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22 May 2019, 23:23
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:56) correct
34%
(02:08)
wrong
based on 227
sessions
History
Date
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Not Attempted Yet
In 1990, the annual salaries of clerks in Town Q ranged from $40,000 to $55,000. In 2000, the salaries of the same group of clerks ranged from $70,000 to $110.000 The percent increase in the annual salary of a clerk in Town Q between 1990 and 2000 could be which of the following?
I. 50
II. 100
III.150
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
I. 50
II. 100
III.150
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Archit3110
23 May 2019, 09:40
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Bunuel
least and the greatest possible increase.
70-55/55 = 27.3 %
110-40/40 = 175 %
all three options are valid IMO E
24 May 2019, 10:19
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This is a moderately difficult question on the concept of percentages. Because it is a ‘Could be’ kind of a question, the strategy here will be to take simple cases and try to prove each statement true, ONCE.
You can also adopt the minimization and maximization approach and see how many of the percentage values fall between the bounds. Let us look at both the approaches.
In 1990, the annual salaries of the clerks ranged from $40000 to $55000. In 2000, the annual salaries of the clerks ranged from $70000 to $110000.
If we consider the annual salaries in 1990 as $40000 and in 2000 as $80000, the percentage increase will be 100%. So, statement II could be a possible percentage increase. Therefore, options A and can be ruled out since they say only I statement could be true/only statement III could be true, which of course is wrong.
If the annual salaries in 1990 were $40000 and they were $10000 in 2000, the percentage increase will be 150%. So, statement III could be a possible percentage increase. Therefore, we can eliminate option B now.
If the annual salaries in 1990 were $50000 and were $75000 in 2000, the percentage increase would be 50%. So, statement I also could be a possible percentage increase.
Therefore, the correct answer option HAS to be E.
The other approach is to look at what could be the minimum and the maximum percentage increases possible.
For the minimum percentage increase, we have to take the biggest value of the salaries in 1990 and the smallest value of the salaries in 2000 i.e. $55000 to $70000. This is a percentage increase of approximately 27%.
For the maximum percentage increase, we take the smallest value in 1990 and the biggest value in 2000 i.e. $40000 to $11000. This is a percentage increase of 175%.
Clearly, all the percentage values given in the statements are in this range and therefore all of them could be the percentage increases.
Obviously, each method has its own merits. The value method is simple and quick, but only if you are able to figure out the values like the ones shown above. The conceptual method may seem more convincing to the purist in you. Regardless of the method that you adopt, this question should take you about a minute and a half, to come out with the right answer.
Hope this helps!
You can also adopt the minimization and maximization approach and see how many of the percentage values fall between the bounds. Let us look at both the approaches.
In 1990, the annual salaries of the clerks ranged from $40000 to $55000. In 2000, the annual salaries of the clerks ranged from $70000 to $110000.
If we consider the annual salaries in 1990 as $40000 and in 2000 as $80000, the percentage increase will be 100%. So, statement II could be a possible percentage increase. Therefore, options A and can be ruled out since they say only I statement could be true/only statement III could be true, which of course is wrong.
If the annual salaries in 1990 were $40000 and they were $10000 in 2000, the percentage increase will be 150%. So, statement III could be a possible percentage increase. Therefore, we can eliminate option B now.
If the annual salaries in 1990 were $50000 and were $75000 in 2000, the percentage increase would be 50%. So, statement I also could be a possible percentage increase.
Therefore, the correct answer option HAS to be E.
The other approach is to look at what could be the minimum and the maximum percentage increases possible.
For the minimum percentage increase, we have to take the biggest value of the salaries in 1990 and the smallest value of the salaries in 2000 i.e. $55000 to $70000. This is a percentage increase of approximately 27%.
For the maximum percentage increase, we take the smallest value in 1990 and the biggest value in 2000 i.e. $40000 to $11000. This is a percentage increase of 175%.
Clearly, all the percentage values given in the statements are in this range and therefore all of them could be the percentage increases.
Obviously, each method has its own merits. The value method is simple and quick, but only if you are able to figure out the values like the ones shown above. The conceptual method may seem more convincing to the purist in you. Regardless of the method that you adopt, this question should take you about a minute and a half, to come out with the right answer.
Hope this helps!
