Data Sufficiency

Carefully 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/...

Simple 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.
...

Absolute Values (AVs) questions in GMAT can be a time saver for you if you understand a few rules. Capture the following notes and use it as a reference for your GMAT exam.

1. Absolute Value equations are two equations disguised as one

You can split up any equation involving absolutes into two, and solve for each solution. One will look identical to the given, and the other is found by multiplying the inside by -1. Remember to multiply the entire expression by -1.

| (x + 5)/3 | = 11 turns into:

(x + 5)/3 = 11, and

(x+5)/3 = -11

x + 5 = 33

x + 5 = -33

x = 28 x = -38

Note that plugging either x = 28 or x = -38 into the original equation will check out. Also note that solutions for variables within absolute value questions can be negative. What is spit out of the AV cannot be negative, but what goes in can be anything.

2. Think of Absolute Values as distances from zero

If an AV = 15, that means whatever is inside the AV is exactly 15 above or below zero on the number line.

| x + 5 | = 15

_____-20_____-15_____-10__________0__________+10_____+15_____+20_____

x = -20 and x = 10. Note that this is a SHIFT of -5 from the constant on the...

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.



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...

Even 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...

A sizeable number of GMAT math test questions belong to the Geometry section.  Some of these questions test  a candidate’s ability to understand 2-Dimensional Geometry by asking the candidate to calculate the area, perimeter or circumference of a geometrical shape.

The following geometrical shapes are most common – Triangles, Quadrilaterals, Rectangles, Rhombuses, Squares, Circles and Trapeziums.

Triangles – A triangle represents an enclosed shape made by joining three straight lines. The area of a triangle can be calculated as follows:

Area = ½*Base Side*Height of the triangle

In this formula, the Base Side can be any side of the triangle. However, depending on the base side chosen, height of the triangle needs to be ascertained. Height of the triangle is the shortest perpendicular distance from the Base side to the height of the Apex of that triangle.  Note that the height of a triangle may need to be calculated outside the triangle, depending on the base side chosen.  


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True to their name, Data Sufficiency questions ask you to determine when you will have enough information to make a conclusive decision.  In doing so, these questions can assess your ability to plan ahead for a task; to elicit an effective return-on-investment (remember, you can’t use both statements if one of them is, alone, sufficient), to find flaws with conventional wisdom, and to think flexibly. Data Sufficiency questions also strike fear and loathing in the hearts of many GMAT examinees, but hold a special place in the hearts of a select few who love the nuance that these questions permit.  

There’s a hard-and-fast rule regarding Data Sufficiency that people don’t know and use as much as they should: the statements can never contradict each other.  Knowing this, if your answers for statement 1 and statement 2 are different, you must go back and reconsider your math; as Boston GMAT tutor David says, that’s an “answer choice F”, meaning that you just effed up the math somehow.

Consider the question:

Is x < 0?

1) x^2 = 9x

2) The absolute value of x = -x

...

Perhaps no GMAT item is as symbolic of the test as is a Data Sufficiency question.  It is an iconic question format, unique to the GMAT and true to the aims of this specific test: to reward those who show the higher-order reasoning skills that will lead to success in business.

The corporate world is full of “yes men” and “groupthink” – of the kind of inertia that leads companies to think in the same direction without considering alternate points of view.  To combat that, employers and business schools seek those who can see the entire array of possibility, and the GMAT tests for that in many Data Sufficiency problems.  Consider a problem like:

Is the product jkmn = 1?

(1) jk/mn = 1

(2) j, k, m, and n are integers

Considering statement 1 it’s quite easy to get the answer “NO”.  Using 1, 8, 2, and 4, for example, satisfies statement 1?s constraints but clearly gives a product unequal to 1.  So does 1, 20, 5, and 4.  But having just one “NO” should immediately change your focus toward getting the other answer.  A series of nos using similar numbers (1, the product of two integers, and those two integers is the formula...

Data Sufficiency questions are supposed to be hard; more so than any other question type they tend to represent a chess match between you and the author, as the author has two chances to get you to make a mistake.  She won’t likely waste either statement giving you an easy pass – the questions have to elicit something from you in terms of efficiency or ingenuity in order to answer them correctly, so if an answer choice seems obvious within 15-20 seconds and you can’t spot a trap, well, you just fell into the trap.  Consider the question:

What is the value of x?

1) 3x + 2y = 15

2)  y = (-3/2) (x – 5)

This should pretty obviously be C. 

Two equations, two variables, neither works alone but both work together, right? 

But that is too easy, and the GMAT won’t often give you the answer that quickly.  Much as though the author had moved a pawn...

Data Sufficiency questions are not the same as your regular "Find the value of x" question. GMAT DS Questions require you to adjust in your approach to Math Problems. You are not primarily concerned with the final answer, but rather whether you have enough information to get you to that answer. For example, if you’re asked to find the value of x, and a statement tells you that 300x + 257 = 1345, you know that this statement is sufficient, because you can perform arithmetic on that equation to isolate x. Are you going to perform it? No, because it’s too complicated and you don’t need to! All you’re concerned with is whether you can find the answer.

It might strike you as odd, but because of this principle, you can tackle some supposedly difficult DS questions without writing down a single equation or calculation! Sounds too good to be true, but in actuality, it makes a lot of sense. Remember, in business school you’ll be given data in case studies, and you’ll be expected to determine relatively quickly what information is relevant. DS questions are perfect for testing this ability because you have to look at the information given to you and cut to the heart of what is most important about that information.

As an ex