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# For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is  [#permalink]

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29 Nov 2019, 01:41
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[GMAT math practice question]

For the equation $$3 - 2[x] = 3[x] - 12, x$$ satisfies $$p ≤ x < q.$$ What is the value of $$p + q?$$ ($$[x]$$ denotes the greatest integer less than or equal to $$x$$.)

A. $$6$$

B. $$7$$

C. $$8$$

D. $$9$$

E. $$10$$

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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" Senior Manager Joined: 13 Feb 2018 Posts: 496 GMAT 1: 640 Q48 V28 Re: For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is [#permalink] ### Show Tags 29 Nov 2019, 03:00 I will try but I cant swear I fully understood the stem 1) Simplify the equation 3[x]+2[x]=15 5[x]=15 [x]=3 So the minimum value of p is 3 and the maximum value of q is 4 Their sum is 7 I have one question Must there be "What is the possible value of p+q?" instead of "What is the value of p+q?" IMO Ans: B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8425 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is [#permalink] ### Show Tags 01 Dec 2019, 21:08 => Since $$[x]$$ is the greatest integer less than or equal to $$x$$, if we have $$n ≤ x < n + 1$$, where n is an integer, we define $$[x] = n.$$ $$3 - 2[x] = 3[x] - 12$$ => $$15 = 5[x]$$ => $$[x] = 3$$ => $$3 ≤ x < 4$$ Then we have $$p = 3$$ and $$q = 4.$$ So $$p + q = 7.$$ Therefore, B is the answer. Answer: B _________________ 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: For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is  [#permalink]

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02 Dec 2019, 01:24
LevanKhukhunashvili wrote:
I have one question
Must there be "What is the possible value of p+q?" instead of "What is the value of p+q?"

When it says "for the given equation" 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q...it means that the given range covers all possible values of x. And the only possible range is 3 ≤ x < 4.

So, I don't think there is any ambiguity as such. Maybe, just maybe, to ensure there's no shred of doubt, we could have written the statement this way:
"The given range, p ≤ x < q covers "all" possible values of x that satisfies the given equation 3 - 2[x] = 3[x] - 12."
Re: For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is   [#permalink] 02 Dec 2019, 01:24
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