Quantitative

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Exponents

Thursday, September 2nd, 2010

An exponent refers to the number of times the base is a factor. For example, 4³= 4 x 4 x 4 = 64. For a term with a coefficient in front of a variable raised to an exponent, it’s important to remember that the exponent only affects the variable. Knowing the order of operations is helpful to avoid simple exponent mistakes. For 2x², first you would square x and then multiply the result by 2.

Any number to the ²power is referred to as being “squared.” Any number to the ³ power is called being “cubed.”

When you multiply two terms with the same base, you can add the exponents.: 2⁵ x 2³ = 2⁵⁺³= 2⁸

When you divide two terms with the same base, you can subtract the exponent of the numerator from the exponent of the denominator: 6⁸÷ 6²= 6⁶

If two exponents are separated by a parenthesis, you can multiply them: (8²)⁵ = 8¹⁰

On the GMAT look for ways to rewrite bases so they are the same.

9⁷ x 3^x= 3¹⁷

(3²)⁷ x 3^x = 3¹⁷

3¹⁴ x 3^x = 3¹⁷

14 + x = 17

x = 3

There is no quick way of combining exponents when the bases are added. Don’t be fooled if you see something like 3²+ 3⁶= ?. The answer is NOT 3⁸. To solve, you must multiple out each term and then find the sum.

Any nonzero number raised to a power of zero is equal to 1.

3⁰ = 1

However 0⁰ = undefined.

A negative exponent is another way of expressing a fraction: x^-1 = 1 / x¹

4^-2= 1/4² = 1/16

A fractional exponent is another way of expressing a root: x^1/n = ⁿ√x¹

7^2/3 = ³√7²

8^1/3= ³√8 = 2

When a fraction is raised to an exponent, you must distribute the power both to the numerator and the denominator:

(1/2)³ = 1³/ 2³ = 1/8

Notice how the fraction will actually decrease in number as the exponent increases.

(1/2)⁴ = 1⁴ / 2⁴ = 1/16

A negative number raised to an even exponent will always be positive. The negative sign will cancel itself out.

(-2)² = -2 x -2 = 4

However a negative numbers raised to an odd exponent will remain negative.

(-3)³= -3 x -3 x -3 = -27

Large numbers and very small decimals are often expressed with exponents using scientific notation. Scientific notation involves writing the number as a product of a decimal and the number 10 raised to a certain power.

The number of the exponent indicates the number of places the decimal moves.

10⁷= 1 + 7 zeros = 10,000,000

.036 x 10⁴ = 360 (the decimal moves four places to the right)

.0000000857 x 10⁶= .0857

5.6 x 10^-4 = .00056 (Since it’s a negative exponent, the decimal will move to the left.)

Tags: exponents
Posted in GMAT, Problem Solving, Quantitative | No Comments »

Exponents on the GMAT

Thursday, August 19th, 2010

Tags: exponents
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Speed and Accuracy: Divisor Tests

Friday, July 30th, 2010

For those of you who didn’t know, you can’t use a calculator on the GMAT. The following quick tips well help you figure out what a certain number is divisible by. Remember, calculators are not allowed on the test, so these tips may very well help your speed and accuracy.

Divisible by 2: Any number divisible by 2 ends in 0, 2, 4, 6, or 8. (even numbers)

Divisible by 3: To determine if a number is divisible by 3, just add up the digits; if the sum of the digits is divisible by 3, then your number is divisible by 3 also. Hint: If your number is so large that the sum of its digits is also too large, just add the digits of the sum and see if this new sum is divisible by 3.

Example: Is 1636668 divisible by 3?

1+6+3+6+6+6+8= 36

3+6=9, which is divisible by 3

Divisible by 4: If the final two digits of the number form a number divisible by 4 OR form a double zero, then the number is divisible by 4. (Hint: Memorize this pattern of two-digit numbers that are divisible by 4: even0, even4, even8, odd2, odd6. By this pattern, I instantly know that numbers like 60, 80, 88, 52, 96, 124, 348, 556, etc, are divisible by 4)

Example: Is 141424 divisible by 4?

Is 24 divisible by 4? Yes, so the number is divisible by 4.

Example: Is 535892800 divisible by 4? Yes, the last two digits are zero.

Divisible by 5: All numbers divisible by 5 or 0

Divisible by 6: All numbers divisible by both 3 and 2. In other words, all even numbers divisible by 3.

Example: Is 20712 divisible by 6?

Is it even? Yes
2+0+7+1+2=12, which is divisible by 3; yes, it’s divisible by 6.

Divisible by 7: Much too complicated, in my opinion. I am fairly certain that you are better off just dividing by 7.

Divisible by 8: The last three digits are divisible by 8. Sorry guys, this might not be the most helpful tip, but if you find yourself having to work with a very large number, it will certainly save you time. If anybody else has a divisor test for 8, please post!

Example: Is 7953408 divisible by 8?

Is 408 divisible by 8?

408 / 8 = 51. Yes, the number is divisible by 8.

Divisible by 9: Just like the 3 rule. Add the digits; if the sum is divisible by 9, then the number is also.

Example: Is 207 divisible by 9?

2+0+7= 9. Yes, it is.

Divisible by 10: Ends in 0

Divisible by 11: This one is pretty awesome. Add up the odd-numbered digits (the 1st, 3rd, 5th, etc) and add up the even-numbered digits (the 2nd, 4th, 6th, etc) and subtract them. If the difference is 0, or if it is divisible by 11, then your number is divisible by 11. (Hint: You can also just alternate signs: e.g. with 352, I can do 3 – 5 + 2 = 0, or with 7458, I can do 7 – 4 + 5 -8 = 0.

Example: Is 5027 divisible by 11?

(5+2) – (0 + 7) = 0; yes, it’s divisible by 11.

While these divisor tests may seem like superfluous information since nearly all of us can perform these operations the old fashioned way, they will save us precious time on the exam. Oh, and after you learn these, don’t be afraid to astonish your friends with your amazing mental math abilities.

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Fractions, Decimals, Percents

Wednesday, July 21st, 2010

Fractions, decimals and percents are different ways of expressing the same value. Here’s how to convert them from one form to another.

Converting decimals to fractions

For any decimal, you should be able to figure what the last place in your decimal is. For example, .125 has digits in the tenths’, hundredths’ and thousandths’ place. Thus, .125 is essentially 125 thousandths which translates to 125/1000.

Converting decimals to percentages

Percent literally means “over 100”. i.e. x% = x/100.

So if you want to find what percent 12.5 is, you are trying to find x in this equation

If you rearrange the equation to isolate x on one side, you’ll see that to find x, you just need to multiply your decimal by 100. Thus, in this case, 12.5 = 1250%

Converting fractions to decimals

Converting any fraction to a decimal involves long division. A fraction is essentially the numerator divided by the denominator. Thus 3/5 is simply 3 divided by 5, which you can work out by long division to be 0.6

Of course the GMAT is not going to use such as fractions, so be sure to know how to do long division!

Converting fractions to percents

As mentioned earlier, x% is x/100 – meaning that it is a fraction with 100 as the denominator. So to find out what percent a fraction is, you need to manipulate the fraction you have to have 100 in the denominator and the numerator will be the percentage.

Suppose we need to convert into its percentage form. You need to convert it to an equivalent fraction with 100 as the denominator and find the numerator.

Thus, you are solving . (Solve this on your own and see if you get 37.5%)

Converting percents to fractions

This one is very easy and you should know by now that x% is x/100. Thus if you wanted to convert 320% to a fraction, it would be which you can simplify to be

Converting percents to decimals

From earlier, we learned that to convert decimals to percents, we multiplied the decimal by 100. To do the reverse (i.e. convert percents to decimals) we do the opposite – divide by 100.

This table summarizes what you need to do when you’re trying to convert something in the left column to a form in the top row.

Now practice fractions, decimals, and percents on Grockit!

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REPEAT AS NECESSARY – TIPS FOR ACING GMAT QUANT

Thursday, June 24th, 2010

So you are starting the initial phases of your GMAT preparation and you are probably wondering how to ace that quantitative section score. You feel pretty well versed when it comes to verbal, but the math is what is nagging at you. You spend many sleepless nights tossing and turning about those combination/permutation questions, as well as rate and distance problems, not to mention multi-variable calculus questions that just might pop up (ok, that is a joke, there will be no calculus on the GMAT). But all kidding aside, what are the best ways to increase that math score to put you over that 700 milestone? Good question, and I hope to answer some of these concerns and calm some of the nerves so that you are confident going into the final weeks of your test preparation.

Back to the Basics

No matter how good you are at math, I would suggest buying a GMAT guide (Princeton Review has a good one, think it is called “Guide for Cracking the GMAT”, or something along those lines) and brushing up on all the different kinds of math questions that they might throw at you on test day. This might sound very rudimentary and obvious, but the fact is test-takers fail to realize and understand what types of math questions they will face come test day. If you have a solid working knowledge of the typical questions, this is the first step in boosting your GMAT quant score. As you are probably aware, there are some areas in quant that the last time you saw such math was when you were wearing tube socks and playing wall ball at recess. “What is the difference between a multiple and a factor?” you say? If you don’t know the answer to this, you definitely should get up to speed with these elementary, yet key fundamentals.

Make a Plan

Nothing big was ever accomplished without a plan. Organize your game plan, your plan of attack if you will, before you start studying. I’m not here to tell you how you should structure your plan, but lay out on paper how long you think you will need to review, do practice problems and practice tests, and then brush up on weaker areas. This will probably take at least two months, so have an idea of how you want to allocate your time and stick to it. If you don’t keep up with your plan or feel that you are pressed for time, perhaps you need to think about pushing your test date back. Regardless, just thinking about how you approach your studies will serve you well in the end.

Practice Practice Practice

As you go along in your studies, more specifically when doing hundreds of practice problems, you will invariably get a feel for and find your weaker quant areas. This is a good thing!! Don’t get discouraged when you come across these areas, it is an absolute blessing that you have identified your Achilles heel. You won’t be able to find these weaker areas if you aren’t practicing literally hundreds of questions (I suggest the Official Guide for GMAT Review for good practice problems). After hundreds of questions, you will be able to tell what your strengths and weaknesses are. As far as strengths go, it probably doesn’t make too much sense to keep practicing these types of problems that you are comfortable with. As you go along, start to hone in on the areas that are giving you trouble. Perhaps you can keep a spreadsheet or notes of what types of questions are holding you back.

Repeat as Necessary

Now that you have found your weak areas, I suggest doing multiple iterations of these types of questions. In your final few weeks, make it your goal to really focus on these areas and master these types of questions. This will give you confidence as your test day nears, as well as the ability to tackle those problems that you are missing. The key here is repetition; just do as many as you can. Soon you will discover a comfort level with once more difficult types of questions and you will be on your way to acing the exam. Most folks seem to struggle with time on the GMAT quant section, and increased exposure to hundreds of questions within your “bad” areas will really serve you well on test day. As you go from question to question during your exam, you will really thank yourself for your efforts. You will be amazed how many similar questions you see and will probably even tell yourself “Cool, I just did a question very similar to this last week” and the preparation will come in very handy. The Boy Scouts don’t have the motto “Be Prepared” for nothing. Put in your time and it will pay off. Good luck!!

Posted in Data Sufficiency, GMAT, GMAT Preparation, Problem Solving, Quantitative | 2 Comments »

Properties of Numbers

Wednesday, May 26th, 2010

Math is all about numbers and you can imagine that quite a few concepts fall under properties of numbers. Practice is the only way of familiarizing yourselves with this type of question but there a few things that you can keep in mind as you work your way through Grockit.

Even and Odd Numbers

Sometimes, all that a question tells you is that the product of two distinct numbers x and y is not even. It then wants to know if x – y is always even. How do you figure this out?

One way is to plug in numbers. Suppose x = 5 and y = 3. The product of x and y is 15 (odd) and x – y is 2 which is even. Try this with a few other numbers and you can safely guess that x – y is always even if xy is odd.

Another way is to remember that

ODD * ODD = ODD

EVEN * EVEN = EVEN

ODD * EVEN = EVEN

In addition, for any number n, 2n is always even and 2n+1 is always odd. Try it. If n = 4, 2n = 8 which is even and 2n+1 = 9 which is odd. If n = 5, 2n = 10 which is even and 2n+1 = 11 which is odd.

Knowing this, you can use it to solve the above problem. If xy is odd, that means x and y must both be odd. That means that if x = 2n + 1 and y = 2m + 1, then x – y = 2n – 2m = 2(n – m). 2 times of anything is always even, and thus, you have just proved algebraically that x – y is always even.

Other good things to remember is that

EVEN + EVEN = EVEN

ODD + ODD = EVEN

ODD + EVEN = ODD

Estimating quickly

Being about to round up and down and estimate quickly is always a good skill. Knowing how to estimate fractions, in particular, can save you a fair bit of time on the GMAT.

Given this question: which of the following fractions is greater than ¼?

12/50
3/11
2/9
4/17
6/24

You should be able to recognize quickly that 6/24 = ¼ so choice E is out. Next look at choices C and D. 9 is close to 8 and ¼ of 8 is 2. That means 2/9 is less than 2/8 i.e. 2/9 is less than ¼. The same can be said of 4/17. 17 is close to 16 and ¼ of 16 is 4. That means that 4/17 < 4/16.

Looking at choice A, any fraction over 25 or 50 can easily be converted into its decimal form. 12/50 = 24/100 = .24 < .25 So choice A is out too. That leaves us with Choice B as the answer

Prime Numbers

By definition, prime numbers are only divisible by 1 and themselves. This is a very useful property to know. For example, if x and y are distinct prime numbers, then you know that x/y is not an integer because y is not a factor of x, or x would not be prime.

Prime factors

Knowing how to prime factorize will help you tackle almost any factorization problem. Take the number 70 for example. In order to find the prime factors of 70, divide 70 by the smallest prime, 2. If that’s not possible, move on to the next prime. 70 is divisible by 2, which gives you 35.

Try dividing 35 by 2 again. If that’s not possible, more on to the next prime. 35 is not divisible by 3, so try 5. 35/5 = 7 and since you are left with a prime number itself, you can stop there.

Through this constant dividing process, we can determine that 70 = 2*3*5

Try and see if you can find the prime factors of 244.

(You should get 168 = 2*2*2*3*7)

Let’s try applying it to this problem: The product of three positive integers is 70. If all of the integers are greater than 1, what is the sum of the greatest two integers?

We worked out just not that 70 = 2*5*7, meaning that the two largest integers are 5 and 7. That means that the sum is 12.

Squares

The last important thing to know about numbers is what perfect squares are. A perfect square is an integer that is the square of another integer. For example, 4, 9, 16, 25, 36 are perfect squares since they are integers and they are the squares of 2, 3, 4, 5 and 6 respectively.

The following is a simple application of the above concept. The only thing that might confuse you at first is the phrasing of the question. Which of the following is NOT equal to an integer squared?

Root 16
Root 9
27/3
37-12
49

The question is essentially asking, which of the 5 choices is not a perfect square. After you simplify the choices, pick the one that cannot be square rooted. (Did you get choice B?)

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GMAT Solving Two Linear Equations with Two Unknowns

Thursday, May 20th, 2010

Now that we’ve covered linear equations with one unknown (Solving Linear Equations with One Unknown), we can move on to tackle equations with two unknowns. In order to solve such equations, you need at least 2 distinct equations involving these unknowns.

For example, if we are trying to solve for x and y, we won’t be able to solve it using these 2 equations.

2x + y = 14
4x + y – 14 = 14 – y

Why? Because the two equations on top are the same. If you simplify the second equation, you get 4x + 2y = 28 which reduces to 2x + y = 14 – the same equation as the first. If the two equations are the same, then there will be infinitely many values for x and y that will satisfy the equations. For example, x = 2 and y = 10 satisfies the equation. So does x = 4 and y = 8. And so does x = 6 and y = 2.

In order to solve for an actual value of x and y, we need 2 distinct equations.

For example, if we had
2x + y = 14 ——–(1)
x – y = 4 ———-(2)

Then from equation (2), we can get x = 4 + y and substitute that into equation (1) to get:
2(4 + y) + y = 14 We can then solve for y. See if you got y = 2 Once you’ve got y = 2, you can substitute that into x= 4 + y to get x = 6.

An important lesson here is that you need as many distinct equations as you have variables. So if you are doing a data sufficiency question, you can sometimes just note that as long as you have two distinct equations, you will be able to solve for x and y. Disregard or other equivalent equations.

Sometimes, however, its possible for there to be no solution to the set of equations. This occurs when one side of each equation is the same, but the other side is different. For example,
2x + y = 14
2x + y = 0
has no solution. Its like saying that the same steak costs $14 and $0 at the same restaurant. Of course, the GMAT is not going to make it so obvious that the equations contradict each other. Usually, you would have to simplify one of the equations to check if it is
1. the same same as the other equation, in which case, you have infinitely many solutions
2. the same as the other equation on one side, but different on the other side of the equal sign. In this case, you have no solution
3. a distinct equation, in which case x and y has an exact value.

The GMAT might also require you to translate a word problem into a pair of simultaneous equations to solve. Let’s try this question from Grockit.

A package contains nothing but 35 DVDs and 15 videotapes. What is the total weight, in pounds, of the contents of the package?

(1) Each videotape weighs twice as much as each DVD.

If we let the weight of a DVD be x and a videotape be y, then according to this statement y = 2x

(2) The total weight of 2 of the videotapes and 2 of the DVDs is 1 pound.

Following the previous notation, 2y + 2x = 1

We clearly have 2 distinct equations meaning that we need both statements together to solve this question. Practice more on Grockit and you’ll start to get the hang of constructing and simplifying equations to see if they are distinct and, thus, solvable.

Posted in Data Sufficiency, GMAT, Quantitative, Series | No Comments »

Rate Problems on the GMAT

Wednesday, May 12th, 2010

The rate at which anything occurs usually involves some measurable quantity over time. Take speed for instance. Speed is distance over time and to solve any data sufficiency question involving speed, you need to know 2 out of 3 of these variables: either speed and time to find distance, or distance and time to find speed or speed and distance to find time.

Let’s start with a speed-distance-time question

What distance did Marty drive?
(1) Wendy drove 15 miles in 20 minutes.
(2) Marty drove at the same average speed as Wendy.

The question is asking for distance, so the statement you need has to provide some information relating to Marty’s speed and time.

Statement (1) gives you the distance and time (and hence speed if you need it) of some other person – Wendy. Statement (2) tells you that Marty drove at Wendy’s speed. Thus the two statements together give you Marty’s speed, BUT tell you nothing about Marty’s time. Hence the statements are insufficient.

Here’s another question: if Danielle ran a race at a constant speed, at what time did she finish?
(1) Danielle started the race at 8:00 a.m.
(2) At 9:30 a.m. Danielle was halfway through the race, and at 10:00 a.m., she was ²/₃ of the way through the race.

To know what time she finished, you need some data regarding the distance Danielle ran and the time she took to run said distance.

Statement (1) tells you what time she started, which might be important to know what time she finished but doesn’t give you data about the two things you need. Statement (2) tells you that she took 30 minutes to run 1/6 of the race that gives you both distance and time taken to run that distance. Thus, statement (2) is sufficient.

How about a general quantity-time-rate question?

Working at a constant rate, Keith can paint 7200 linear feet of shelving in 90 minutes. How long would it take Keith and Samantha, working together, to paint 7200 linear feet of shelving?
(1) Working alone, it takes Keith twice as long to paint the shelving as it takes Keith and Samantha working together.
(2) Both Keith and Samantha paint the shelving at same rate.

This question involves linear feet, time and rate. It is asking for the time Keith and Samantha would take together. Since the prompt already tells us Keith’s rate, we need to find Samantha’s rate. Normally, I would tell you that you need to have some data regarding Samantha’s time and linear feet of shelving she can paint in that time. But each of the statements relate Samantha’s rate to Keith’s directly.

Statement (1) tells you that Keith and Samantha take half the time as Keith alone. So the answer is 90 minutes / 2 = 45 minutes.

Statement (2) tells you that they paint at the same rate. So the answer would also be 90 minutes.

Clearly, each of the statements alone is sufficient. Generally, data sufficiency questions involving rates tend to be simpler if it is not a question involving distance and time. Because distance-speed-time formulas are supposed to be so familiar, the GMAT tends to make those questions a little more complicated. If it is a question involving the rate of flow of a liquid or how fast someone paints or works, then it will usually just require you to look at the rates of the various people or things in question.

Please visit the Grockit forum or leave a comment here to discuss further.

Tags: rate problems, speed/distance/time
Posted in Data Sufficiency, GMAT, Quantitative | No Comments »

How to start preparing for the Quant section of GMAT:

Monday, May 3rd, 2010

Some of you have left math behind, planning never to touch it again, and all of a sudden the GMAT comes along. You know that you were good in math but now that there has been a lag, you’re afraid you won’t be able to catch up on the fundamentals. The lines, polygons, integers, triangles, and (worst of all) the permutations and probabilities start to bother you. You know you knew this stuff– in fact you were always a grade A student—but now you have to get back up to speed.

What’s the best way to do that? Well, that’s probably a little different for everyone. But always remember this: if you were good in math at one point of time, you are still good in math. You have not lost your Quant skills, so don’t lose your self-confidence! It’s just a matter of logging the hours of study time before your math skills come back to you, and then, believe it or not, GMAT Quant practice can be fun!

The best way to begin your Quant preparation is to get the Official Guide notes and go through them. Try to not only read them but also to find and work out similar formulas. This will help you to brush up on some of the formulas and the topics. For faster results, though, try this method: read a topic from the Official Guide, and immediately get to the Grockit site and play a game on that topic, preferably in a group. That will help you pinpoint your weak areas, and the practice games will help your brain find those math skills that are lurking in there somewhere. Do this for each of the topics, starting with what you consider the easier ones and working your way up to the tougher ones.

Next, identify your weak areas. We all hate some topics but still we know that we have to prepare to face them—that’s a reality both on the GMAT and in life. The best thing to do for those topics is to schedule a game with a tutor who can help you and whom you consider strong in that particular area. Follow this process, topic by topic, and you’ll start to see your skills return.

Once you have refreshed your Math fundamentals and played games with the Grockit website, it’s time to see where you stand on with your GMAT score.

Here’s how you do it: Go to mba.com (the official GMAT® website) and download GMATprep software. The software has two mock tests and is the most accurate practice software available. Use the tests wisely since there are only two of them.

Take your first test after you have figured out the Quant and Verbal fundamentals. For verbal, follow the same strategy as mentioned above for the Quant. Do not try to complete the Official Guide (OG) before taking GMATprep Test 1. The software has some questions that are repeated from the OG and may skew your score.

After the first GMATprep test, you’ll start to see the results that you get from studying the OG and using Grockit for collaborative learning. Happy studying, and we hope to see you in a Grockit game sometime soon!

Posted in GMAT, GMAT Preparation, Quantitative | No Comments »

Operations on Rational Numbers

Tuesday, April 27th, 2010

Integers are numbers like -10, 0, 2, 5, 189. You might know them as whole numbers or numbers that do not have decimals. Rational numbers, in contrast, are numbers that can be expressed as a/b where a and b are integers. This would include numbers such as ½, ¼ -4 (which you can think of as -4/1), 0 and so on.

Most problem solving GMAT questions that deal with operations on rational numbers essentially require you to understand defined operations, to translate word problems into equations and to be able to do conversions.

Question Defined Operations

There are certain established operations. We all know that + represents addition and – represents subtraction and / represents division and ² represents squaring a number and so on. Aptitude tests often come up with their own symbols to represent a particular operation. Let’s examine the operation represented by ∆ below.

The question reads: let x ∆ y = x²/_y for all positive values of x and y.

This means that ∆ wants you to square the first number and divide that by the second number. Thus 6 ∆ 9 = 6²/9 = 36/9 = 4

Word Problems

Word problems may look tricky but if you work through each bit of information at a time, you might find that they are not as difficult as you imagined.

Let’s try an algebraic word problem: Allyn has t tattoos, which is half as many as Krystal and 4 times as many as Joshua. How many tattoos do the 3 of them have together?

Look at the first bit of information. Allyn has t tattoos. It is half as many as Krystal’s, meaning Krystal has 2t tattoos. Allyn has 4 times as many as Joshua, meaning Joshua has t/4 tattoos. Thus, they have t + 2t + t/4 = 13t/4 tattoos in total.

Here’s a much longer, wordier problem: In the first leg of a dog-sledding competition, the teams raced across a 120-mile route. If the Swiss team took 10 hours to finish the first leg, and the average speed of the Canadian team was 25 percent greater than the average speed of the Swiss team, how many hours did it take the Canadian team to finish the first leg of the competition?

What do you know?

The Swiss team took 10 hours to complete 120 miles. So their average speed is 120miles / 10hours = 12mph
The Canadian team’s average speed was 25% greater. 25% greater than 12mph is 15mph.
The Canadian team traveled 120 miles at 16mph meaning they took 120miles/16mph = 7.5 hours.

You can do the same for this question involving percentages: A barrel contains 40 kilograms of syrup that is 35% sugar by weight. If 10 kilograms of sugar are added to the barrel, the resulting syrup will be what percent sugar by weight?

What do you know?

35% of a 40kg of syrup is sugar. So 12kg of the syrup is sugar.
10kg of sugar is added. There is now 22kg of sugar. Overall, the syrup weighs 50kg now.
So the sugar percentage is now 22/50 %

Given the choices

you should be able to figure the answer without even calculating the precise answer of 22/50 simply by estimating. 22/50% is close to 25/50% which is 50%. Since 22/50 is less than 25/50, the answer should be choice D: 48%.

Conversions

One of the simplest operations on numbers is to know how to convert between units. Sometimes the GMAT will make up units such as in the following question.

If 100 “fnords” is equal to 1 “norton”, then how much bigger is 53 “nortons” than 23 “nortons” in “fnords”?

If you break this question down like you did the word problems, you would realize that it is essentially asking: how many fnords are there in 30 nortons.

Since 1 norton = 100 fnords

30 nortons = 3000 fnords.

Posted in GMAT, Quantitative | 2 Comments »

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