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18 Jun 2019, 09:24
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Difficulty:
95%
(hard)
Question Stats:
51% (02:47) correct
49%
(02:36)
wrong
based on 195
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A company had 1000 employees at the beginning of the year 2011. If p percent of the employees present at the beginning of the year left the company during the year and the number of employees at the end of the year was r percent greater than the number of employees at the beginning of the year, how many employees joined the company during the year 2011?
I. p + r = 30
II. Had the number of employees leaving the company been r percent of the employees at the beginning of the year and the number of employees at the end of the year been p percent greater than the number of employees at the beginning of the year, the number of employees who joined the company would have remained the same.
I. p + r = 30
II. Had the number of employees leaving the company been r percent of the employees at the beginning of the year and the number of employees at the end of the year been p percent greater than the number of employees at the beginning of the year, the number of employees who joined the company would have remained the same.
20 Jun 2019, 02:31
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In this question, although it may look like plugging values for ‘p’ and ‘r’ could be the easier way to solve, analyzing the question stem is the better and effective way. Plugging values might actually prove counter productive here.
Let us assume ‘x’ new employees joined the company during the year 2011. We also know that ‘p’ percent of 1000 employees left the company. Therefore, the number of employees in the company should be,
1000 (1 – \(\frac{p}{100}\)) + x.
But, the question also says that, by the end of 2011, the number of employees of the company had increased by ‘r’ percent. This means, it should have become 1000 (1 + \(\frac{r}{100}\)).
Therefore,
1000 (1-\(\frac{p}{100}\)) + x = 1000 (1+\(\frac{r}{100}\)).
On simplifying the above equation, we get,
x = 10 p + 10 r, which can also be written as
x = 10 (p+r).
So, essentially, if we are to calculate the number of employees who joined the company in 2011 (i.e. x), we need the value of (p+r).
Statement I, therefore, is clearly sufficient. The possible answers are A or D. Options B, C and E can be eliminated.
Statement II says that if we interchange the positions of ‘p’ and ‘r’ in the equation above, x will still remain same. But, that is not sufficient to find the VALUE of x.
1000 (1-\(\frac{r}{100}\)) + x = 1000 (1 + \(\frac{p}{100}\)), which, on simplification yields
x = 10 (p + r).
But, since we do not know the values of p and r, we will not be able to calculate the value of x uniquely. Statement II alone is insufficient.
The correct answer option is A.
Had we taken values for the first statement, we would have to deal with an assortment of them. Instead, the idea was to break down the question stem to obtain an equation/expression, from which to figure out the variable/combination of variables to look for in the statements. It made it easy for us by telling us WHAT to look for in the statements.
Hope this helps!
Let us assume ‘x’ new employees joined the company during the year 2011. We also know that ‘p’ percent of 1000 employees left the company. Therefore, the number of employees in the company should be,
1000 (1 – \(\frac{p}{100}\)) + x.
But, the question also says that, by the end of 2011, the number of employees of the company had increased by ‘r’ percent. This means, it should have become 1000 (1 + \(\frac{r}{100}\)).
Therefore,
1000 (1-\(\frac{p}{100}\)) + x = 1000 (1+\(\frac{r}{100}\)).
On simplifying the above equation, we get,
x = 10 p + 10 r, which can also be written as
x = 10 (p+r).
So, essentially, if we are to calculate the number of employees who joined the company in 2011 (i.e. x), we need the value of (p+r).
Statement I, therefore, is clearly sufficient. The possible answers are A or D. Options B, C and E can be eliminated.
Statement II says that if we interchange the positions of ‘p’ and ‘r’ in the equation above, x will still remain same. But, that is not sufficient to find the VALUE of x.
1000 (1-\(\frac{r}{100}\)) + x = 1000 (1 + \(\frac{p}{100}\)), which, on simplification yields
x = 10 (p + r).
But, since we do not know the values of p and r, we will not be able to calculate the value of x uniquely. Statement II alone is insufficient.
The correct answer option is A.
Had we taken values for the first statement, we would have to deal with an assortment of them. Instead, the idea was to break down the question stem to obtain an equation/expression, from which to figure out the variable/combination of variables to look for in the statements. It made it easy for us by telling us WHAT to look for in the statements.
Hope this helps!
