# 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

# 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.

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.

# 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.

# GMAT Success Stories – Get Inspired!

Occasionally, I like to post some “GMAT Success Stories” — cool, first-person accounts of how others have rocked their GMAT. One of my favorite sayings is that success leaves footprints, and it’s 100% true! Most of these “success stories” come from the awesome site Beat the GMAT. I’ll try to post some of my favorites! Today’s is reposted here from Brett, a former student of mine.

Hope you enjoy!

My 700 & awesome tips to make it happen. You’re welcome

I officially started my GMAT preparation in November of ’11. Here is a little background about me I’m a white male 27 years old. I’m originally from Boston but have lived everywhere from Barcelona, to South Beach, to my current residence in Las Vegas, Nevada. I have a very friendly and outgoing personality and have held very unconventional jobs such as being a professional online poker player, a personal trainer/model, etc.

Since I was not carrying a job at the moment I studied for the GMAT around the clock for a month, I viewed it kind of like a poker game always searching for that advantage, that edge. Poker will be a theme throughout this post because I come from a high-stakes poker background and I brought a lot of those transferable skills to my GMAT preparation. I had the Official Guide, the blue and green books (Math/Verbal Review). On my 1st attempt I strolled into my testing center which was hilariously right on the Strip in Las Vegas and crashed out with a mediocre 590. I was not happy. What does a smart person do after a setback? He/she continues to work hard but also examines their approach/strategy.

Strategy Tips: Sentence Correction

The key to the Verbal Section revolves around Sentence Correction. If you want to have a great Verbal score your sentence correction has to be just lights out. You need to lean off of this section to support you throughout the entire verbal section and try to eliminate the potential for strings of incorrect answers. This is the most important part of the GMAT to make flashcards on. It is the area most largely represented on the Verbal Section and a spot you really need to be looking to actively bank time.

On another note, don’t be one of those fools who tries to memorize every idiom, that is completely useless and a waste of time. The idioms aren’t tested very often and unfortunately you have to kind of feel it out based on the meaning of the sentence. If you do miss an idiom however make sure to make a note of it on your own personal “IDIOMS” flashcard.

Here is the optimal way to approach sentence correction. As the Verbal tutorial ticks down (1 minute) as you prepare to begin this section, write ABCDE horizontally on the right side of you pad 4x on each of the 1st four pages you are going to use. Make them neat with slight spacing between the letters and leave space so the 4 aren’t clustered on top of each other. It is optimal to write these keys on the right side because your Critical Reasoning and Reading Comprehension notes will naturally flow from left to right as you write, so keeping these sentence correction on the right will help keep you more organized and you won’t become flustered, where as you might if you do each question on a random part of the page. The key to success is being calm and organized and your scratch pad strategy should be no different. This move will save you time and keep you organized on the Verbal section which equals points.

Once you see an SC read A, you do the standard stuff look for errors. If you see one you snap cross it off and look for that error repeated in other answer choices. You only job when you read choice A is to do one of 3 things. You either cross it off if you’re sure it’s wrong and can identify a grammatical rule violation that proves it. You put a – (a minus sign) if you don’t really like choice A but you can’t see anything to eliminate it, and you right a + on top of answer choice A if you like it, and the sentence seems correct and clear. This move really takes the pressure off and allows you to find the worst choices first instead of having to make a strict yes/no judgment call on choice A Then a standard elimination strategy occurs, as you reach tougher SC questions this +/- system increases in value because it allows you to identify whether you kind of liked or didn’t like an answer. Trust me in a pressured time situation you will basically instantly the forget the choice you just read and having that helpful +/- reminder can keep you on track as you approach the final couple of choices.

Stop doing sentence correction on feel. How committed are you to the GMAT? To the Verbal Section? To Sentence Correction? You can scrape by with knowing some subject verb agreement and avoiding the word “being” right? Wrong answer buddy, you need to build this thing from the ground up. If you can’t tell me what the difference is between a gerund and participle right now or when it is correct to use “would + verb root tense”, you’re just flat out not that serious about sentence correction. I’m giving a shout out right now to fellow Bostonians Dave and Jen who’s 4-part SC lesson on Knewton Prep is the best I’ve seen and really teaches you the underlying grammar structure of what you need to know. So stop just doing a bunch of SCs because even when you do ok and think you’re “improving” as your time to completion decreases. I can assure you when test days comes and you use a little too much “feel” on your practice tests when nothing was on the line, you will start breaking down on the real thing under the pressure. You will second guess yourself, you will spend time you can’t afford to be spending which will prevent you from crushing. Trust me, I know this from experience. As a final note I was rather furious when I took my test yesterday to find 4 SC’s that incorporated the use of dashes in the middle of the sentence, sometimes intertwined with the underlined portion. I had no formal training in how exactly to operate with all these dashed portions and this hurt my score a bit. Kinda feel like writing the GMAC a letter cursing them out, hah.

Ok, back to my journey. So after this score I wrote an email describing my experience to my family and a few close friends. Some people supported me, especially two of my closest friends. However my dad wrote me a vicious e-mail screaming at me about getting my life on track. I wonder if he would have wrote that had I came back with a great score? As we say in the poker community, it was a pretty “results oriented” e-mail. After that I envisioned the day I could write a victorious and sarcastic e-mail with a great score and thanking everyone who supported me. So things were looking up, I studied hard night and day for the next month, and I purchased the Verbal Section of the GMAT Pill. The RC was great, the SC was good. The CR was some questions with random diagrams you’d never actually have time to draw on the actual test and just wasn’t very good (get POWERSCORE book for CR). When trying to improve at something it’s never a bad idea to model/learn from the people who are the best. So I decided to book a coach, her name is Vivian Kerr (Grockit) she’s a Cali girl who’s a flat out stud at standardized tests so I decided to sign her to a long term deal.

Strategy Tips – Tutoring:

Provided you can afford it, it’s never a bad idea to have a superstar in your corner to spot things you can improve and keep you real sharp. While its obviously important to attack your weak areas, its also important to note how a tutor approaches questions stylistically. Sometimes a tutor can help you find the best way for you to approach a question type, but sometimes figuring out what doesn’t work for you is just as helpful. I talked to my tutor about specific areas but also strategies of what to study, and how to study most effectively. It was definitely helpful and got me thinking about things the right way.

Test Day Recap: I woke up at 8am and had a real chill morning, I flipped thru my flashcards I ate some cheerios and I watched a tennis match on TV. My roommate woke up at 12 like the tool that he is and we went to eat breakfast together at a diner. After this late breakfast I texted a few of my closest friends who had been supporting me through these hard times. Here’s a txt convo with me and one of my closest buddies.

Brett: Wake up George, it’s judgment day
George: the bell tolls for thee
Brett: Haha, light a candle for me, I’ll call you at 8pst after it ends no matter what the score, love you baby, my time to shine
George: Fly like an angel Brett, it’s too beautiful

Haha yeah we’re pretty weird. After that I went to my desk and did 3 problems of each type just to warm up a bit. And since I’m being completely honest in this review at this risk of sounding like a lunatic… for 10 minutes I paced around our house yelling things like “Lets fkn ball, I’m bout to wreck shop, lets fkn go” or some combination of rallying phrases to psych myself up. It’s was like the 8 mile soundtrack “if you had…one shot” This was my last shot.

I left for the test center at 2:45pm for my 4pm start giving myself plenty of time to hang out. Usually it takes 15 minutes to get to this testing center. There was a huge accident on the highway and I was forced to exit and enter the strip on the opposite side of where I needed to be I fought thru immense traffic and arrived at the testing center at 4:10pm. The guy informed me there was a 15 minute grace period and if I was 5 minutes later the appointment would have been cancelled, whew. Then there was some problem where these clowns on MBA.com copied down my birthday as 5-5 instead of 5-10 so they had to call in and get the green light.

I neglected to mention earlier that the one positive from my first GMAT attempt was I got 6.0 on both essays which isn’t the easiest thing to do. I had decided beforehand to spend 15 minutes on each essay, to get a bit of a warm-up but I certainly wasn’t going to expend any energy actually caring about what I wrote. The 1st question was “what has more influence in a nation or a community, a powerful business leader or a government official” My first paragraph was entirely devoted to ripping on the question, claiming that this was the worst GMAT essay question I’d ever seen. “To combine two vastly different entities such as an nation or community into a entity is downright ludicrous and makes this essay question the worst one I’ve ever laid eyes on.” I was laughing at my own essay staying really loose and calm. The second essay involved me berating a business owner and more hilarity ensued. Whoever reads my essays are definitely going to be cracking up. I wrote personal messages at the end too, like “hey have a good weekend, god bless you” just random stuff like that.

It was all business on the math section I started off ripping, it was a battle between me and the GMAT. I’m pretty sure I snapped off 9 of the first 10 and after that I could feel the test start to get angrier and angrier that I was doing well. A huge bright spot for me was an area I worked very hard on and that was data sufficiency. One of the pointers I had gotten from my tutor was to spend a bit more time trying to break-down the prompt and not sprinting directly to the statements, this definitely pays a lot of dividends.

Strategy Tips Data Sufficiency:

Here is my best data-sufficiency tip, you won’t find it in an online course, or on a forum, or from your friend who took the GMAT last year, but I’m a big believer in it. Start with the easier/shorter statement! I do this every time. This just makes your life so much easier you get insight into the problem dealing with a much more basic statement. You build momentum and confidence if you can correctly analyze it too. Sometimes if it’s sufficient you know the true answer to a value question, and although you obviously don’t want to carry-over information. Knowing the real answer will help you look at the harder statement in a more intelligent fashion

Guessing Strategies: So back to the test, I was rolling thru with a gleam in my eye as the test continued. I ran into a long word problem-ish DS with a few complicated formulas which is definitely a weak spot of mine. I practice what I preach guys I used the 5-second chalk. Obviously on DS you want a strong bias against answer choice E, especially on harder ones. This is because most people think logically and when their giving up and feel like they’re outclassed they choose E which is akin to the fold button. We need to be thinking one step ahead of the GMAT. They’re banking on us doing what the majority of test takers would do. If they’re expecting us to fold we need to call. I would have a slight bias against C as well and usually pick A or B. Ok this is advanced but listen carefully. A GMAT problem is supposed to take you 2 minutes. Therefore if it’s a long prompt and two pretty tough statements as in the aforementioned problem, probably one of the statements is going to be a bit easier to get through and the other is going to be tougher because after all if both statements were super hard…is it really solvable in 2 minutes? As a final bias I would choose whichever one looks harder because often times if you were to actually do the problem, the easier statement will pan out as insufficient way and the hard one will be sufficient in a way that’s hard for you to see or figure out. This is obviously not always going to be true but it is the percentage play.

Ok back to the test I was just in a zone and was basically right on pace effectively guessing and hanging as tough as I could. I finished just on time. As a final pointer on the math section to those of you trying to increase your score. Remember, I moved up from a 580 to a 700 so it was basically a completely different test. When I got the 580 I had racked up extra time and easily was able to finish so I spent it in the middle of the test. If you’re looking for a Q49/Q50 you have to keep the big picture in mind. Assume your talent and that the questions are going to get tough, and really try to hold on to the extra time you bank early on in the 1st 10 questions. Once the test realizes you’re a stud they’re going to try to take the hammer to you near the end and this is where you really need to try to have this time to use. So don’t needlessly waste it like I did in the early/middle of the test because double checking a problem you’re 90% sure of because that will hurt you later on down the road, those 4-5 minutes you saved up seems like a good chunk of change, but you can go broke quickly..This happened to me, the last 3 problems were really tough and to be honest on question #35 I started breaking down under the time pressure and couldn’t think straight on a problem I felt I was supposed to get. I was really wishing I had been a bit more urgent earlier on as I was forced to basically guess on 36 and run a 1/3 on #37. I probably had a Q50 going into the last 3 problems and settled for a pretty sweet Q49.

~Brett

# GMAT Quant: Question of the Day!

Today let’s work on a sets problem using Venn diagrams!

In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

(A) 11N/12
(B) 7N/12
(C) 5N/12
(D) 6N/7
(E) N/7

This question can be solved using a Venn diagram or a matrix to make sense of the information:

The key to understanding this question lies in the last sentence:

who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).

If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12-4 = 8 are from one of the six states but NOT applied science. y = 8.

3 + 8 = 11

So we are looking for an answer choice that gives us 11 when N = 12; the answer is (A).

# What’s the Triangle Inequality Theorem?

Triangle Inequality Theorem is fair game on the SAT, ACT, GRE, or GMAT. It’s often forgotten by test-takers, but when it pops up, you’ll be glad you know it! The theorem essentially states that the third side of a triangle must be between the difference and sum of the other two sides.

For example, if we had a triangle in which two sides were 6 and 9, then the third side must be between 3 (9-6) and 15 (9+6). The third side cannot actually equal 3 or 15, it’s important to remember.

Let’s try a practice question utilizing this math rule!

If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

A) None
B) I only
C) II only
D) II and III only
E) I,II and III

If two of the sides are 2 and 5. Then the range of possible values for the third side can be expressed as:

3 < x < 7

Perimeter is the sum of the sides. Let’s choose 3 and 7 as values for the 3rd side (even though we know they are the end-limits only) to create a range for the perimeter.

On the low end:

2 + 5 + 3 = 10

On the upper end:

2 + 5 + 7 = 14

So the perimeter range can be expressed as:

10 < x < 14

The perimeter must be BETWEEN 10 and 14. The answer is (A).

Here’s a link to a lot of great Triangle review topics if you want more Geometry practice: http://www.beatthegmat.com/mba/category/tags/gmat-math/geometry/triangles.

# Learnist: How to Study for the GMAT in 30 Days

Need to cram for the GMAT in only a month? Here’s how to get the most out of 30 days of study-time!

There’s only one “Official Guide,” so whether you have 30 days or 6 months to study, you’ll definitely want to pick up a copy! Learn the format, content, and do a general overview of the GMAT test itself using the OG 13th edition. Make sure to go to MBA.com and take advantage of the official prep material provided there!

Study every day, and don’t procrastinate! You will need to be disciplined about your studies. Work backwards from your test date. Don’t cram on the weekends only! With only one month to study, you’ll need to do at least some GMAT every single day.

If you need a bit more structure, Magoosh offers a free 30 Day Study Schedule that you can amend to your needs.

If you struggle with GMAT Verbal and really can only emphasize one of the three question-types, you’re better off memorizing the tested-concepts for Sentence Correction:

• Among/Between, As/Like
• Correlative Constructions
• Diction
• Forms of Comparison
• Fragments and Run-on sentences
• Grammatical Construction
• Idioms
• Logical Predication/Modification
• Mass/count words
• Noun-verb agreement
• Parallelism
• Passive vs. Active Voice
• Prepositions
• Pronouns
• Rhetorical Construction
• Verb Form
• Wordiness/Redundancy

If you can spot these errors, you’re likely to move through the SC questions quickly, and thus you’ll have more time to analyze the Critical Reasoning and Reading Comprehension passages. Learn more 30-Day Study Tips on Learnist!

# Tough GMAT: Quant Question of the Day

Today, we’ll take a look at a question from the Official Guide from GMAC dealing with sets! As always, try it on your own, then scroll down for an explanation! 🙂

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both chemistry and biology could be any number from:

A) 20 to 50
B) 40 to 70
C) 50 to 130
D) 110 to 130
E) 110 to 150

The question asks what “x” could be.

150 = B + X

130 = C + X

B + C + X = 170

The MAXIMUM overlap is 130, since the Chemistry circle cannot be GREATER than 130. From there we know the answer must be either (C) or (D).

Plugging in our first two equations:

(150 – X) + (130 – X) + X = 170

150 – X + 130 – X + X = 170

150 – X + 130 = 170

150 – X = 40

– X = 40 – 150

-X = -110

X = 110

# GMAT Data Sufficiency Problem of the Day!

Check out this mean and consecutive numbers question from GMAT Prep!

What is the average (arithmetic mean) of 11 consecutive integers?

1) the average of the first nine integer equals 7
2) the average of the last nune integer equals 9.

To start, recognize that this is a “value” DS question, so we need to know the exact average in order to have sufficiency.

Average = sum of terms/ # of terms

Avg = (a + b + c + d + e + f + g + h + i + j + k) / 11

We know the 11 numbers are consecutive, so we need to know at least one of the numbers and its placement to find the set.

STATEMENT 1.

7 = (a + b + c + d + e + f + g + h + i) / 9

63 = a + b + c + d + e + f + g + h + i

What 9 consecutive numbers sum to 63?

Let’s call the middle number x. We can re-write the sequence as:

63 = (x – 4)+(x – 3)+(x – 2)+(x – 1)+(x)+(x + 1)+(x + 2)+(x + 3)+(x + 4)

63 = 9x

7 = x = middle number of the first 9 terms. We can find the other numbers now since we know they are consecutive integers.

The set is 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

SUFF.

STATEMENT 2.

The same logic applies. We can determine the set. The answer is (D).

# Learnist: How the GMAT Tests “Volume”

Volume is the three-dimensional area — the amount of space enclosed by a shape or object. Remember that you need three different values to find volume and surface area (the length, the width and the height) on the GMAT.

Think of any box — a “rectangular solid” is a just a 3-D rectangle. Find the volume by calculating the length x width x height. Find the surface area by calculating 2lw + 2lh + 2wh.

Like the rectangular solid, to find the volume of a cylinder you will calculate the area of the base and multiply it by the height. For a cylinder, the area of the base will always be equal to the area of a circle: pi x r^2. Just multiply it by “h” to find the volume!

Try a couple practice questions on this GMAT – Volume learnboard!