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Problem Solving

Categories : Problem Solving

Work problem is another common topic tested during GMAT . About 2-4 questions are asked from this topic. Work is a specific task assigned to one or more persons that are required to be completed in 'n' amount of time.

Here n is represented as days.

Suppose Jim works for N days then he can do 1/N of the work in 1 day
Suppose Tim work for M days then he can do 1/M of the work in 1 day

Now if Jim and Tim works together for 1 day then they can do ( 1/N + 1/M ) work in 1 day

So in 1 day then can do (M+N)/M*N

Now lets plug in some real numbers

N=10
...

Categories : Problem Solving

Active Thinking for GMATQuick brainteaser for you: If 3 bunnies can eat 3 carrots in one hour, how many carrots can 1.5 bunnies eat in one hour?

Really take a moment to think about it.

Do you have an answer?

Ok. If you answered, or even were tempted to answer, “1.5 carrots,” then I’m glad that you’re reading this article! The thing is, while the bunnies are eating carrots at the rate of one per hour, it doesn’t follow that 1.5 bunnies will eat 1.5 carrots. 1.5 bunnies will only eat one carrot, because 1.5 bunnies is really just 1 bunny. (That half a bunny isn’t feeling very well and doesn’t want any carrots.)

I don’t mean to say that this is a GMAT-style problem, but if you found yourself answering “1.5 carrots,” then you are prone to operating on autopilot. Students who operate on autopilot will often fall into traps, and they may become overwhelmed by questions that don’t fall clearly into easily recognized patterns. And let me tell you – you will likely see many problems on the GMAT that don’t fall into common patterns!

Active Thinking...


GMAT Process of Elimination - Data RangeWhat worries GMAT test takers in Problem Solving is the lengthy calculations, and translation of statements to equations. Lot of students prefers the use of calculators. If you have started solving a few GMAT PS questions, you might have realized that solving some of the toughest GMAT 800 questions does not require even solving them in a traditional manner. Process of Elimination is an often-neglected technique when it comes to solving time consuming and tricky GMAT Problem solving questions.

In this article, we will cover how to classify answer choices into groups, and guess the probable range of the answer based on the facts provided in the question. In order to be successful with this strategy, find out how many answers are close to each other in value. Group them together, and then start with data substitution.

Let us look at an example:

Q) Tim and Phil together can complete the flooring on 2nd floor in 6 days. When Phil was on leave, Tim completed a similar flooring job in 18 days. How long will...

Categories : Problem Solving

GMAT Clock ProblemsClock based math problems are among the most challenging and interesting problems to crack.

Basics
  
For every 60 units that a minute hand move in an hour , the hour hand moves 5 units.

For 12 hours the hour hand completes 360 degrees

1 hour  =  360/12 = 30 degrees
60 minutes = 30 degrees
Degrees turned by hour hand in 1 minute = 0.5 degrees

For 1 hour the minute hand completes 360 degrees

1 hour = 360 degrees
60 minutes = 360 degrees
Degrees turned by minute hand in 1 minute = 6 degrees



Lets test what we have learned:

Q) Find the degree between hour hand and minute hand at 3:32'

Hour hand = 3

1 minute ( hour hand) = 0...


GMAT Weighted AverageAverage Question is an important topic in GMAT problem solving and data sufficiency. Let us start with the Basics.
 
Average (Arithmetic Mean)


Average of n numbers a1, a2, a3, a4, a5....an

(An) = (a1+a2+.....an) /n

Example: Find the average of 34, 56, 75 and 83

Answer

a1 = 34
a2= 56
a3=75
a4 = 83

Total Number of Elements (n) = 4

Average (An) = (a1+a2+a3+a4)/n
= (34 + 56 + 75 + 83)/4 = 62

Shortcut to Remember:  An x n = a1+a2+.......an

Let us straight away apply this shortcut

Q) The average of four numbers is 20. If one of the numbers is removed, the average of the remaining numbers is 15. What number was removed?

(A) 10
(B) 15
(C) 30
(D) 35
(E) 45

Answer:

Four Numbers = a1, a2, a3, a4

n=4

An = 20

An x n = a1 + a2 + a3 + a4

20...

Categories : GMAT Tips, Problem Solving

GMAT Problem Solving TipsThe Problem Solving (PS) section of the GMAT may not be as quirky as the Data Sufficiency section of the test – but that doesn’t mean you don’t need to study for it! PS questions require more “straight math” than Data Sufficiency questions; in other words, they’ll probably be more like the questions you’re used to seeing on high school and college math tests. The best way to study? Master the basic concepts from geometry, algebra, statistics, and arithmetic — then check out these 10 helpful tips!

1. Make sure your fundamentals are strong.

The GMAT doesn’t allow you to use a calculator—which means you need to be quick and accurate with basic calculations. Be able to multiply and divide decimals. Know common higher powers and roots. Have fractions down to a science: Knowing right away whether 3/8 is less than 5/12 will mean you have more time later to work on more complicated calculations.

2. Choose numbers wisely.

Even questions that don’t contain variables can still be tackled by choosing numbers wisely. For example, if a question asks you about “a multiple of 6,” it’s probably quicker...


Work Rate ProblemsCarefully go through the following question types. These are the standard work rate problems that you would encounter in your GMAT Exam.

Working Together

In questions where individuals work at different speeds, we typically need to add their separate rates together. Make sure you keep your units straight. This doesn’t mean wasting time and writing each and every one out, but rather simply recognizing their existence. Note that when working together, the total time to complete the same task will be less than BOTH of the individual rates, but not necessarily in proportion. Nor, are you averaging or adding the given times taken. You must add rates.

Q) A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

The rate of worker #1 is 1 truck/6 hours. This can also be 1/6 trucks/1 hour. The rate of worker #2 is 1/7. When together, they will complete 1/6 + 1/...


Compound and Simple Interest GMATSimple interest and compound interest - essential topics for an MBA. GMAC thinks the same too. So you will find these questions randomly distributed in your GMAT Exam.

Simple interest is the most basic and is a function of P, the principle amount of money invested, the interest rate earned on the principle, i, and the amount of time the money is invested, t (this is usually stated in periods, such as years or months).

The resulting equation is:

Interest = iPt

In basic terms, the above equation tells us the amount of interest that would be earned on a principle amount invested (P), for a given time (t) at a given interest rate (i).

Example
If you invested $1,000 (P = your principle) for one year (t = one year) at 6% simple interest (i = given interest rate), you would get $60 in interest at the end of the year and would have a total of $1,060.

For compound interest, you would earn slightly more. Let’s look at similar type problem, though this one involves compound interest.
...


Have you wondered how writers can make a seemingly simple GMAT topic like fractions into time-consuming calculations. One strategy that GMAT test takers must adopt to simplify the calculations. For example

Dividing by 5 is the same as multiplying by 2/10. For example:

• 840/5 = ?
• 840/5 = 840*(2/10) = 84*2 = 168

Multiplying or dividing by 10’s and 2’s is generally easier than using 5’s. 90% of the time, fractions will be easier to perform arithmetic. Decimals are sometimes more useful when comparing numbers relative to one another, such as in a number line, but these questions are the exception. Even if given a decimal (or percent) looks easy, quickly convert to a fraction. Some common ones to memorize:

• 1/9 = 0.111 repeating
• 1/8 = 0.125
• 1/7 = ~0.14
• 1/6 = 0.166 repeating
• 1/5 = 0.20
• 1/4 = 0.25
• 1/3 = 0.333 repeating
• 1/2 = 0.5 repeating

Note: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easily be derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)

Denominators are super important. A denominator of a reduced fraction with a multiple of 7 will not have a finite...


Rectangular Solid

Learn the concepts behind volume and surface area before you start solving GMAT Solid geometry problems. All solid geometry problems come down to this - length, breadth and height. For data sufficiency questions, look out for values of l, b and h. if any of them are missing then it would be easy to eliminate answer choices.

GMAT Rectangle

6 rectangular faces constitute a rectangular solid
 
The formulas you need to remember for a rectangular solid are

Volume = Length (l) x Width (w) x Height (h)

Surface Area = (2 x Length x Width) + (2 x Length x Height) + (2 x Width x Height)


"If length = width = height, that means that the rectangular solid is, in fact, a cube."


Terminologies

Vertex: Wow! quite a confusing word? Not really

Vertex = Corner

a) Vertex is the number of corners in a...


Number Properties GMATGMAT Number properties may sound scary, but they just constitute elementary mathematical principles. You probably know most of these principles by memory; if not, you could easily execute a calculation to ascertain them. The best option, though, is to study these principles enough that they seem intuitive. The GMAT Quantitative section is all about saving time; making number theory second nature will definitely save you some valuable seconds.

1.Odds and Evens

Addition
Even + even = even (12+14=36)
Odd+ Odd = even (13+19=32)
Even + Odd =  odd (8 + 11 = 19)

To more easily remember these, just think that a sum is only odd if you add an even and an odd.
Multiplication

Even x even = even (6 x 4 = 24)
Odd x odd = odd  (5 x 3 = 15)
Even x odd = even (6 x 5= 30)

To more easily remember these, just think that a product is only odd if you multiply two odds.

Example Question

If r is even and t is odd, which of the following is odd?

A. rt
B. 5rt
C. 6...

Categories : Equations, Problem Solving

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...


GMAT Word ProblemsWord problems on the GMAT get an unfair reputation for being especially challenging. However, it’s helpful to think of them as just dressed-up algebra. The real challenge is that they are (1) long, (2) boring, and (3) require translation from ‘English’ to ‘Math.’ Here are a few questions to ask yourself to make sure you fully break down and understand the problem BEFORE you start to solve!

What is the problem really asking?

    Make sure to understand what the answer choices represent. Are they the total number of dollars of profit? The profit accumulated by Jenny only? The percent increase in profit from June to July? Taking the time to do this will also ensure you never leave a problem half finished. If you dive into setting up an equation too quickly, you may realize half-way through that you’re solving for the wrong variable. Sometimes word problems will add an extra step at the end. You may be busy solving for “x” and forget that the problem is asking for the value of “1/x”.

What information am I given?

    The best...


GMAT StatisticsEven if you fear statistics by its reputation, it is one of the easiest sections in the GMAT because a standard set of questions is asked and anyone who understands the fundamentals that I shall describe will be able to ace the questions. The three most basic topics in stats are mean, mode, and median. Usually, the GMAT will go one step further into range and standard deviation.

Mean: Mean is the average. Let’s say there are two numbers: 6 and 8. The mean would be:
(6+8)/2 =14/2 =7. If you analyze the number 7, it makes sense that it is average of 6 and 8. Using the same approach, the mean of n numbers a1,a2,a3…….an would be (a1+a2+a3…..+an)/n. If you remember this formula, you should be able to do well with mean questions. We shall discuss some of the standard questions in subsequent blogs, but for right now, remember the key formula and start doing some mean and average questions from Grockit games.

Mode: Let’s say that you are given a set of numbers, such as {4,3,7,9,9,11,10}. In order to find the mode, you have to arrange the numbers in ascending...


You will encounter the following three types of Profit/Loss problems in the GMAT:

Profit/loss as percentage of Cost Price

In this case you will be given the cost price and sales price, and will be asked to simply calculate the profit/loss incurred by the seller by entering into the given transaction. This will be done by dividing the difference between the Sales Price and the Cost Price by the Cost Price. To convert the decimal into a percentage, you will multiply it by 100.

Profit Percentage = ((Sales Price - Cost Price)/Cost Price) x 100

Selling price = Z x (Cost price)

Where Z is any positive number. When Z < 1 we have a loss. When Z = 1 we have neither profit nor loss. When Z > 1 we have a profit.

Profit or Loss % = (Z - 1) x 100.

Selling price = [(Y / 100) + 1]x (Cost price)

Where Y is the profit or loss percentage. When Y < 0 we have a loss. When Y = 0 we have neither profit nor loss. When Y > 0 we have a profit.

Profit/loss as percentage of Sales Price

Sometimes the problem will be worded differently and will require the test taker to calculate...




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