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The frequency table above shows the number of surveyors together with

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Bunuel
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The frequency table above shows the number of surveyors together with [#permalink] New post   24 May 2018, 06:23
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75% (hard)

Question Stats:

54% (02:15) correct 46% (02:20) wrong based on 152 sessions
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Number of surveyors : Number of people surveyed per surveyor
                x : 0
                2x : 1
                2x : 2
                4 : 10
                1 : 20

The frequency table above shows the number of surveyors together with the corresponding number of surveyed people per surveyor. What is the value of x?

(1) The average (arithmetic mean) of the number of people surveyed per surveyor is 3
(2) Exactly half of the surveyors have surveyed at most one person
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D
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zishu912
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Re: The frequency table above shows the number of surveyors together with [#permalink] New post   24 May 2018, 12:05
Bunuel wrote:
Number of surveyors : Number of people surveyed
x : 0
2x : 1
2x : 2
4 : 10
1 : 20

The frequency table above shows the number of surveyors together with the corresponding number of surveyed people. What is the value of x?

(1) The average (arithmetic mean) of the number of people surveyed per surveyor is 3
(2) Exactly half of the surveyors have surveyed at most one person



statement 1: (0 + 1+ 2 + 10 + 20) / (x + 2x + 2x + 4 + 1) = 33 /(5x +1) = 3 so x can be calculated

statement 2: 2x + x = 2x + 5, from this statement too we can find the value of x

Hence both the statement alone is sufficient (D)
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sadhanapriya
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Re: The frequency table above shows the number of surveyors together with [#permalink] New post   18 Dec 2023, 07:58
Bunuel, need more clarity on statement 2.
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Bunuel
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Re: The frequency table above shows the number of surveyors together with [#permalink] New post   18 Dec 2023, 09:43
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sadhanapriya wrote:
Bunuel, need more clarity on statement 2.


Number of surveyors : Number of people surveyed per surveyor
                x : 0
                2x : 1
                2x : 2
                4 : 10
                1 : 20

The frequency table above shows the number of surveyors together with the corresponding number of surveyed people per surveyor. What is the value of x?

(1) The average (arithmetic mean) of the number of people surveyed per surveyor is 3

The total number of surveyed people equals x*0 + 2x*1 + 2x*2 + 4*10 + 1*20 = 6x + 60.
The total number of surveyors equals x + 2x + 2x + 4 + 1 = 5x + 5.

Therefore, based on this statement, the average is (6x + 60)/(5x + 5) = 3. Solving this equation gives x = 5. Sufficient.

(2) Exactly half of the surveyors have surveyed at most one person

This implies that the number of surveyors who surveyed 0 or 1 person was half of the total number of surveyors. The number of surveyors who surveyed 0 or 1 person is x + 2x = 3x. Hence, it is given that 3x = 1/2*(5x + 5). Solving this equation also results in x = 5, which is sufficient.

Answer: D.
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Re: Number of surveyors : Number of people surveyed x : 0 2x : 1 [#permalink] New post   18 Dec 2023, 09:44
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Re: Number of surveyors : Number of people surveyed x : 0 2x : 1 [#permalink]
18 Dec 2023, 09:44
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