Of the 14,210 employees of the anvil factory, 2/7 are journeymen. If

VERITAS PREP OFFICIAL SOLUTION:

The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.

If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.

What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 16.67%.

Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.

The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?

The correct answer is 2nd place.

Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.

\(\frac{2}{7}*\frac{1}{2} = \frac{1}{7}\)

Percentage of Journeymen = \(14.28\) %

Thus, answer will be (A)

Hi Abhishek009,

You should reread this prompt (you've made a logical error in your work and chosen the wrong answer).

GMAT assassins aren't born, they're made,
Rich

Point to be noted here that, we don’t need the no. of total employees in order to answer this question. This question can be also converted into a DS question.

And also feel this is not really 700+ level question, solved in 40 sec.

Journeyman = 2/7

After removing half journeyman, Remaining Journeyman = (1/2)*(2/7) = 1/7

Remaining employees = 1-(1/7) = 6/7

Remaining Journeyman as percentage of total employees remaining \(= (1/7)*100/(6/7) = (1/6)*100 = 16.67%\)

Answer: Option B

As Brunuel mentioned the number of employees doesn’t matter. I did what he did as well. 2/7 divided by 2 equals 1/7. However I forgot to subtract the remaining part to equal 1/6. Thus I put 14.3%. Hopefully you all look for this simple mistake I made and remember it.

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Keep in mind, the GMAT is (generally) not testing your ability to divide large/messy numbers. Seeing the number 14,210 should be a reminder that there is likely an easier way to solve the problem.


Original number of journeymen: \(\frac{2}{7}\) * Total Employees

New number of journeymen: \(\frac{2}{7}\) * \(\frac{1}{2}\) = \(\frac{1}{7}\) * number of employees

Total number of employees after layoff: 1 - \(\frac{1}{7}\) = \(\frac{6}{7}\)

Answer: \(\frac{journeymen}{Total Employees}\)

instead of dividing, we can multiply \(\frac{1}{7}\) by the reciprocal of total employees \(\frac{7}{6}\)

\(\frac{1}{7}\frac{7}{6}\) = \(\frac{1}{6}\) = .1667 * 100 = 16.67%

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