Posts filed under 'Math'
The data sufficiency is really unlike any other type of math question. You don’t actually answer the math question, rather you must determine if you have enough information to answer the question. These style questions do not require any skills beyond those needed for the other math on the GMAT. Given the unique nature of this type of question, you should practice them and familiarize yourself with the directions. We discussed them in this previous post. The main purpose of these questions is to lure you into making an unwarranted assumption.
The first thing you should do when you see a data sufficiency question is list the answer choices as follows. (We’ll get to why this is important in second):
AD
BCE
Additionally, the initial information given can often be presented in a convoluted manner. If you can translate this into something more easily decipherable, you will help yourself. For example, if one of the conditions is X is a factor of Y, you can rewrite this as “Y/X is an integer”. 3x=9y can be simplified to x=3y.
If you see a question like this, you should manipulate it as best you can into a simple algebraic expression.
Is x divisible by 2? Can be expressed as: Is x even?
Is X greater than 0? Can be rephrased as: Is x positive?
Once you have simplified the initial information, look at statement 1. Can you determine the answer to the question? Remember, you do not need to solve the problem just evaluate if you have enough information to calculate an answer.
If Statement 1 is sufficient, cross off BCE as there is no way any of those choices could be the correct answer. If you find that you need more information after evaluating the first statement, cross off AD as neither of those answers can be correct.
Once you have eliminated several answer choices, look at statement 2 independently. Using only the information in statement 2, determine if there is enough information to answer the question. Based on your answer, you should be able to cross off more answer choices.
If neither statement provided sufficient data independently, try to solve the problem using the information in both statements. You can then determine if your answer is C (combined, the two statements provide enough information) or E (not enough information).
If you are being asked to solve for a variable, remember you must have as many expressions or algebraic sentences as you do variables. To solve for X, you only need one statement with the one variable X in it. If you have two variables, you need two independent statements to determine the values of each variable. Three variables would require three statements, and so on. Be careful, though, because the test writers like to trick people into thinking they have two distinct algebraic statements when they really don’t. We’ll cover this trap in a later post, so stay tuned.
Remember – practice, practice, practice – and it will get easier!
April 10th, 2008
Units Digit Problems
Although a lot of the math on the GMAT has useful applications in b-school and beyond, sometimes the GMAT tests your knowledge of obscure number facts that will be of little use to you – ever.
One such enjoyable topic is the topic of units digit patterns. These questions test your understanding of the behavior of the units digit of a number when raised to a certain power.
Quick: What is the units digit of 4,67432?
Yes, that’s what we’re talking about. The GMAT thinks you should know it.
The good news is, it’s not so hard. There are exponent patterns with each of the digits from 0 – 9, and knowing them will get you through these questions in a snap. Did you know, for example, that any number ending in 4 will always end in 4 if raised to an odd power? It will always end in 6 if raised to an even power. So the answer to our question above is 6, because 32 is even.
Why? Look what happens to just the units digit of powers of four:
41 = 4
42 = 16: When you multiply by 4, the first calculation is 6×4=24, so the units digit is 4
43 = 64: When you multiply by 4, the first calculation is 4×4=16, so the units digit is 6
44 = 256: Again, 6×4 is the first calculation, leaving a 4 in the next power
45 = 1024
When it comes to 4, then, the units digit simply alternates 4, 6, 4, 6, 4, 6.
Let’s try it with all the digits. You will see that not only does each digit have its own pattern, but that at the 5th power, every digit starts over again! This is a quirky property of numbers, but one the GMAT LOVES. See if you can create the table below. If you can, you’ve mastered this topic.
Think you got it? Check back on Tuesday, we’ll put this concept to the test in our next IL700 Challenge Question, so stay tuned!
March 3rd, 2008
Of the many types of math questions that you may encounter on the GMAT, interest rates are one. There are two types of interest rate questions, and it is important to note the difference.
The first one is simple interest, meaning that you do not earn interest on the interest. Let’s say you have $100 dollars in a CD and you are earning 5% every month. (Clearly, this is a hypothetical situation.) In a non-compounding situation, you would receive a check for $5 every month.
If your interest was compounded (the second type of question), your $5 interest payment would be added to the balance. The next month, you would earn 5% on $105, or $5.25. The following month, you would earn interest on $110.25, and so on.
So how do you solve these problems? The formula for simple interest is, not surprisingly, easier:
Interest = interest rate * principle * time
Principle is the amount of money you start with. Think of the time variable as the number of times that the interest is paid out. And, remember that interest rate must be in decimals. So if interest is paid monthly and the question asks for the interest gain over two years, t=24. If the interest is paid annually, t=2. Now, this formula yields the answer for how much interest is earned, not the total amount money in the bank. To figure that out when simple interest is at play, simply add the interest earned to the principle.
Compounded interest is more complicated. To calculate the amount in the bank, we can use the following formula:
Future Amount = Principle * (1 + interest rate)number of payment periods
Of course, you may be asking yourself how you’re supposed to calculate such large exponents. If you had a problem that said there was $1,000 principle, and a 6% annual compounded interest rate paid over 15 years, it would take you forever to calculate that out by hand (no calculator, remember?)! Never fear – the GMAT will never ask you to do that. In fact, if you encounter a problem like this, expect the answers to be given in terms of the formula:
A) 1000(.06)
B) 1000(.06)15
C) 1000(1.06)
D) 1000(1.06)15
E) $15,000
The answer here would be D, and you’d have it by just understanding the concept and a bit about the formula.
To be sure, compound interest problems are much more prevalent on the GMAT. No surprise, since the world of business uses compound interest every single day. In fact, learning compound interest won’t just help you on the GMAT, but you’ll rock your finance class as well!
To get up to speed quickly, spend some of your study time calculating the simple and compounded interest with the same set of numbers. You will see the discrepancy between the two and get a better understanding of this important topic.
February 11th, 2008
There’s nothing like working with an inequality to confuse you on the GMAT.
You can often treat the inequality as an equal sign. Whatever you do to one side of the expression you can do to the other.
HOWEVER, and this is a big HOWEVER, if you need to multiply or divide by a negative number (or variable) you must reverse the inequality sign.
Let’s see why:
-5x>25
we can divide by 5 on both sides
-x>5
some possible values for x include: -5.5, -6, -7.
Essentially anything smaller than –5
Now, let’s go back to the original statement:
-5x>25
Now, let’s divide by –5 on both sides.
If we do not change the sign we’re left with
x>-5, which is incorrect.
From the examples above, we see that X has to be less than –5 and as such, we have to switch the inequality sign. When adding and subtracting negative numbers, there is no need to worry about switching the inequality sign.
If you forget the specifics of this rule, look at an easy statement such as the one above to see how multiplying and dividing with a negative number effects the inequality sign.
January 17th, 2008
The GMAT has a type of question not found on other standardized tests. The data sufficiency will generally state information then definitely ask a question. It will then provide two numbered statements. As the test taker, you must evaluate whether one, both, or neither statement provides enough information to solve the initial question.
A means the first statement is sufficient to answer the question.
B means the second statement is sufficient to answer the question.
C means that the first and second statement combined provide sufficient information to answer the question.
D means both statements individually are sufficient.
E means neither statement is sufficient.
Add these answer choices to your list of things to memorize. You do not want to waste valuable test taking time trying to think of what each letter represents.
If the answer to the question is “no”, do not fall for the common trap of selecting E.
For example, let’s say the question asks, “is x positive?” You may find that X is negative, but that does not mean the answer is E.
If I bet you five dollars to ask your boss for a raise and you do, and she says no, do I owe you five dollars? Yes. I did not wager that you would get the raise, only that you ask. Same goes for the GMAT, the answer can still be no, but you must determine which sentence provides enough information to determine that.
January 8th, 2008
The GMAT asks you to do a lot of math. It would not be so bad if you had a calculator or unlimited time, but you have neither. Using the test format of multiple choice answers to your advantage, you can employ some clever math shortcuts to save you time.
Look at your answer choices. If there is a large size discrepancy between the numbers, then you can guesstimate. Round your numbers to the nearest 10 or 100 or 1000 depending on their value.
If the answer choices seem close together and you are not comfortable rounding, you can perform the “last number trick”. Let’s say you have to multiply two large numbers: 534,326 and 1,456,399. Rather than multiply both numbers and waste time, you can determine what the last digit of the product will be by multiplying the last digit of each multiplier. So, in this case, 6 times 9 is 54 which means that the last digit of the product will be 4. Should there be two multiple choice answers with the last digit as 4 – just multiply out another digit.
You just saved yourself a chunk of time.
January 3rd, 2008