Bunuel wrote:
At a certain company, 40% of the women are over 50 years old and 50% of the men are over 50 years old. What percentage of the company are men?
(1) 42% of all employees are over 50 years old.
(2) There are 500 employees at the company.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Today’s article comes courtesy of Veritas Prep GMAT instructor and BTG expert, David Newland.
Data Sufficiency is different from problem solving in that there are certain things that you can do to eliminate answer choices or to work your way into a problem even if you are having trouble understanding it. I call this “Data Sufficiency Jujitsu.”“Do More with Less”There are certain subjects on Data Sufficiency that lend to your being able to Do More with Less Information. The classic example of this is Geometry. Some time ago I observed that in Geometry you can (as we say at Veritas Prep) “leverage your assets” so that you are usually provided with enough information to solve each Geometry question on the Data Sufficiency portion of the GMAT. This led to my now famous rhyme
“Take the E out of Geometry on Data Sufficiency.”Now let me explain this rhyme a little more – obviously there will be times when E is the correct answer to a Data Sufficiency Geometry question and if you can see that there is information missing of course you should pick choice E! What I mean is that when you are having trouble working through a geometry problem and you come down, for example to “C versus E” – just remember that when in doubt there probably is a way to get that answer since you can do more with less on geometry. So if you are stuck and if you need to choose between the remaining possible answers, that is when you should “take the E out of geometry.”
But it actually means more than this, being able to do more with less means that if you are forced to guess or if you are simply stuck on a geometry problem you should really work to see if you can solve the problem with the least possible amount of information. So if you are deciding between BOTH statements TOGETHER (choice C) and a single statement ALONE (Choice A or B) really try to make the problem work using the single statement. And if you are forced to guess, you might want to consider the remaining possible choice that does the most with the least – in this case A or B instead of C.
Remember that this is just the general tendency. The ideal situation is for you work the problem correctly, from the beginning, and move quickly to the correct answer. However, knowing what to expect on the GMAT can be very helpful in guiding you toward the correct answer.
The BAD SubjectsThe subjects on the GMAT that lend themselves to “doing more with less” are the B-A-D subjects. I call them this because you can often get the answer to these questions with one (or each) of the statements ALONE – and that means answers D, A, or B. A partial list of the BAD subjects includes Geometry, Venn Diagrams, and any problems involving percents or ratios. These are subjects that tend to require less information than you might think.
Example: Percentage ProblemThe following is a question from the Veritas Prep Word Problems book:
At a certain company, 40% of the women are over 50 years old and 50% of the men are over 50 years old. What percentage of the company are men?
(1) 42% of all employees are over 50 years old.
(2) There are 500 employees at the company.Do you have the answer?
JUJITSUThe question stem should catch your attention here. This is a percentage problem and it is one of the “B-A-D subjects” – so you should immediately be thinking about doing more with less information. Percentage problems can often be solved with relationships between categories without knowing how many people or items are actually in those categories.
On this question if you take a quick glance at statement 2) you will see that it is not sufficient. You are looking to discover what percentage of the company is men and just learning that there are 500 people working for the company does not indicate how many of these people are men.
So you can eliminate choices B and D since statement 2 is not clearly sufficient alone.However, using a little Data Sufficiency Jujitsu, you can eliminate choice C as well.
Statement 2 is not sufficient but it also is not particularly helpful. When looking for the percentage, the only way that knowing the total number could help you is if the question stem provided actual numbers of men and women, but in this case the question stem provides percentages of men and women over 50, so the total number of workers is simply not helpful!
That means that the answer to this question has to be either A or E. Either statement number 1 will be sufficient ALONE, or the statements will not be sufficient at all. Since percentages are one of the “BAD subjects” you expect to be able to do more with less and so A will likely be the correct choice. In this case choice A is correct as the explanation will show.
But the point is that with a little “Jujitsu” you can move through the answer choices, clearly eliminating some and playing the odds on others, so that even on a question that you do not fully understand you do not need to blindly guess as you might on Problem Solving.ExplanationStatement 1 indicates that 42% of all employees are over 50 years old. Given the information from the question stem this is enough to solve this “weighted average” problem. You can simply compute the difference between the overall average (42%) and the stated averages for each of the groups: men (50%) and women (40%). The distance from the average is 8 for men (50 – 42) and 2 for women (42 – 40); so the ratio is M:W = 8:2. You then reduce that ratio to M:W = 4:1 and finally INVERT the ratio so that the final answer is M:W = 1:4.
(The reason for inverting the ratio is that the “weight” of a group is exactly inverse to the distance that group is from the average. You can logically see that there must be more women since the overall average of 42% is much closer to the women’s average of 40% and therefore the women must make up a greater portion of the group in order to have influenced the average so much).Now since this is a Data Sufficiency question you would not need to actually compute the difference or invert, right? In other words you would not need to actually solve, you would just need to know that you could!
But if this were problem solving we would have one final step. This question asks you “What percentage of the company are men?” So you have to convert that ratio of M:W = 1:4 into a percentage. Remember that a ratio of 1:4 actually means that only 1 of every 5 people in the room is a man. So that means 20% not 25%.
How to Use “Jujitsu”Obviously if you are able to work a problem through perfectly right from the start then you should do that. But just remember that a little Data Sufficiency Jujitsu – such as recognizing “B-A-D Subjects” – can help you with your approach to the problems, can help you catch any little errors you might have made, and can be very useful in eliminating answer choices on a problem that you do not fully understand. As you are practicing Data Sufficiency take note of the BAD subjects and try to Do More with Less
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