GMAT Quant: Question of the Day!

Try Picking Numbers with the GMAT practice problem of the day!

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

A. k/m
B. (k – m)
C. [100 (k – m)]/ (100 + k)
D. [100 (k – m)]/(100 + m)
E. [100 (k – m)]/ (100 + k + m)


If the original price per share of Stock X = 100
Let’s say k = 20
New price per share = 120

Original earnings per share of Stock X = 100
Let’s say m = 5 (since k > m)
New earnings per share = 105

Old ratio of price/earnings = 100/100 = 1
New ratio of price/earnings = 120/105 = approx 1.14

The percent increase is approx 14%.

Plug in our numbers into the answer choices, and look for the choice that also yields 14%:

A. k/m = 20/5 = 4 too small

B. (k – m) = 20 – 5 = 15 too big

C. 100 (15) / 100 + 20 = 1500 / 120 = 12.5 too small

D. 100 (15) / 100 + 5 = 1500/105 = approx 14. CORRECT!

E. 100 (15) / 100 + 20 + 5 = 1500/125 = 12

The answer is (D).

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3 Ways of Looking at “Profit” Questions on the GMAT

As someone who is about to shell out hundreds of dollars in MBA application fees, you know that money makes the GMAT-world go round. Profit is an essential concept for any aspiring MBA admissions applicant. The GMAT tests this concept in both Problem Solving and Data Sufficiency questions in three main ways. Let’s examine the need-to-know formulas with three GMAT practice questions.

1. A firm increases its revenues by 10% between 2008 and 2009. The firm’s costs increase by 8% during this same time. What is the firm’s percent increase in profits over this period, if profits are defined as revenues minus costs?

(1) The firm’s initial profit is $200,000.

(2) The firm’s initial revenues are 1.5 times its initial costs.

In this question from Grockit, we can start with our most basic Profit formula:

Profit = Revenue – Cost

Using Statement (1), we can say that 200,000 = R – C.
(1.1)r – (1.08)c = 200,000(1 + x), where x equals the amount of the increase. We still do not know R and C so we can’t find x. Insufficient.

Using Statement (2), 1.5c – c = p and (1.1)(1.5)c – (1.08)c = (1 + x)P. Here we can simplify.

.5c = p

.57c = (1 + x)p
Without continuing to solve, we can see that we can solve for x using substitution. .57c = (1 + x)(.5c), and dividing both sides by c will cancel out that variable and allow us to isolate x. Statement 2 is sufficient. Now to a more challenging question!

2. A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the stores gross profit on the 20 coats?

(1) If the selling price per coat had been twice as much, the store’s gross profit on the 20 coats would have been $2400.

(2) If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440.

This GMAT Prep question asks about gross profit.

Gross Profit = Selling price – Cost

For the value Data Sufficiency question, we need to know the price of each coat and the selling price of each coat. From the given information, we can use our known formula to set us the equation: P = 20 (s – c). So either we’ll need a value for s and a value for c, or we’ll need the value of (s – c).

Statement (1) tells us that $2400 = (20(2s – c)) or 2400 = 40s – 20c. We can divide both sides by 20 and simplify it to: 120 = 2s – c. We still don’t know s and c. Insufficient.

Statement (2) tells us that 440 = 20(s + 2 – c). Let’s simplify: 440 = 20s + 40 – 20c. 400 = 20s – 20c. 400 = 20 (s – c). 20 = s – c. Sufficient. Even though we didn’t solve for s and c separately, we were able to find the value of (s – c). Sometimes DS will surprise you!

3. If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?

A. 25% loss
B. 25% profit
C. 20% loss
D. 20% profit
E. 5% profit

Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100

The question asks about % profit or loss. It tells us that 20c = 25s, or 4c = 5s. So the ratio of the sales price to the cost price is 4/5.

Let’s simplify our Profit/Loss % formula by dividing each term by the cost price:

Profit/Loss % = (S/C – C/C) x 100

P/L% = (S/C – 1) x 100
We know that S/C = 4/5 for this problem. So we can plug in and solve:

P/L% = (4/5 – 1) x 100

P/L% = (-1/5) x 100

P/L% = -20%. The answer is a 20% loss.

Circular Permutations Questions

We’ve all seen those tricky Permutation/Combination questions involving people around a circular table. How do we solve them? Well, they’re actually pretty ridiculously easy!

Let’s examine one:

There are 7 people and a round table with 5 seats. How many arrangements are possible?

This question might seem complex at first because there are more people than there are seats. It’s kind of a Permutation AND a Combination in one!

So first we’re wondering, how many ways to choose 5 from 7? This is a simple Comb:

7C5 = 7! / 5!2! = 7 x 6 / 2 = 42/2 = 21 ways

So now for each of those ways, we’re wondering, how many ways can we order 5 people around a table?

For any table with “x” seats, the number of possible arrangements is (x-1)!, so here 4! = 4 x 3 x 2 = 24.

21 x 24 = 504

The correct answer is 504.

The key takeaway here is that “choosing” X from Y always allows for the Combination formula (x! / (x-y)! y!), and the number of arrangements around a circular table with “X” seats is always (X-1)! There’s actually not that much to memorize!

700+ GMAT: Rock Set Theory

Venn diagrams and matrices getting you down? No clue what “elements” are? Sets on the GMAT have a reputation for being tough, but that’s just because most students are less familiar with them. This GMAT board will fill you in on the basics!

The “Intersection” is an upside-down U symbol, and is the OVERLAP of the sets. That is, the intersection contains all the elements that are in BOTH sets. Notice the Venn diagram is used to show the Intersection.

It makes sense that the symbol for “Union” would be a “U” shape. The Union is always the total combined elements. If an element is in EITHER of the sets, then it’s in the Union.

Sometimes Sets questions will be combined with other concepts, such as percentages. They often will not require fancy Venn diagrams or the ability to use a matrix to solve. Watch this Grockit video to see an example of this. You probably didn’t even know this could be considered a “sets” question! 🙂

Like a Venn diagram, a Sets Table (or matrix) is a great way to systematically organize a lot of information, especially for a Sets word problem. Read through this blog on how to set one up! Notice how the table is set up 3 x 3.

 

Learnist: Best Math Strategies for the GMAT

Even if you aren’t a math whiz, better GMAT scores are within your reach! Here are the best strategies for GMAT Quant that will take your GMAT practice CATs to the next level.

Backsolve when there are numbers in the answer choices. Sometimes just doing the algebra will be the simplest way to the get the correct answer, but backsolving is a great strategy to check your work as you go. To backsolve, go through the answer choices and plug each one into the question. This video from Ron Purewal’s “Thursdays with Ron” series at Manhattan GMAT explains exactly how to work backwards.

Pick Numbers as much as possible on GMAT Problem Solving questions. Substituting abstracts like “x” for easy-to-worth-with integers like “2” and “3.” Keep the numbers small and make sure they are allowed by the definitions in the question. Notice how in this Kaplan video, variables can appear in the question stem and/or in the answer choices.

Here’s how it works:

  1. Pick numbers for variables in the question stem
  2. Solve for what the question is asking with your picked numbers
  3. “Translate” the answer choices using your picked numbers
  4. The correct answer will match what you found after Step 2!

Rock Statistics Problems on the GMAT!

Statistically-challenged? GMAT tests only a few stats concepts: mean, median, mode, range, standard deviation, min/max, and weighted averages. You probably have seen some of these already!

This sample video question will introduce you to the concept of “average” or the “arithmetic mean.” This is the most highly-tested Statistics concept on the GMAT. The takeaway formula is Average = sum of terms / # of terms.

This video explains how to find weighted averages, which is different from the arithmetic mean (though frequently confused with it). Find the SUM of the each group first, then add the SUMS for the numerator, and combine the total number of elements for the denominator to find the weighted average.

Check out video explanations for other stats concepts such as median, mode, mean, and standard deviation on this Learnboard!

Learnist: Simplifying Algebraic Expressions on the GMAT

Algebra is fundamental to GMAT Quant. A great way to get started on your GMAT prep is to refresh your skills in simplifying algebraic expressions!

PEMDAS is an acronym for the order of operations, which are the basic rules which govern the simplification of algebra. Notice how division/subtraction is always done in order from left to right.

Addition and multiplication are both “commutative” which means it doesn’t matter the order in which the operation is performed. This means that A + B = B + A, and A x B = B x A.

The Associative Property for addition and multiplication means that the numbers can be re-grouped in parentheses without a different outcome. For example, 2 + (3 + 7) = (2 + 3) + 7. Like the Commutative law, this is ONLY true for addition and multiplication.

The Distributive law allows us to “distribute” a factor among terms being added or subtracted. That is, a(b + c) = ab + ac. This law, along with the commutative and associative laws, will become second-nature to you the more you practice!

Remember this rule: you can ONLY cancel factors. Try to simplify the numerator and the denominator as much as possible if you’re looking for things to cancel.

Notice that algebraic expressions can be made more complicated with exponents, including negative exponents. Remember your exponent rules! When you have the same base in the numerator and the denominator, you can subtract the exponents.

Watch some video walk-throughs of some GMAT algebra problems involving order of operations and algebraic expressions on the GMAT – Simplifying Algebraic Expressions learnboard.