$ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1) [#permalink] ### Show Tags 29 Nov 2019, 01:40 => When we substitute x and y with $$1’s$$, we have a1 + a2 + a3 +…..+ a7 + a8 + a9 = a1$$(1)^2(1)^2$$ + a2$$(1)^2(1)$$ + a3$$(1)^2$$ +…..+ a7$$(1)^2$$ + a8$$(1)$$ + a9. $$= (203(1)^2 - 199(1) - 3)(72(1)^2 + 27(1) + 1)$$ $$= 1*100$$ $$= 100$$ 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$79 for 1 month Online Course"
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Re: The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)   [#permalink] 29 Nov 2019, 01:40
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