Well, if you’re a GMAT student, you can think about what the odds mean in terms of probability and you can watch the announcers miss Critical Reasoning lesson after Critical Reasoning lesson. For example:
Probability
Before the last piece of confetti hits the turf on Sunday, oddsmakers will have posted their odds on next year’s winner. For example, New England and Seattle might open at 4:1, Green Bay might come in at 7:1, etc. And while you might look at those odds and think “if I bet $100 on the Packers I’ll win $700!” you should also think about what those mean. 7:1 for Green Bay is really a ratio: 7 parts of the money says that Green Bay will not win, and 1 part says that it will. So that’s a good bet if you think that Green Bay has a better than 1 out of 8 chance (so better than 12.5%) to win next year’s Super Bowl. And if those are, indeed, the odds (4:1 for two teams and 7:1 for another), Vegas is essentially saying that there’s a less than likely chance (1/5 + 1/5 + 1/8 = 52.5% chance that one of those two teams wins) that someone other than Green Bay, New England, or Seattle will win next year.
So consider what the probability of those bets means before you make them. Individually odds might look tempting, but when you consider what that means on a fraction or percent basis you might have a different opinion.
Probability #2
As you watch the Super Bowl, there’s a high likelihood that at some point the screen will start showing a line indicating the season-long field goal for either Steven Hauschka or Stephen Gostkowski (the Seattle and New England kickers…there’s a huge probability that someone named Steve will be incredibly important in this game!). And the announcers will use that line to say that it’s likely field goal range for that team to win or tie the game.
Where’s the flawed logic? If that’s the longest field goal he’s made all year, is it really likely that he’ll make another one from a similar spot with all that pressure? Or, in the case of a low-scoring game like many predict between these two elite defenses, how likely is either kicker to make two consecutive field goals from a relatively far distance?
Sports fans are pretty bad with that probability. Say that a kicker has been 70% accurate from over 50 yards. Is it likely that he’ll make two straight 50-yard field goals on Sunday (assuming he gets those attempts)? Check the math: that’s 7/10 * 7/10 or 49/100 – it’s less than likely that he makes both! Even a kicker with 80% accuracy is only 8/10 * 8/10 = 64% likely to make two in a row…meaning that fail to perform that feat 1 out of every 3 times he had the chance! Think of the probability while announcers talk about field goals as a near certainty on Sunday.
Critical Reasoning
The announcers on Sunday will try to use all kinds of data to predict the outcome, and in doing so they’ll give you plenty of opportunities to think critically in a Critical Reasoning fashion. For example:
“For the last 40 Super Bowls, the team with the most rushing yards has won (some massive percent) of them; it’s important for New England to get LeGarrette Blount rolling early.”
This is a classic causation/correlation argument. Do the rushing yards really win the game? It could very well be true (Weaken answer!) that teams that build a big lead and therefore want to run out the clock run the ball a lot in the second half (incomplete passes stop the clock; runs keep it going). Winning might cause the rushing yards, not the other way around.
Similarly, the announcers will almost certainly make mention at halftime of a stat like:
“Team X has won (some huge percentage) of games they were leading at halftime, so that field goal to put them up 13-10 looms large.”
Here the announcer isn’t factoring in a couple big factors in that stat:
-A 3-point lead isn’t the same as a 20-point lead; how many of those halftime leads were significantly bigger?
-You’d expect teams leading at halftime to win a lot more frequently; based on 30 minutes they may have shown to be a better team plus they now have a head start for the last 30 minutes. Over time those factors should bear out, but in this one game is a potentially-flukey 3-point lead significant enough?
Regardless of how you watch the game, it can provide you with plenty of opportunities to outsmart friends and announcers and sharpen your GMAT critical thinking skills. So while Tom Brady or Russell Wilson runs off the field yelling “I’m going to Disneyland!”, if you’ve paid attention to logical flaws and probability opportunities during the game, you can celebrate by yelling “I’m going to business school!”
Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
By Brian Galvin
]]>How is it that you can confidentially answer question after question while obviously missing quite a few questions that felt “easy?”
One culprit is the subtlety of the official GMAT questions overall. No other questions do as good a job of luring you into confidently choosing the wrong answer. This can happen on problem solving, but today I would like to focus on Data Sufficiency.
I sometimes refer to Data Sufficiency as “the Silent Killer” because the very structure of the Data Sufficiency question invites you to choose the wrong answer. This is because you do not know that you have forgotten to consider something. There are no values in the answer choices to help you see what you might have overlooked. That is why the person choosing the incorrect answer is often more confident than is the one who got the question right.
As you can see it is often difficult to gauge how you are doing on Data Sufficiency. And because the Quantitative section adapts as a whole, missing these data sufficiency questions results in the computer selecting lower-level questions in problem solving. So the problem solving questions may have seemed easier because they actually were at a lower level.
This is a pattern that I have seen repeated many times on practice exams. Students miss mid-level data sufficiency questions in the first part of the exam. This results in lower level questions being offered, and the student keeps missing just enough problems (of both Data Sufficiency and Problem Solving) to keep the difficulty level from increasing.
The result? A quant section that felt comfortable because most of the questions were below the level that would really challenge the student. This may be what happened to you.
How to avoid this fate:
With Data Sufficiency questions there are no answer choices to provide a check on your assumptions or calculations. You must be your own editor and look for mistakes before you confirm your answer. Fortunately, there are several things you can do:
Think with your pen. Do not presume that you will remember what the question is asking, the facts you are given, or the hidden facts that are implied by the question stem. Note these things on your scratch paper so that you do not forget them. It may seem unnecessary to write “x is integer” or “must be positive” but just think of how dangerous it would be to forget this information!
Do your work early. Rewording the question is a great way to make data sufficiency more fool-proof. For example, it is much easier to comprehend the question “Is x a multiple of 4” than it is to wrestle with the questions “Is x/2 a multiple of 2?” Think about what the question is really asking and re-word it when you can.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.
As an example, remember open-book tests. These tests always seemed easier when they were discussed in theory than when they were attempted in practice. An open book test must necessarily test you on more obscure and convoluted material, otherwise the test becomes too easy and everyone gets 100. Closed-book tests, by contrast, can concentrate on the core material and gauge how much preparation each student has put in. Adding more tools only serves to make the test more difficult in order to overcome these enhancements.
With a calculator, asking you to calculate the square root of an 8 digit number or the 9^{th} power of an integer is trivial if you only have to plug in some numbers. However, if you need to actually reason out a strategic approach in your head, you have accomplished more than a thousand brute force calculations would. On the GMAT, the mathematics behind a question will always be doable without a calculator, but the strategy chosen and the way you set up the equations will generally be the difference between the correct answer in two minutes and a guess in four.
Let’s look at a question where the math isn’t too difficult, but can get tedious:
Alice, Benjamin and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8 and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3 / 140
(B) 1 / 28
(C) 3 / 56
(D) 3 / 35
(E) 7 / 40
This is a probability question, and therefore we must calculate the chances of any one event occurring. However, the question is asking about several possibilities, specifically any occurrence where two players win and the third loses (think of any romantic comedy). This means that we have to calculate several outcomes and manually add these probabilities. This is entirely feasible, but it can be somewhat tedious. Let’s look at the best way to avoid getting bogged down in the math:
Firstly, the three players’ are suitably abbreviated as A, B and C (convenient, GMAT, convenient). We therefore want to find the probability that A and B occur, but that C does not occur (denoted as A, B, ⌐C). This represents one of our desired outcomes. However, this is not the only possibility, as any situation where two occur and the other doesn’t is acceptable as well. Thus we can have A and C but not B (A, ⌐B, C), or B and C but not A (⌐A, B, C). The sum of these three outcomes is the desired fraction, so only some math remains.
Let’s do them in order. For (A, B, ⌐C), we take the probability of A, multiplied by the probability of B, and then multiplied by the probability of 1-C. If the chances of C are 2 / 7, then the probability of them not occurring must be the compliment of this, which is 5 / 7. The calculation is thus:
1 / 5 * 3 / 8 * 5 / 7.
In a multiplication, we only care about multiplying the numerators together, and then multiplying the denominators together. There is no need to put these elements on common denominators. The math gives us:
(1* 3 * 5) / (5 * 8 * 7). This is 15 / 280.
There is a strong temptation to cancel out the 5 on the numerator and on the denominator to make the calculation easier, but you should avoid such temptation on questions such as these. Why? (I’m glad you asked). If you simplified this equation, you would get the equivalent fraction of 3 / 56, which is easier to calculate, but since we still have to execute two more multiplications, we will end up adding fractions that have different denominators. This is not a pleasant experience without a calculator, and likely will cause us to revert to our common denominator for all three fractions, which is 5 * 8 * 7 or 280. Additionally, now that we’ve calculated it once, we don’t need to worry about the denominator for the following fractions, it will always be the same. Let’s continue and hopefully this strategy will become apparent.
The next fraction is (A, ⌐B, C), which is equivalent to
1 / 5 * 5 / 8 * 2 / 7. Note that ⌐B is (1 – 3/8)
Executing this calculation yields a result of 10 / 280.
Finally, we need (⌐A, B, C), which is equivalent to
4 / 5 * 3 / 8 * 2 / 7. Note that ⌐A is (1 – 1/5)
Executing this last fraction gives us 24 / 280.
Once we have these three fractions, we must add them together in order to get the probability of any one of them occurring (“or” probability, as opposed to “and” probability”). This is simple because they’re all on the same denominator, so we get 15 / 280 + 10 / 280 + 24 / 280 which is 49 / 280.
Now that we have this number, we can try to simplify it. 49 is a perfect square that is only divisible by 1, 7 and 49, whereas 280 has many factors, but one of them fairly clearly is 7. We can thus divide both terms by 7, and get 7 / 40. Since the numerator is a prime number, there is no additional simplification possible. 7 / 40 is answer choice E, and it is the correct pick on this question.
Had we simplified each probability as much as possible, we would have ended up with 3 / 56, 2 / 56 and 3 / 35. While the addition would not be impossible, it would become much more difficult. In fact, to correctly add these numbers together, you’d have to put them on their least common multiple, which would be 280 again. There is usually no point in simplifying fractions in questions like this because they must usually be recombined at the end. Save time and don’t convert once only to convert back.
The math on this question is not difficult, but having to add together multiple fractions and simplifying expressions can be quite time-consuming. With a calculator, you could simply add the decimals together, regardless of their fractional equivalents. However, the GMAT doesn’t allow you that shortcut on test day (unless you approximate in your head), so you must find a better tactic. The difference between solving all the questions and running out of time on the math section is often the approach you take on each question. Keep up a consistent strategy and you’ll solve a large fraction of the questions you face on test day.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
]]>The exciting thing is that pre-thinking is useful in Quant too. If you take a step back to review what the question asks and think about what you are going to do and what you expect to get, it is highly likely that you will not get distracted mid-way during your solution. Let’s show you with the help of an example:
Question: Superfast train A leaves Newcastle for Birmingham at 3 PM and travels at the constant speed of 100 km/hr. An hour later, it passes superfast train B, which is making the trip from Birmingham to Newcastle on the same route at a constant speed. If train B left Birmingham at 3:50 PM and if the sum of the total travel time of the two trains is 2 hours, at what time did train B arrive at Newcastle?
Statement I: Train B arrived at Newcastle before train A arrived at Birmingham.
Statement II: The distance between Newcastle and Birmingham is greater than 140 km.
Following are the things that would ideally constitute pre-thinking on this question:
- Quite a bit of data is given in the question stem with some speed and time taken.
- Distance traveled by both the trains is the same since they travel along the same route.
- We could possibly make an equation by equating the two distances and come up with multiple answers for the time at which train B arrived at Newcastle.
- The statements do not provide any concrete data. We cannot make any equation using them but they might help us choose one of the answers we get from the equation of the question stem.
Mind you, the thinking about the statements helping us to arrive at the answer is just speculation. The answer may well be (E). But all we wanted to do at this point was find a direction.
The diagram given above incorporates the data given in the question stem. Train A starts from Newcastle toward Birmingham at 3:00 and meets train B at 4:00. Train B starts from Birmingham toward Newcastle at 3:50 and meets train A at 4:00. Let x be the distance from Birmingham to the meeting point.
Speed of train A = 100 km/hr
Speed of train B = Distance/Time = x/(10 min) = x/(1/6) km/hr = 6x km/hr (converted min to hour)
If we get the value of x, we get the value of speed of train B and that tells us the time it takes to travel from the meeting point to Newcastle (a distance of 100 km). So all we need to figure out is whether the statements can give us a unique value of x.
By 4:00, train A has already travelled for 1 hour and train B has already travelled for 10 mins i.e. 1/6 hour. Total time taken by both is 2 hrs. The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.
Time taken by train A to reach Birmingham + Time taken by train B to reach Newcastle = 5/6
Distance(x)/Speed of train A + 100/Speed of train B = 5/6
x/100 + 100/6x = 5/6
3x^2 – 250x + 5000 = 0
3x^2 – 150x – 100x + 5000 = 0
3x(x – 50) – 100(x – 50) = 0
(3x – 100)(x – 50) = 0
x = 100/3 or 50
So speed of train B = 6x = 200 km/hr or 300 km/hr
Statement 1: Train B arrived at Newcastle before Train A arrived at Birmingham.
If x = 50, time taken by train A to reach Birmingham = 50/100 = 1/2 hour and time taken by train B to reach Newcastle = 100/300 = 1/3 hour. Train B takes lesser time so it arrives first.
If x = 33.33, time taken by train A to reach Birmingham = (100/3)/100 = 1/3 hour and time taken by train B to reach Newcastle = 100/200 = 1/2 hour. Here, train A takes lesser time so it arrives first at its destination.
Since train B arrived first, x must be 50 and train B must have taken 1/3 hour i.e. 20 mins to arrive at Newcastle. So train B must have arrived at 4:20.
This statement is sufficient alone.
Statement 2: The distance between Newcastle and Birmingham is greater than 140 km.
Total distance between Newcastle and Birmingham = (100 + x) km. x must be 50 to make total distance more than 140.
Time taken by train B must be 1/3 hr (as calculated above) and it must have arrived at 4:20.
This statement is sufficient alone.
Answer (D)
So our speculation was right. Each of the statements provided us relevant information to choose one of the two values that the quadratic gave us.
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
]]>Some will say it’s a heinous act committed by serial cheaters. Others will say it’s a minor violation and that “everybody does it.” And still others will say it’s an inadvertent mistake that happened to run afoul of a technicality. What does it mean for you, a GMAT aspirant?
Be careful about honest mistakes that could be construed as cheating!
While the NFL isn’t going to kick the Patriots out of the Super Bowl, the Graduate Management Admission Council won’t hesitate to cancel your score if you’re found to be in violation of its test administration rules. So beware these rules that honest examinees have accidentally violated:
1. You cannot bring “testing aids” into the test center.
Don’t bring an Official Guide, a test prep book, or study notes into the test center with you. You may want to have notes while you’re waiting to check in, but if you’re caught with “study material” in your hands during one of your 8-minute breaks – which has happened to students who were rearranging items in their lockers to grab an apple or a granola bar – you’ll be in violation of the rule, and GMAC has cancelled scores for this in the past. Don’t take that risk! Leave watches, cell phones, and study aids in your car or at home so that there’s no chance you violate this rule simply by having a forbidden item in your hand during a break.
2. You cannot talk to anyone about the test during your administration.
You’ll be at the test center with other people, and someone’s break might coincide with yours. Holding a restroom door or crossing paths near a drinking fountain, you might be tempted to socially ask “how is your test going?” or sympathetically mention “man these tests are hard.” But since those innocent phrases could be seen as “talking about the test” you would technically be in violation of the rule, and GMAC has cancelled scores for this in the past. Your 8-minute break isn’t the time to make new friends – don’t take the risk of being caught talking about the test.
You know that you’re not a cheater, but as most New Englanders feel today it’s very possible to be considered a cheater if you end up on the wrong side of a rule, however accidentally. Learn from the lessons of test-takers before you: avoid these common mistakes and ensure that the score you earn is the score you’ll keep.
Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
By Brian Galvin
]]>Firstly, if you’ve never heard the song, please feel free to listen to it now. The chorus is discussing how Ariana would have “one less problem” without the person she’s currently serenading (surprisingly this isn’t a Taylor Swift song). The issue with the lyric is that problems are countable, and as such she should actually be singing “one fewer problem without you”. Perhaps the extra syllable messed up the harmony, or perhaps the songwriter hadn’t brushed up on their grammar prior to writing the song, but this is the type of issue students often struggle with because they don’t understand the underlying rule.
When it comes to counting things, there are two broad categories: items that are countable, and items that are not countable. The former comprises most tangible things we can imagine: computers, cars, cats, cookies, cans of Coke and countless conceivable commodities (This sentence brought to you by the letter C). The latter comprises things that are uncountable, such as water, sand or hair. You can count grains of sand or strands of hair, but you cannot count actual sand or hair, so these words get treated a little differently.
The rule is that for any noun that is countable, you must use “fewer” if you are going to decrease it. For any noun that is not countable, you must use “less” to decrease it. As an example, I want less water in my cup; I do not want fewer water in my cup. That example makes sense to most people. However, the converse is just as true: I want fewer bottles of water, not less bottles of water. If the item in question is scarce, similar words will be used. You can say that there is little water, but you wouldn’t say that there is few water left. Note how these words have the same etymology as “less” and “fewer”, respectively.
If the sentence calls for an increase, more is acceptable for both countable and uncountable elements. As an example, you can say that you want more water in your cup, or you can say that you want more bottles of water. Other synonyms exist as well, of course, but the delineation is much cleaner for decreases than for increases, so that structure appears more often on the GMAT. If the item in question is in abundance, similar words will also be used. You can say that there is much water, but you can’t say that there is many water. Much and many follow these same countable/uncountable rules.
The difference between items that are countable or uncountable is not unique to the GMAT, these rules apply to everyday language, they are simply enforced more rigorously on this test. Failure to choose the proper word in a Sentence Correction problem will result in an incorrect answer choice. As such, it behooves us to be aware of the grammatical difference between countable and uncountable elements, as it regularly comes up on the GMAT.
Let’s look at an example to illustrate the point:
The controversial restructuring plan for the county school district, if approved by the governor, would result in 20% fewer teachers and 10% less classroom contact-time throughout schools in the county.
A) in 20% fewer teachers and 10% less
B) in 20% fewer teachers and 10% fewer
C) in 20% less teachers and 10% less
D) with 20% fewer teachers and 10% fewer
E) with 20% less teachers and 10% less
Looking at the answer choices, it becomes fairly clear that the correct answer will hinge primarily on the difference between “fewer” and “less”. If we recall the rules for countable vs. uncountable, anything that we can count must use the adjective “fewer”, while anything that is not countable must use the adjective “less”.
For this example, the first reduction is in the number of teachers. Teachers are human beings (often handsome ones!), and are therefore countable. You can want to spend less time with a specific teacher, but you cannot (correctly) say that you want the school to have less teachers. The request must be for fewer teachers. This already eliminates answer choices C and E because they use the incorrect term.
The second reduction is about classroom time. Time is a wondrous and magical thing (or so young people tell me), but it is not countable. Yes, you can break up time into countable units, such as seconds or minutes, just as you can break up sand into grams or ounces, but holistically time is intangible and therefore uncountable. The plan calls for less time in the classroom, not fewer time. This eliminates answer choices B and D because they use the incorrect term. Only answer A remains and it is indeed the correct answer.
As mentioned earlier, the rules around countable and uncountable nouns are fairly precise, but you are unlikely to be corrected in everyday conversation if you misuse a term. Since the GMAT is testing logic, precision and general attention to detail, it is a perfect type of question to try and trap hurried students who don’t always notice the difference. In daily conversation (and on the radio), you can often get away with imprecision in language. However, if you understand the nuances between countable and uncountable nouns, to paraphrase Ariana Grande, you’ll have one fewer problem on the GMAT.
Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
]]>A few months back, we had discussed a 700 level ‘Races’ question.
Question 1: A and B run a race of 2000 m. First, A gives B a head start of 200 m and beats him by 30 seconds. Next, A gives B a head start of 3 mins and is beaten by 1000 m. Find the time in minutes in which A and B can run the race separately.
(A) 8, 10
(B) 4, 5
(C) 5, 9
(D) 6, 9
(E) 7, 10
Check out its complete solution here.
Now, what if we had only 30 seconds to guess on it and move on? Then we could have easily guessed (B) here and moved on. Actually, the question implies that the only possible options are those in which the time taken by B is somewhere between 3 mins and 6 mins (excluding) – we would guess 4 mins or 5 mins. Since only option (B) has time taken by (B) as 5 mins, that must be the answer – no chances of error here – perfect! Had there been 2 options with 4 mins/5 mins, we would have increased the probability of getting the correct answer to 50% from a mere 20% within 30 seconds.
Now you are probably curious as to how we got the 3 min to 6 min range. Here is the logic:
Read one sentence of the question at a time -
“A and B run a race of 2000 m. First, A gives B a head start of 200 m and beats him by 30 seconds.”
So first, A gives B a head start of 1/10th of the race but still beats him. This means B is certainly quite a bit slower than A. This should run through your mind on reading this sentence.
“Next, A gives B a head start of 3 mins and is beaten by 1000 m.”
Next, A gives B a head start of 3 mins and B beats him by 1000 m i.e. half of the race. What does this imply? It implies that B ran more than half the race in 3 mins. To understand this, say B covers x meters in 3 mins. Once A, who is faster, starts running, he starts reducing the distance between them since he is covering more distance than B every second. At the end, the distance between them is still 1000 m. This means the initial distance that B created between them by running for 3 mins was certainly more than 1000 m (This was intuitively shown in the diagram in this post). Since B covered more than 1000 m in 3 mins, he would have taken less than 6 mins to cover the length of the race i.e. 2000 m. A must be even faster and hence would take even lesser time.
Only option (B) has time taken by B as 5 mins (less than 6 mins) and hence satisfies our range! So the answer has to be (B).
Let’s try the same technique on another question.
Question 2: If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?
(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days
Solution: If we try to use algebra here, the calculations involved will be quite complicated. The options are not very close together so we can try to get a ballpark value and move forward. Let’s take each sentence at a time:
“If 12 men and 16 women can do a piece of work in 5 days”
Say rate of work of each man is M and that of each woman is W. This statement gives us that
12M + 16W = 1/5 (Combined rate done per day)
In lowest terms, it is 3M + 4W = 1/20
“13 men and 24 women can do it in 4 days,”
This gives us 13M + 24W = 1/4
“how long will 7 men and 10 women take to do it?”
Required: 7M + 10W = ?
Solving the two equations above will be tedious so let’s estimate:
(3M + 4W = 1/20) * 6 gives 6M + 8W = 1/10
So 6 men and 8 women working together will take 10 days. Hence, 7 men and 10 women will certainly take fewer than 10 days.
(13M + 24W = 1/4) / 2 gives 6.5M + 12W = 1/8
So 7 men and 10 women might take about 8 or perhaps a little bit more than 8 days to complete the work. There is only 0.5 additional man (hypothetically) but 2 fewer women to complete it. So we would guess that the number of days would lie between 8 to 10 and closer to 8 days.
Answer (C) fits.
Note that it seems like there are many equations here but all you have actually done is made two equations. Once you write them down, you don’t even need to actually multiply them with some integer to get them close to the required equation. Just looking at the first one, you can say that 6 men and 8 women will take 10 days. It takes but a couple of seconds to arrive at these conclusions.
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
]]>Thou doth protest too much. Meaning:
We all think we can write verbal questions better than the authors of the test.
When it comes to GMAT verbal questions, we critique but don’t solve Critical Reasoning problems, we correct rather than solve Sentence Correction problems, and we try to write but don’t thoroughly read Reading Comprehension questions. And this hubris can be the death of your GMAT verbal score, even if it comes from a good place and a good knowledge base.
Wander into a GMAT class or scan a GMAT forum and you’ll see and hear tons of comments like:
“I feel like the question should say people and not individuals.”
“I would never use the word imply like that.”
“I don’t think that’s the right idiom.”
“I would have gotten it right if it said X…I think it should have said X.”
Or you’ll hear questions like:
“But what if answer choice D said and and not or?”
“If that word were different would my answer choice be right? And if so would it be more right than B?”
And while these questions often come from a genuine desire to learn, they more often come from a place of frustration, and they’re the type of hypothetical thinking that doesn’t lend itself to progress on this test. Even if it’s not always perfect, the GMAT chooses its words very carefully. When the word in the Reading Comprehension correct answer choice isn’t the word you were hoping it would be (but it’s close), they picked that word for a reason – it makes the problem more difficult. When none of the Sentence correction answer choices match the way you or your classmates would have phrased it, that’s not a mistake – that’s an intentional device to make you eliminate four flawed answers and keep the strange-but-correct one. The GMAT can’t always match your expectations, not just because doing so would make it too easy but also because it’s trying to test other critical-thinking skills. It has to test your ability to see less-clear relationships, to make logical decisions amidst uncertainty, to find the least of five evils, and it has to punish you for jumping to unwarranted conclusions.
GMAT verbal is constructed carefully, and as you study it you have to learn how to answer questions more effectively, not to write better questions. The only thing you get to write on test day is the AWA essay; everything else you must answer on the GMAT’s terms, not on your own, so as you study you have to resist the urge to protest the problem and instead learn to see the value in it.
So as you study, remember your mission. Your job isn’t to find a flaw with the logic of the question, but rather with the logic of the four incorrect answers. When you get mad at a wrong answer, use that energy to attack the next problem with the lessons you learned from that frustrating mistake. Take the GMAT as it is and don’t try to justify your mistakes or fight the test.
Save your writing energy for the AWA essay; on the verbal section, you only get to answer the problem in front of you. When you accept that the test is what it is and commit yourself to learning how to attack it through critical thinking and not just general angst, you’ll have a competitive advantage over most frustrated examinees. Think like the testmaker, but don’t try to be the testmaker.
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By Brian Galvin
]]>To quickly recap some of the main points from the original article, I mentioned that both the GMAT and the Hobbit movie require a significant allocation of your time and that both should contain very few surprises. The Hobbit (pick any of the three movies) is about three hours between run time and previews, whereas the GMAT is just short of four hours if you take all the breaks (which I recommend). Since you know you’ll be there for a while, you should plan accordingly in terms of snacks, medication and fatigue. Bring anything you might need to manage the lengthy endeavour.
The other main point I brought up is that the Hobbit movies should contain very few surprises because the source material is already known. If you want to know what happened in the Hobbit, you could read the book first published in 1937. If you want to know what’s on the GMAT, you can read the OG (or other specialized GMAT study guide). All the material you need to know is contained within. The only thing that will change is the execution. Indeed, just knowing there will be a question about triangles doesn’t guarantee you’ll get the right answer, but you shouldn’t be surprised if you find yourself using the Pythagorean theorem to solve the second quant problem. If you don’t want to be surprised, do your research.
However, while watching the newest installment of the franchise, I noticed more elements that are similar to the GMAT. Specifically, I was struck by how the first sequence of this movie was essentially a warm up for the main event, how the protagonists constantly had to think strategically, and how the entire movie was the culmination of an arduous journey. For the purposes of this analogy, I will assume you have seen the movie (or at least read the book). It’s hard to spoil a book published during the great depression, but I want a disclaimer noting that there might be some minor spoilers ahead (#spoilers).
The Warm Up Section
The Hobbit: The Battle of the Five Armies begins with the dragon Smaug unleashing his fury on nearby Laketown. This continues from where the last movie leaves off, but even though there is much action from the start, viewers know that this scene will not take very long to conclude. Why? Because the movie is called “The Battle of the Five Armies”, and not “Smaug Burns Everything” (or even “Smaug Gets his Comeuppance”). The scene certainly looks frightening, but we know it is just a matter of time before one of the dwarves gets his mystical arrow and shoots it perfectly at a specific weakness on the dragon whizzing around at hurricane speed. The movie will then get on with the gathering of multiple armies to face off in a grandiose climax of sword and steel.
Similarly, the opening act of the GMAT, the AWA and IR, are simply warm ups to the main event commencing at around the one hour mark. Certainly no one wants to do poorly on these early sections, but just doing okay on them and performing well on the verbal and quant sections of the GMAT will do just fine. The score out of 800, which is really what most people look for, is composed entirely of your blended verbal and quant scores. You still have to go through the first two sections, but if you could conserve mental energy for the final two sections, you’ll typically see your score improve. (I could see this exam being called “GMAT: the Struggle of Verbal and Quant”).
Strategic Thinking
Having never engaged in warfare (beyond Starcraft), I cannot say definitively that having one opponent is easier than having four, but it certainly seems that way. If you only have one enemy to deal with, you can focus all of your attention on them. However, if five separate armies are entering the fray, as was the case in the movie, you had to coordinate strategically among your allies and adjust to your enemy’s changes rapidly. If the orcs suddenly overrun the dwarves, then the elves have to switch strategies and defend their vulnerable flank. Similarly, if a new army appears from a different direction, you may have to redeploy to avoid being surrounded.
The GMAT is very similar, as the exam is designed to test your mental agility. If you are great at algebra, that can help you with a lot of questions, but some questions will be almost impossible to solve purely through algebra (and without a calculator). You must consider other options such as backsolving or using the concept to avoid wasting time and getting frustrated. Some questions are designed to be time-consuming if approached in a straightforward way, so you always have to think strategically. If your approach looks like it will take 4-5 minutes, you might be better off thinking of it in another way.
The Culmination of a Long Journey
The final installment of the Hobbit has a runtime of about 2.5 hours, but it is the conclusion of something much greater. Two other movies (some might argue five) are closed at the end of this spectacle, so even if it only took a few hours to complete, it is the ending of months or even years of preparation. Few people spontaneously decide to take the GMAT without studying or at least researching the exam a little. For most, hundreds of hours are devoted to the 3-4 hour endeavour that is the exam. Just because the exam is over in the blink of an eye (more or less), doesn’t mean that there weren’t hours of studying, of wondering, of panicking and of persevering that all concluded in one day at the Pearson center.
You can learn a lot about the GMAT from this final Hobbit movie, most remarkably that the beginning is just a set up for the second portion. You should also recognize that you must always think strategically on this test, for it is designed to trick people who consistently depend on one single approach. Finally, you can also note that the GMAT, like the Hobbit is the last step on a long (and unexpected) journey. Ironically, in both cases, it is often the beginning of an even greater journey, but I’ll save that analogy (LotR/MBA) for another day.
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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
]]>In your haste to complete the test on time, don’t overlook the important details. Getting too many easy questions wrong is certainly disastrous. Take a step back and ensure that what they asked is what you have found and that your logic is solid. To illustrate the problem, let’s give you a question – people gloss over it, consider it an easy remainders problem, answer it incorrectly and move on. But guess what, it isn’t as easy as it looks!
Question: If m and n are positive integers such that m > n, what is the remainder when m^2 – n^2 is divided by 21?
Statement 1: The remainder when (m + n) is divided by 7 is 1.
Statement 2: The remainder when (m – n) is divided by 3 is 1.
First let’s give you the incorrect solution provided by many.
Question: What is the remainder when (m^2 – n^2) is divided by 21?
Statement 1: The remainder when (m + n) is divided by 7 is 1.
(m + n) = 7a + 1
Statement 2: The remainder when (m – n) is divided by 3 is 1.
(m – n) = 3b + 1
Therefore, remainder of product (m^2 – n^2) = (m + n)*(m – n) = (7a + 1)(3b + 1) when it is divided by 21 is 1.
Answer (C)
This would have been correct had the statements been:
Statement 1: The remainder when (m + n) is divided by 21 is 1.
Statement 2: The remainder when (m – n) is divided by 21 is 1.
Statement 1: (m + n) = 21a + 1
Statement 2: (m – n) = 21b + 1
(m^2 – n^2) = (m + n)*(m – n) = (21a + 1)*(21b + 1) = 21*21ab + 21a + 21b + 1
Here, every term is divisible by 21 except the last term 1. So when we divide (m^2 – n^2) by 21, the remainder will be 1.
But let’s go back to our original question. If you solved it the way given above and got the answer as (C), you are not the only one who jumped the gun. Many people end up doing just that. But here is the correct solution:
The statements given are:
Statement 1: The remainder when (m + n) is divided by 7 is 1.
(m + n) = 7a + 1
Statement 2: The remainder when (m – n) is divided by 3 is 1.
(m – n) = 3b + 1
This gives us (m^2 – n^2) = (m + n)*(m – n) = (7a + 1)(3b + 1) = 21ab + 7a + 3b + 1
Here only the first term is divisible by 21. We have no clue about the other terms. We cannot say that 7a is divisible by 21. It may or may not be depending on the value of a. Similarly, 3b may or may not be divisible by 21 depending on the value of b. So how can we say here that the remainder must be 1? We cannot. We do not know what the remainder will be in this case even with both statements together.
Say, if a = 1 and b = 1,
m^2 – n^2 = 21*1*1 + 7*1 + 3*1 + 1 = 21 + 11
The remainder when you divide m^2 – n^2 by 21 will be 11.
Say, if a = 2 and b = 1,
m^2 – n^2 = 21*2*1 + 7*2 + 3*1 + 1 = 21*2 + 18
The remainder when you divide m^2 – n^2 by 21 will be 18.
Hence, both statements together are not sufficient to answer the question.
Answer (E)
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
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