GMAT Rate Conversions
July 23, 2012
One of the simplest arithmetic rules is that when you divide something by itself, you get 1.
What’s 3/3? 1.
What’s x/x? 1
By the same logic, what do you get with, say, inches/inches?
That’s also equal to 1.
So let’s say that you need to find the number of seconds in 2 minutes. You can probably do this in your head! Multiply two by sixty and it’s 120 second. But have you ever stopped to wonder why that works? Well, you want seconds to remain, so you want to get rid of minutes—that means you want minutes on the top and on the bottom. You did the math instinctively, but if you had broken it down step by step it would look like this:
Minutes on top and bottom cancel:
Now, on test day you’d never go through all the steps just for something as simple as that last example. But that basic principle makes it easy to solve much more complex conversions on the GMAT. For instance, my car has a 17 gallon gas tank and gets 32 miles per gallon on the highway. If I’m highway driving at an average speed of 68 miles per hour, how long can I drive without needing to stop for gas? (Assume I don’t take bathroom breaks)
The question asks for hours. Once everything has canceled, we’ll be left with the unit we want on top–so to get hours on top, we start with the reciprocal of my speed:
Now, miles is extraneous. Since it’s on the bottom, we multiply by a proportion that puts miles on top:
Then, finally, to get rid of gallons, use the same strategy:
Most rate conversion problems in the GMAT quantitative section, however complex, function similarly. You’re just multiplying a series of fractions together—all that’s challenging is keeping the fractions the “right way” up so that you keep the units you want and cross of the units that you don’t.
Check out this video from our YouTube Channel for even more on the topic. Then try the practice question below. Good luck!
Question:
Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in
crates, each holding b boxes. What is the price charged per magnet, in cents, if
Magnabulk charges m dollars for each crate?
Solution:
Step 1: Analyze the Question
A complicated setup, with oodles of variables. Picking
Numbers will probably be a safe approach.
Step 2: State the Task
Our task is to calculate the price per magnet. The word per
signals a rate
Many GMAT word problems have wrong answers that can
be eliminated logically, and this is no exception. Since the
answer is the amount of money that each magnet costs,
we can be sure that the more dollars charged per crate (m),
the more money each magnet would cost. In other words,
the right answer would have to get bigger as m gets bigger.
Answers (A), (C), and (E) have m in the denominator, so
those expressions would get smaller as m gets bigger.
Those answers can be eliminated.
Step 3: Approach Strategically
We need to solve for “magnets” and “cents.”
What do we know about the number of magnets? Scanning
through the question stem, we find “Magnabulk Corp sells
boxes holding d magnets.” That means d magnets per box:
What do we know about boxes? “Boxes are shipped in
crates, each holding b boxes.” That’s b boxes per crate:
What do we know about the crates? “Magnabulk charges
m dollars for each crate.” That’s m dollars per crate:
And, of course, dollars convert to cents at the rate of
100 cents per dollar:
Then set up multiplication such that cents are in the
numerator, magnets in the denominator, and everything
else cancels:
That’s answer (B).
GMAT Ratio Problems: Avoid the Algebra
July 14, 2012
Mastering ratio questions on the GMAT requires systematic organization of the individual pieces and a solid understanding of how ratios are typically presented and tested on test day. One of the most common presentations of ratios on test day is a question that presents a part:part or part:whole relationship and asks for the actual number of a part, the whole, or a difference between the parts.
The first thing to note about ratios is that they represent relationships between items. On the GMAT Quantitative Section, the ratio is usually in the simplest form; I call this multiple level 1 because it represents the smallest potential positive quantity for each aspect of the ratio. For instance, if a question tells you that the ratio of apples to oranges is 2:3, you know immediately that the minimum number of apples possible is 2 while the minimum number of oranges is 3 and the minimum total pieces of fruit is 5. Also, the actual number for those items must be a multiple of that minimum. Selecting the correct answer quickly on ratio questions commonly revolves around your ability to determine a multiple for one of the parts in a ratio relationship.
In order to manage all of the information in the question well, let’s pull out a tried-and-true tool, the basic chart. I know that most of us set up a proportion for these questions and solve algebraically. We absolutely can deal with ratios in a traditional math route through a proportion and algebraic equation; however, setting up the algebra traditionally leaves more room for error and can take a bit more time depending on the complexity of the question. The method is ultimately up to you, but in your GMAT prep you always want to learn to choose the most efficient and effective route for the particular question at hand. If you love the algebra, go for it (For those who want to avoid it more often, check out this additional GMAT strategy). In this post, I want to introduce and explain my favorite way to deal with this typical ratio question type – the ratio grid:
| Multiple Level | ||||
|
1 |
Step 1: Identify Ratio Parts
First, let’s take a look at the different pieces of data that can be presented in a ratio question. The first things to identify about the given ratio are the individual parts. In the example ratio of apples to oranges from above, we have a base ratio of 2:3. The stated parts of the ratio are apples and oranges, so we plug these into the chart with their respective minimums.
| Multiple Level | Part 1: Apples | Part 2: Oranges | ||
|
1 |
2 |
3 |
Step 2: Finish Level 1 Quantities
Next, finish out your base minimums, determining the minimum total by adding the minimum individual parts and determining the minimum difference by subtracting the smaller part from the larger part.
| Multiple Level | Part 1: Apples | Part 2: Oranges | Total Fruit | Difference |
|
1 |
2 |
3 |
5 |
1 |
Step 3: Strategically Eliminate
At this point, pause and eliminate answer choices strategically based on the minimums you have identified. The answer MUST be a multiple of the corresponding minimum that the question is asking for. Often this one step is the last thing that you will need to solve the question. For example, using our hypothetical apples : oranges scenario above, if a question asked for the total number of apples, eliminate anything that is not a multiple of 2 because the total number of apples must be some kind of multiple of 2. If the question is looking for the total number of oranges, eliminate all choices that are not a multiple of 3. If the question is asking for the total number of fruit in the basket, eliminate all choices that are not a multiple of 5 and so on. If that does not eliminate 4 choices, we move on to the next level to evaluate those choices that are left.
Step 4: Plug in the Actual Value From Question
In a typical ratio question, along with the base ratio, the test-makers will give you an actual total for one of the parts, the total, or the actual difference. Your task at this point is to plug the actual value in at the appropriate place in the chart and to determine which multiple level that actual value is sitting at. For instance, for our scenario of the apple to orange ratio of 2:3, if the question told you that there are 30 total pieces of fruit in the basket, we would plug 30 in below the original 5 and determine the multiple level by identifying what 5 must be multiplied by to get to 30. Since, 30 is 5 times 6, we are working on level 6.
| Multiple Level | Part 1: Apples | Part 2: Oranges | Total Fruit | Difference |
|
1 |
2 |
3 |
5 |
1 |
|
6 |
30 |
Step 5: Determine Your Answer
At this point you can solve for any of the remaining parts. For instance, if the question told you that in a basket the ratio of apples to oranges was 2:3 and the total pieces of fruit in the basket was 30 and asked for the actual number of apples in the basket, you would multiply 2 by 6 to get 12.
| Multiple Level | Part 1: Apples | Part 2: Oranges | Total Fruit | Difference |
|
1 |
2 |
3 |
5 |
1 |
|
6 |
12 |
30 |
Now, let’s walk through these steps using a realistic GMAT question:
The ratio of girls to boys in a class is 6:7. If there are 18 girls, how many total students are in the class?
A) 18
B) 21
C) 27
D) 28
E) 39
Step 1: Identify the Parts and Step 2: Fill in the Remaining Level 1 Quantities
First, look at just the base ratio to establish the minimums for level 1. The ratio of girls to boys in a class is 6:7.
| Multiple Level | Boys | Girls | Total Students | Difference |
|
1 |
6 |
7 |
13 |
1 |
Step 3: Strategically Eliminate
Because we are ultimately solving for the total number of students in the class, we need to eliminate anything that is not a multiple of 13, our minimum number of total students.
A) 18 – eliminate
B) 21 – eliminate
C) 27 – eliminate
D) 28 – eliminate
E) 39 – keep (MUST be the answer)
And we are done! Always check your multiples before you deal with the rest of the question. Sometimes, this is all that you need to correctly and strategically solve.
Let’s look at one more that is a bit more difficult.
Three investors, A, B, and C, divide the profits from a business enterprise in the ratio 5:7:8, respectively. If investor A earned $3,500, how much money did investors B and C earn in total?
A) $4,000
B) $4,900
C) $5,600
D) $9,500
E) 10,500
Step 1 & 2: Identify Parts and Finish out Grid
First we look at the base ratio to establish some minimums. Three investors, A, B, and C, divide the profits from a business enterprise in the ratio 5:7:8, respectively. In this chart, I modified the total column slightly because the goal of the question is to deal with the sum of B and C.
| Multiple Level | A | B | C | Sum of B and C |
|
1 |
5 |
7 |
8 |
15 = (7+8) |
Step 3: Strategically Eliminate
The goal is to solve for the sum of investors B and C, so the answer MUST be a multiple of 15. Eliminate every choice that isn’t a multiple of 15.
A) $4,000 – eliminate
B) $4,900 – eliminate
C) $5,600 – eliminate
D) $9,500 – eliminate
E) $10,500 – Keep – MUST be the answer
Let’s look at one last variation of this pattern.
At a certain zoo, the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions at the zoo, how many sea lions are there?
A) 24
B) 36
C) 48
D) 72
E) 132
Steps 1 & 2: Set up the base ratio
At a certain zoo, the ratio of sea lions to penguins is 4 to 11.
| Multiple Level | Sea lions | Penguins | Total together | Difference |
|
1 |
4 |
11 |
15 |
7 |
Step 3: Strategically Eliminate
Since we are solving for the number of sea lions, eliminate any choice that is not a multiple of 4.
A) 24 – Keep
B) 36 – Keep
C) 48 – Keep
D) 72 – Keep
E) 132 – Keep
Step 4: Plug in Actual Value and Determine Multiple Level
“If there are 84 more penguins than sea lions at the zoo” is the given difference between the pieces. To get to 84 you must multiply 7 by 12, so we are at multiple level 12.
| Multiple Level | Sea Lions | Penguins | Total Together | Difference |
|
1 |
4 |
11 |
15 |
7 |
|
12 |
84 |
Step 5: Determine your answer
Since we are looking for the number of sea lions, multiply the base 4 by the multiplier 12. Therefore, “C” is our final answer.
| Multiple Level | Sea Lions | Penguins | Total Together | Difference |
|
1 |
4 |
11 |
15 |
7 |
|
12 |
48 |
84 |
The big takeaway for ratio questions on the GMAT is that most are about multiples. Make sure that you check multiples before you waste too much time walking through the problem completely. Also, organize your information systematically on test day to efficiently and effectively walk through every question on the test.
Do you have a favorite way to approach these questions? Post it in the notes so that we can all check it out.
GMAT Fences
June 4, 2012
In my years of teaching, I’ve seen all kinds of clever solutions to GMAT math problems. I’ve also seen all kinds of errors. Some are utterly bizarre—and fortunately, seldom repeated, because the students who make those mistakes usually face-palm when they review their tests and go on to learn from their missteps. But some errors are so common and so often repeated that they earned their own names. One such example is the “fencepost error.”
Here’s a simple example: Say we are setting up a straight fence that’s exactly 100 ft long, with posts every 10 feet. How many posts do we need?
Did you say 10? Tempting, but that’s the right answer to the wrong question. There are 10 sections of fence, each 10 feet long. But there are actually 11 fenceposts, because you start with a fencepost, at 0 feet!
See?
This error can trap the unwary GMAT student in a few different ways. The most common is in finding sums of series consecutive integers. The formula for the total of an evenly spaced list is to multiply the average value of that list by the number of items. So, you need to know exactly how many numbers you’re adding. So if a question asks for the sum of numbers between, say, 37 and 59, some students might just say there are 59 – 37 = 22 numbers on that list—but that doesn’t count 37, the first number. To ensure you solve for the correct value, you need to add the first “fencepost” and count all 23 numbers (write them out and count if you want to confirm!)
Also, rather oddly, this error shows up on the verbal section in sentence correction too. Clauses are the “fenceposts” in sentences, in a sense, and connecting words (therefore, however, so) are the fence sections. You can tell a sentence is improperly constructed if you don’t have exactly one more clause than you have connecting words.
Keep this error in mind as you solve your practice problems—and today’s question of the day. It’s a common mistake, but also an easy one to avoid once you’re aware of it. Practice will make sure you’re not fooled on Test Day.
Question of the Day:
In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 166 feet long?
A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Solution:
Step 1: Analyze the Question
Though this is not a Geometry question, a quick sketch of the situation will help illustrate how to solve it. 
So we know that the unit of one tree and one space is 1 foot + 14 feet = 15 feet.
Step 2: State the Task
To find how many trees can be planted, determine the feet required for a tree and the space between trees. Divide the total length of the street by the unit of one tree and the space between trees.
Step 3: Approach Strategically
Each tree takes up 1 foot, and each space takes up 14 feet. Together they take up 15 feet. Now find how many times 15 goes into the total number of feet on one side of the street:
166 / 15 = 11, with a remainder of 1 foot.
We can plant one last tree in the remaining foot, bringing the total number of trees to 12. This means along the street, we can plant 12 trees with 11 spaces between them, as long as we start and end with a tree. (E) is correct.
Step 4: Confirm Your Answer
Make sure your answer makes sense in the context of the question. Did you take into account the remainder of the division? Will an entire tree fit in the remaining space? You can use these questions to confirm your work.
GMAT Average Speed Problems
May 30, 2012
Imagine you are driving from Chicago to Los Angeles, and you want to know what your average speed needs to be to reach Los Angeles in a certain number of hours. You would probably start by determining the speed you will be able travel during certain parts of your journey. Since most of the distance will be covered by highway, you might plan to travel most of the distance at 70 miles per hour. However, you will also want to plan for some traffic when you are still in or near Chicago and when you get close to Los Angeles. During these parts of your journey let’s say you can plan to travel at 30 miles per hour.
When calculating the average speed at which you will be traveling, you need to avoid the trap of just averaging these speeds together and planning on an average speed of 50 miles per hour. Because the vast majority of your journey will take place at 70 miles per hour and only a relatively small portion will take place at 30 miles per hour, simply averaging the speeds is not sufficient. You need to account for the difference in the amount of time you will be driving at each speed. Once you do so, your average speed will be much closer to 70 miles per hour than 30 miles per hour.
The same principle will apply when you see average speed questions on the GMAT. Average speed is defined as total distance divided by total time, rather than the average of the speeds. Additionally, the average of the speeds will almost always be offered as an answer choice, so be sure to avoid it.
This can be especially tricky when a problem gives little information other than the two speeds. On test day, you should think strategically and pick a number for the distance, calculate the times using this number, and then plug into the average speed formula described above. Give it a try on the following problem.
Problem:
A canoeist paddled upstream at 10 meters per minute, turned around, and drifted downstream at 15 meters per minute. If the distance traveled in each direction was the same, and the time spent turning the canoe around was negligible, what was the canoeist’s average speed over the course of the journey, in meters per minute?
(A) 11.5
(B) 12
(C) 12.5
(D) 13
(E) 13.5
Answer
Step 1: Analyze the Question
A canoeist goes one rate in one direction, turns around, and goes back at a different rate. Whenever you deal with one entity that has different rates at different times, set up a chart to track the data. Otherwise, you’ll find yourself in a six-variable, six-equation system that will take a long time to work through. Also, notice that although the distance and time are never mentioned, there are no variables in the answer choices. Whenever variables will cancel out, consider Picking Numbers.
Step 2: State the Task
Our task is to calculate her average speed for the whole journey.
Step 3: Approach Strategically
The formula is this:
Average Speed = Total Distance / Total Time
But we’re seemingly told nothing about time, and the only thing we know about distance is that it is the same in both directions. So what to do? As with almost every problem involving a multistage journey, set up this chart:
| Rate | Time | Distance | |
| part 1 of trip | |||
| part 2 of trip | |||
| entire trip |
Now plug in the data we’re given:
| Rate | Time | Distance | |
| upstream |
10 |
||
| downstream |
15 |
||
| entire trip |
Now we see clearly that we’ll be able to know the time if we know something about the distance. Since we know whatever variable we put in place will cancel out by the time we get to the answer choices, let’s just pick a number for distance—one that will fit neatly with a rate of 10 and a rate of 15. A distance of 30 should work well:
| Rate | Time | Distance | |
| upstream |
10 |
30 |
|
| downstream |
15 |
30 |
|
| entire trip |
At this point, we can fill in the rest of the chart very straightforwardly. The entire distance is 60. The time taken upstream must be 3, and the time taken downstream must be 2. That makes the entire time 5.
| Rate | Time | Distance | |
| upstream |
10 |
3 |
30 |
| downstream |
15 |
2 |
30 |
| entire trip |
5 |
60 |
The speed for the entire trip, then, is 60 / 5 = 12. Answer (B).
Step 4: Confirm Your Answer
Reread the question stem, making sure that you didn’t
miss anything about the problem.
To all of you strategic thinkers out there, can you spot a way to quickly eliminate 3 of the answer choices without doing any calculations?
GMAT Word Problems Unravelled
May 23, 2012
Sometimes, you’ll come across a GMAT problem that gives you a lot of information. The relationship between the pieces of information may not even be clear at first. In my experience as a GMAT teacher, I’ve found that these types of questions tend to confuse students, especially when students try to immediately write one big equation to solve. Instead of attempting to reach a solution all at once, take a step back and follow a few standard steps.
First, do not panic. The question may look like it has too much data to consider in the two minute time frame you are allotted per question. You need to remind yourself that GMAT questions are written to be solved in about two minutes, so a strategy must exist to complete the problem in a timely manner.
Second, in order to find that strategy, start translating the question stem piece by piece. Do not expect to find one big equation; many complex word problems require a system of equations to solve. Even if you end up with four or five equations to start, you will be ok as long as those equations are relatively straightforward.
Third, solve any one variable equations. Use those results to solve two variable equations. Keep the variable you ultimately want to solve for in mind. Doing so may allow you to bypass some of the equations you initially wrote down.
By following the steps outlined here, you will avoid getting the various pieces of information confused, and you will be less likely to put variables in the wrong place. Additionally, you will not rush through the question, which leads to mistakes and ends up taking longer than the method described above.
Try the problem below. As you do, be sure to follow the steps we discussed.
Problem:
A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,020 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Step 1: Analyze the Question
Another two-stage journey. So despite the intimidating presentation, we know that we will transfer the data from the question stem into this chart:
Step 2: State the Task
We’re solving for speed on the first day, which is the top left box of the chart.
Step 3: Approach Strategically
Before you get too worried about what your solution will be, plug the data into the chart to help organize your thinking. The first thing we read is “On the second day, he drove 3 hours longer . . . than he did on the first day.” We know the total time will be 21 hours, so we can’t just pick a number. Let’s use t for time on the first day. That makes time on the second day t + 3.
Similarly, “On the second day, he drove . . . at an average speed of 15 miles per hour faster than he drove on the first day,” allows us to say that if r is speed on the first day, then r +15 is speed on the second day. The rest of the data is simply numerical:
Since the total of the two days’ times will be the time for the entire trip, we can say:
t + (t + 3) = 21
2t + 3 = 21
2t = 18
t = 9
We can put that into the chart:
That allows us to find distance for each day by multiplying (Rate 3 Time = Distance).
Now we have an equation that will allow us to solve for r, which is what we’re looking for—speed on Day 1. Since the total of the two days’ distances will be the distance for the entire trip, we can say:
9r + 12(r + 15) = 1,020
9r + 12r + 180 = 1,020
21r = 840
r = 40
Answer (D).
Step 4: Confirm Your Answer
Reread the question stem, making sure that you didn’t miss anything about the problem.
GMAT Challenges: Finding My Achilles’ Heel
May 20, 2012
Greetings, I would like to announce that I have officially figured out that my biggest challenge on the GMAT is translating word problems into workable equations that allow me to get to the right answer quickly.
When I first started studying for the GMAT, the words from these long and confusing paragraphs would float in one ear and out the other. I would desperately try to hold on to each word, analyzing each one looking for a clue that would help me. Then I would read one question over and over and over like the answer was going to suddenly appear and say ‘I was hear all along!!’ That’s the habit that Kaplan instructors train you NOT to do first. With this strategy, no wonder the words were just swimming around in my head with no meaning!
As I said, my Kaplan instructor showed me how to strategically read questions once and sort through the information provided to isolate exactly what is was needed to answer the question. In particular, he showed me how to identifying keywords in order to extract data and rephrase the facts in my own words. Additionally, he showed me how to pinpoint patterns that appear throughout each GMAT question type. This helped me a great deal on the verbal section, but I realized I was still re-reading quantitative questions. I felt stuck. From my diagnostics and CATs, I could see it was really affecting my score.
It’s not that I can’t extract the right information, but once I have the information I don’t know what to do with it. Should I make an equation? Am I dealing with ratios here or am I just adding & subtracting? Maybe I should draw a graph? For some reason my brain is having a hard time remembering and utilizing the strategies I learned during my course. I am taking quizzes and reviewing the wrong and right answers, and it has been helping. I also made notecards to memorize the strategies and use them as I review the quizzes and tests. What I notice is that I am getting better at translating word problems into workable equations, but I am still re-reading questions. This affects my time per question. Currently, I plan to concentrate a bulk of my preparation on word problems trying to skim down my overall time per question.
What other strategies should I employ? Is there a better approach? Hey Lucas and Brett, any advice?
Do any of you struggle with this problem? What’s your Achilles’ heel on the GMAT?
For about a year, I always used the same method to solve the following GMAT problem:
How many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution?
“This is simple percentages,” I would say. “Just start by taking 3% of 50 liters, which is 3 over 100 times 50, which comes out to 1.5 liters sugar…”
But one day, teaching this same quantitative problem, a student’s hand shot straight up. “Yes, James?” I said. (That wasn’t his real name, by the way, but it will do.)
“Eli, who cares about the sugar?”
I paused. “Well, the sugar will help us figure out the solution.”
“But you don’t need it!” James explained. “I’ve been a chemical engineer for years, so I do this problem all the time. The sugar is a constant. The amount of sugar doesn’t change, and that amount is always equal to the concentration times the volume. So just do CV = CV; 50 times 3 is equal to the final volume times 5!”
I paused, impressed, and amazed—and have taught his timesaving shortcut ever since.
However, there is a bigger lesson here than simple mixture problems. I had approached that problem uncritically. I “knew” how to find the right answer, so I never gave it a second thought. I spent far more time prepping the combination and probability problems given their complexities and hidden challenges. As a result of my complacency, I made extra work for myself.
In other words, the takeaway is this: don’t focus exclusively on your mistakes. Review your correct answers as carefully as your errors. There might be a time-saving shortcut that you missed the first time through. Or better yet, you might have used such a technique that you can notice, reconstruct, and repeat! It’s very tempting to spend all of your time studying those red X’s on your quizzes and CATs. But avoid that trap; looking at your right answers as well as your errors will help you stay positive, and more importantly, will give you many opportunities to raise your score.
On the GMAT, Use Primes to Crack Big Numbers
May 12, 2012
Everyone studying for the GMAT wants to identify the skills that will lead directly to the greatest point increases. While this can be difficult to do, given the adaptive nature of the exam, some skills definitely do come into play more often than others.
One of the most important skills to master for the GMAT is prime factorization. Finding prime factors can be useful on many different types of questions. On test day, if you are stuck on a question and unsure of how to solve, remember the big number rule. The big number rule is simply this: if you see a big number, one that is so large it is unreasonable to work with, find its prime factors. Once you have those factors, you should be able to simplify.
Every positive integer that is not prime, with the exception of 1, can be broken down into a series of prime numbers multiplied together. Additionally, each series of primes is unique and will only result in a single integer.
For example, let’s say you want to find the prime factors of 20. Start by identifying any two numbers that multiply to equal 20. We will choose 4 x 5. 5 is prime, so we cannot break it down further, but 4 is not, so we repeat the process. If you try to think of two numbers that multiply to equal 4, you will only come up with 2 x 2, which are both prime. Thus, the prime factorization of 20 is 2 x 2 x 5.
Now let’s say that instead of choosing 4 x 5, you choose 2 x 10. 2 is prime, so we leave it alone, but we need to break down 10. 10 equals 2 x 5, thus we again find the prime factorization of 20 is 2 x 2 x 5. Notice that no matter what numbers we choose, as long as the math is correct, we reach the prime factors.
Try the question below and see if you can figure out how prime factorization can help you solve.
Problem:
Is q a multiple of 48?
(1) q is a multiple of 6.
(2) q is a multiple of 8
Solution:
The stem asks whether q is a multiple of 48. It’s a yes/no question so you should see if you can answer the question with both a yes and a no. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, so we need four 2’s and one 3 to know that q is a multiple of 48.
Statement 1: This tells you that q is a multiple of 6. The prime factorization of 6 is 2 x 3, so we know q has one 2 and one 3, but we do not know if it has the additional three 2’s we need, so this statement is not sufficient.
Statement 2: If q is a multiple of 8, we know that it must include the prime factors 2 x 2 x 2, which gives us three 2’s. Since we do not know if it will have the additional 2 and one 3, it is insufficient.
Statements 1 & 2: If q is a multiple of 6 and 8, it must have one 2 and one 3 in its prime factors, so it will divide by 6, and three 3’s in its prime factors, so it will divide by 8. This means that q must have three 2’s and one 3. Note that one of those 2’s is being used to divide by 6 and by 8, since we need to be able to divide by both, but not at the same time. However, to reach 48 the prime factors would need to include one additional 2. Since we do not know if q would include a fourth 2 or not, the statements are still not sufficient. Therefore, the answer is (E).
GMAT Quant Problems: Divide and Conquer
May 3, 2012
We all love to impress our friends with tips and tricks, especially geeky GMAT tricks…Come on, admit it. These divisibility tricks are always crowd pleasers. More importantly though, divisibility problems show up regularly enough on the GMAT that to be prepared for test day you should know the divisibility shortcuts for whole numbers 2 through 10. The following list will tell you the quickest way to check if an integer is divisible by each numbers:
Two: If the number is even, it is divisible by 2.
Three: Add up all of the digits. If the result is divisible by 3, then the original number is divisible by 3. For example, 534 is divisible by 3 because 5 + 3 + 4 = 12, which is divisible by 3.
Four: Look at the last two numbers. If that two digit number is divisible by 4, then the entire number is divisible by 4. For example, 544 is divisible by 4 because 44 is divisible by 4.
Five: If the units digit is either 0 or 5, then the number is divisible by 5.
Six: Check if the number is divisible by both 2 and 3, using the rules described above. If it is, then it is also divisible by 6.
Seven: Just do the long division. While you may have learned another way to check if a number is divisible by 7, it will be more time consuming than doing the actual math.
Eight: This one is tricky, because it is conditional. Always start by looking at the hundreds digit of the number. If the hundreds digit is even, the final two digits need to be a two digit number that is divisible by 8. Thus, 5,248 is divisible by 8 because 2 is even and 48 is divisible by 8. If the hundreds digit is odd, however, the final two digits need to be a two digit number that is divisible by 4, but not by 8. Thus, 5,344 is divisible by 8 because 3 is odd and 44 is divisible by 4, but not by 8.
Nine: The rule for 9 is similar to the rule for 3. Add up the digits. If the result is divisible by 9, then the number itself is divisible by 9. For example, 486 is divisible by 9 because 4 + 8 + 6 = 18, which is divisible by 9.
Ten: If the units digit is a 0, then the number is divisible by 10.
Tough GMAT Problems: When Should You Just move on?
April 28, 2012
One of the biggest mistakes students taking GMAT practice tests make is spending too much time on quantitative problems. This is especially true of problems they are unsure of how to solve.
Remember, the quantitative section of the GMAT asks you to complete 37 questions in 75 minutes. This means that you have only two minutes per question. That’s not much time as I am sure many of you already know. Thus, it is important that you use your time in the most efficient manner possible.
While many test-takers feel they will not be able to complete the test in time, you should also keep in mind that the questions are designed so that it is possible to complete each one in an average of two minutes. While some questions will take a little more or a little less time than this, you should never be spending over five minutes on an individual problem. If you do find you are reaching the five minute mark on a question, even if you think you are approaching it correctly, you need to move to the next problem. For someone who knows the correct approach, no GMAT question will ever take five minutes. The time you are taking is itself the clue that you do not know how to reach the answer correctly.
No matter how high of a score you are trying to achieve, you will miss some questions on the GMAT. You are better off identifying those questions quickly and providing yourself with more time to handle the questions you will be able to get right. By following this strategy, you will maximize your GMAT score, which is always the end goal.
