Step-by-Step 4/14/14

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Sometimes we don’t need a whole lot of discussion. We just need a problem broken down step-by-step. This question comes from the GMAT Official Guide, 13th edition, Section 6.3 #110.

“Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?

(1) The price of Tom’s house was $110,000.

(2) The price of Jane’s house was $120,000.”

Step 1: Identify your target and the given information- Here our goal is to find the median home price. We’re given the average price which tell us that the total of the three sales is $360,000.

Step 2: Find paths to sufficiency- in other words, figure out what you’d need to know in order to be able to find the median. When arranged in increasing order, the median is the middle term. In order to find the middle term we’ll either need to know the values of all three terms, or be guaranteed that one of our terms is the middle one.

Step 3: Assess the first statement- If Tom’s house was $110,000 we know that the two other houses sum to $250,000. If Jane’s house was $100,000 and Sue’s house was $150,000 the median would be $110,000. Alternatively if Jane’s house was $120,000 and Sue’s house was $130,000 the median would be $120,000. Since there is more than one possibility statement 1 is insufficient.

Step 4: Assess the second statement- If Jane’s house was $120,000 we know that the two other houses sum to $240,000. On the basis of this statement alone we can’t determine the exact prices of the other two houses. Many students will stop there, call this insufficient and get this question wrong. Remember, we could also have a sufficient amount of information if we could guarantee that $120,000 was the middle value. Since the other two houses sum to $240,000 we only have two options. The first option is that that one house is less than $120,000 and one is more. If that’s the case $120,000 is our median. The only other alternative is that all three houses cost $120,000. In that situation our median is still $120,000. Statement two is sufficient.

Follow all of these steps carefully and you’re well on your way to a great score. In data sufficiency questions you especially don’t want to jump ahead to combining both statements until you’ve fully evaluated each one.

Study hard!

 What Are the Hardest Questions on the GMAT?

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While test makers have long been able to turn even the simplest concepts into some seriously heavy lifting, there are some concepts and question types that are statistically more difficult for students than others. In this brief post I’m going to detail some of the question types and concepts that students have the most trouble with.

Rare Logical Reasoning Questions

There are certain types of Logical Reasoning questions that appear very rarely, and can require some fairly complex reasoning and elimination. Take a look at this example:

GMAT Example Question

In 2001, the unemployment fund collected 7 percent on every dollar. In 2006, that same fund was collecting 11 percent on every dollar in taxes even though the unemployment rate decreased from 2001 to 2006.

Each of the following, if true, would help to explain the apparent paradox presented above EXCEPT:

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Although definitely solvable, this is not a question type that you really want to see on test day.

Data Sufficiency Questions

Anyone who has studied a significant amount of time for the GMAT already knows this hard lesson very well. Data Sufficiency questions are a pain! The only promising aspect of these questions is that as your familiarity with these questions increases, the ease with which you may solve them grows very quickly. Take a look at the example:

GMAT Data Sufficiency Example

Is (x – 1)2 < 3?

(1) x < 5
(2) x > 2

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Solving this question requires not only familiarity with the Data Sufficiency question type, but also intricate knowledge of either number theory and inequalities OR elimination techniques. The correct answer to this question is E (BOTH are NOT sufficient to determine the answer).

Advanced Set Problems

Although rare, Venn Diagram or Set problems with three sets may appear on the test. These problems regularly prove difficult for students because the knowledge that they test is simply not commonly presented or prioritized.

The two-set formula is fairly easy to remember:

Total = Group1 + Group2 – Both + Neither

But there is a specific formula for three-set Venn Diagram problems, which often goes neglected:

Total = Group1 + Group2 + Group3 – (Sum of 2-Group Overlaps) – (n*(All Three) + Neither

The problems that you will face on the GMAT will give you everything that you need in this formula except for one quantity, which makes these very easy to solve – IF you know the formula.

 

This is by no means an exhaustive list; the GMAT is capable of turning even the simplest concepts into devastatingly convoluted quandaries, as you are no doubt well aware of.