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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8572
GMAT 1: 760 Q51 V42
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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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[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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Senior Manager  P
Joined: 13 Feb 2018
Posts: 498
GMAT 1: 640 Q48 V28
Re: For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is  [#permalink]

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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 V
Joined: 16 Aug 2015
Posts: 8572
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]

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=>

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 $$p + q = 7.$$

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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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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."
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It is one of the most advanced test-prep platform, which offers high-quality content, personalized study plan, awesome analytics, and experienced mentors. Re: For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is   [#permalink] 02 Dec 2019, 00:24
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# For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is  