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

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

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New post 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
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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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New post 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
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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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New post 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."
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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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