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13 Nov 2024, 01:30
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The number of researchers in the three pharmaceutical companies A, B and C are in the ratio 2:3:4, respectively. Is the average number of independent research papers submitted by each researcher greater than 40?
(1) The average number of independent research papers submitted by each researcher of the companies A, B and C are 50, 39 and 35, respectively.
(2) The total number of independent research papers submitted by all the researchers is less than 360.
(1) The average number of independent research papers submitted by each researcher of the companies A, B and C are 50, 39 and 35, respectively.
(2) The total number of independent research papers submitted by all the researchers is less than 360.
13 Nov 2024, 22:41
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Given:
The ratio of the number of researchers in companies A, B, and C is
2:3:4.
Let the number of researchers in A, B, and C be
2x,
3x, and
4x, respectively.
We need to determine if the overall average number of independent research papers per researcher is greater than 40.
Statement (1)
The average number of papers per researcher in A, B, and C is 50, 39, and 35, respectively.
Total papers submitted by researchers in each company would then be:
A =2x *50=100x
B=3x*39=117x
C=4x *35=140x
Thus, the total papers across all three companies is:
100x+117x+140x=357x
The total number of researchers is :
2x+3x+4x=9x.
Therefore, the average number of papers per researcher across all companies is:
357x/9x=39.67
Since 39.67 is less than 40, Statement (1) alone is sufficient to answer the question with a "No."
Statement (2)
The total number of independent research papers submitted by all researchers is less than 360.
This information alone does not provide the specific distribution of research papers among the companies or the individual averages in A, B, and C.
Without this breakdown, we cannot calculate the overall average number of papers per researcher.
Thus, Statement (2) alone is insufficient.
Combining Statements (1) and (2)
Since Statement (1) alone is sufficient to conclude the answer (the overall average is 39.67, which is less than 40), we do not need to use Statement (2).
Answer:
The answer is (A): Statement (1) alone is sufficient.
The ratio of the number of researchers in companies A, B, and C is
2:3:4.
Let the number of researchers in A, B, and C be
2x,
3x, and
4x, respectively.
We need to determine if the overall average number of independent research papers per researcher is greater than 40.
Statement (1)
The average number of papers per researcher in A, B, and C is 50, 39, and 35, respectively.
Total papers submitted by researchers in each company would then be:
A =2x *50=100x
B=3x*39=117x
C=4x *35=140x
Thus, the total papers across all three companies is:
100x+117x+140x=357x
The total number of researchers is :
2x+3x+4x=9x.
Therefore, the average number of papers per researcher across all companies is:
357x/9x=39.67
Since 39.67 is less than 40, Statement (1) alone is sufficient to answer the question with a "No."
Statement (2)
The total number of independent research papers submitted by all researchers is less than 360.
This information alone does not provide the specific distribution of research papers among the companies or the individual averages in A, B, and C.
Without this breakdown, we cannot calculate the overall average number of papers per researcher.
Thus, Statement (2) alone is insufficient.
Combining Statements (1) and (2)
Since Statement (1) alone is sufficient to conclude the answer (the overall average is 39.67, which is less than 40), we do not need to use Statement (2).
Answer:
The answer is (A): Statement (1) alone is sufficient.
