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The Secret to Solving Word Problems

Word Problems tend to intimidate kids taking the SAT or ACT or adults taking the GMAT or GRE. Don’t be scared! The math on most word problems is actually easier and less troublesome than the math on a straightforward arithmetic or algebra problem.

The reason the math is easier on these problems is because the problem is made hard in other ways. Word problems are considered hard because you have to convert a word problem into a math question. This involves good reading skills and good critical reasoning skills.

Keep some of the following word problem translations in mind as you navigate some of the toughest word problems.

“Is” means “equal to”

“Is” is “=.” If you see the word “is” in a word problem, have no fear. It simply means “equals.”

The number of brown hats is 5% of the total number of hats. Take “is” and make it “=” and get started! Now you have the number of brown hats = 5% of the total number of hats.

“Of” means “multiplied by”

In a question with fractions, you want to substitute the words “multiplied by” for the “of.”

What is 3/5 of 20? To solve this problem, take the fraction and multiply it by the other number. So, what is 3/5 x 20?

“Per” means “divided by”

If you see a problem discussing rates, or using the word “per” be prepared to switch into fraction or division mode. Per is another way of saying “divided by.”

A car travels 50 miles per hour. The per is literally the line in a fraction. 50 miles/hour.

Note: Sometimes instead of “per” you will see the words “for every.” For every boy, there are two girls. So that means 1 boy divided by 2 girls.

Don’t fear word problems. There are a limited number of word problem types. Learn the basic approach for most of these, and work on your reading and logic when navigating the answer choices. Once you have this vocabulary nailed down, and you study reading and logic, you will have a new perspective on word problems and be able to solve them without difficulty.

Be Neurotic and Take Notes on the GMAT.

It’s OK to be a little neurotic when taking your GMAT. I am not encouraging you to freak out or anything like that. What I am encouraging you to do is to write little notes to yourself. Use your dry-erase board to write little reminders to yourself. You may feel stupid or silly when you are doing it, but feeling silly while getting a problem correct is a way better feeling than not feeling silly while missing a problem you should have gotten right. What is perhaps the best example of a test taker overlooking a very important detail that should have been remembered? Any question involving complementary probabilities. On any such problem, I advise my students to always write themselves a little love note reading, “DO NOT FORGET TO SUBTRACT FROM 1!” I only hope they are following my advice. It’s so easy to forget this little detail, because computing the complementary probability in a problem is no easy task. After putting forth such effort, it is understandable that a test taker would let up his or her guard. The test taker then forgets to subtract this value from one. Sure enough, the complementary probability is one of the wrong answer choices begging the non-neurotic test-taker to choose it.

Another reminder or “love note” I encourage students to write on their dry-erase boards is “a b c d e” for every single data sufficiency problem. It’s complicated enough navigating the flow chart when deciding which answers to eliminate. Why try to keep track of eliminated answers in one’s head? Old test-takers like me had an actual paper test booklet where we could actually cross out answer choices. You won’t have that “luxury.” So, write down “a b c d e” on every data sufficiency question so you can keep track of which answers you eliminate.

One other note regarding “a b c d e.” I encourage students to write “a b c d e” on any question where they are being asked something like, “Which of the following does NOT appear in the passage?” or “which of the following is NOT a possible solution.” In questions like this, a test taker is being asked to find four values or four pieces of information that would be acceptable. They are then asked to eliminate those as correct answer choices. It is easier than you might believe to start out doing just that, and halfway through, finding an answer that would be acceptable and choosing that as your answer to the question that is asking you which answer would NOT be acceptable.

So, take the time to write yourself a reminder or two.  You’ll remember me, and though you might feel stupid doing so, you’ll get the right answer!

Breaking the Rules of Data Sufficiency

Every so often when I am tutoring a student, he or she will change up the rules of data sufficiency.  I’ve seen it before with misunderstanding a “yes/no” data sufficiency question (by erroneously thinking an answer of “always no” means “not sufficient.”)

However, more than once recently, students are creating a new rule that is a score killer.  They are not accepting the numbered statements as absolute truths. 

The GMAT test taker’s job is to assess the sufficiency of the numbered statements.  It is NOT the test taker’s job to disprove the numbered statements.  Those statements cannot be changed they are true. 

How is this done?  Sometimes a test taker picks numbers which violate the numbered statements, and consequently mistakenly determines sufficiency based on that instead of the actual question stem.  

Here is an example

Is x>0?

Statement 1 is “x+12>10.”   The student might erroneously plug in a number that violates “x+12>10” and think “well if x is 20, x+12>10, but if x is -4, then x+12 is not greater than 10.  Therefore this is not sufficient.”  But the overall question is not “Is x+12>10.”  That is a statement that has to be accepted as fact when determining the sufficiency of the real overall question of “Is x>0?”  The only numbers that can be tested for statement 1 are those that fit within the parameters of the statement (x>-2).

It is very important to know very early in your data sufficiency studies that Statements 1 and 2 are facts!  They cannot be disproved and numbers that violate what the statements tell you are not to be used.  If you “disprove” one of the numbered statements, you are asking for trouble!