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16 Sep 2014, 01:49
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (02:18) correct
41%
(02:23)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
The workers at a large construction company reported \(x\) percent fewer safety incidents in 2004 than in 2003, and \(y\) percent more incidents in 2005 than in 2004. If the workers reported a total of 1,000 incidents in 2003, how many incidents did the workers report in 2005?
(1) \(xy = 50\)
(2) \(y - x - \frac{xy}{100} = 4.5\)
(1) \(xy = 50\)
(2) \(y - x - \frac{xy}{100} = 4.5\)
16 Sep 2014, 01:49
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Official Solution:
We need to determine the number of incidents reported in 2005. The problem tells us that 1,000 incidents were reported in 2003. In 2004, \(x\) percent fewer incidents were reported, so \((100 - x) \times 1,000\) incidents were reported. Since a percentage is equivalent to a fraction with a denominator of 100, we can express the number of incidents reported in 2004 as \(\frac{100 - x}{100} \times 1,000\). In 2005, \(y\) percent more incidents were reported than in 2004. This can be expressed as \(\frac{100 + y}{100}(\frac{100 - x}{100} \times 1,000)\). It is this target expression that we must find a value for.
Multiply the numerators and denominators: \(\frac{100 + y}{100}(\frac{100 - x}{100} \times 1,000) = \frac{1,000(100 + y )(100 - x)}{10,000}\).
Cancel 1,000 from the numerator and denominator and FOIL what remains: \(\frac{(100 + y)(100 - x)}{10} = \frac{10,000 - 100x + 100y - xy}{10}\).
Evaluating this expression will require either solving for \(x\) and \(y\) or finding a way to substitute a number for all variable terms.
Statement 1 says that \(xy = 50\). This does not allow us to solve for either \(x\) or \(y\). We can substitute it into our target expression to get \(\frac{10,000 - 100x + 100y - 50}{10}\), but doing so does not eliminate the need to solve for \(x\) and \(y\). Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice is B, C, or E.
Statement 2 says that \(y - x - \frac{xy}{100} = 4.5\). Note that this equation has an \(x\) term, a \(y\) term, and a term containing \(xy\). Thus, substitution will likely be possible.
Divide the original expression by \(10\) to eliminate the fraction: \(\frac{10,000 - 100x + 100y - xy}{10} = 1,000 - 10x + 10y - \frac{xy}{10}\).
Now factor out an additional \(10\) and reorder the terms in the expression: \(10(100 + y - x - \frac{xy}{100})\).
The left side of the equation in statement 2 is contained in this expression. Thus, we know that we can find a value for the expression. Statement 2 alone provides sufficient information to answer the question.
Answer: B
We need to determine the number of incidents reported in 2005. The problem tells us that 1,000 incidents were reported in 2003. In 2004, \(x\) percent fewer incidents were reported, so \((100 - x) \times 1,000\) incidents were reported. Since a percentage is equivalent to a fraction with a denominator of 100, we can express the number of incidents reported in 2004 as \(\frac{100 - x}{100} \times 1,000\). In 2005, \(y\) percent more incidents were reported than in 2004. This can be expressed as \(\frac{100 + y}{100}(\frac{100 - x}{100} \times 1,000)\). It is this target expression that we must find a value for.
Multiply the numerators and denominators: \(\frac{100 + y}{100}(\frac{100 - x}{100} \times 1,000) = \frac{1,000(100 + y )(100 - x)}{10,000}\).
Cancel 1,000 from the numerator and denominator and FOIL what remains: \(\frac{(100 + y)(100 - x)}{10} = \frac{10,000 - 100x + 100y - xy}{10}\).
Evaluating this expression will require either solving for \(x\) and \(y\) or finding a way to substitute a number for all variable terms.
Statement 1 says that \(xy = 50\). This does not allow us to solve for either \(x\) or \(y\). We can substitute it into our target expression to get \(\frac{10,000 - 100x + 100y - 50}{10}\), but doing so does not eliminate the need to solve for \(x\) and \(y\). Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice is B, C, or E.
Statement 2 says that \(y - x - \frac{xy}{100} = 4.5\). Note that this equation has an \(x\) term, a \(y\) term, and a term containing \(xy\). Thus, substitution will likely be possible.
Divide the original expression by \(10\) to eliminate the fraction: \(\frac{10,000 - 100x + 100y - xy}{10} = 1,000 - 10x + 10y - \frac{xy}{10}\).
Now factor out an additional \(10\) and reorder the terms in the expression: \(10(100 + y - x - \frac{xy}{100})\).
The left side of the equation in statement 2 is contained in this expression. Thus, we know that we can find a value for the expression. Statement 2 alone provides sufficient information to answer the question.
Answer: B
bhatiavai
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GMAT Date: 12-03-2014
26 Nov 2014, 11:13
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hi Bunuel,
How would one attempt the question within 2 mins. even though I got the answer It took me 4 complete minutes!!
Thanks
How would one attempt the question within 2 mins. even though I got the answer It took me 4 complete minutes!!
Thanks
