The post Quarter Wit, Quarter Wisdom: Using the Standard Deviation Formula on the GMAT appeared first on Veritas Prep Blog.

]]>Today, we will look at some GMAT questions that involve sets with similar standard deviations such that it is hard to tell which will have a higher SD without properly understanding the way it is calculated. Take a look at the following question:

*Which of the following distribution of numbers has the greatest standard deviation? *

*(A) {-3, 1, 2} *

*(B) {-2, -1, 1, 2} *

*(C) {3, 5, 7} *

*(D) {-1, 2, 3, 4} *

*(E) {0, 2, 4}*

At first glance, these sets all look very similar. If we try to plot them on a number line, we will see that they also have similar distributions, so it is hard to say which will have a higher SD than the others. Let’s quickly review their deviations from the arithmetic means:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2

For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2

For answer choice C, the mean = 5 and the deviations are 2, 0, 2

For answer choice D, the mean = 2 and the deviations are 3, 0, 1, 2

For answer choice E, the mean = 2 and the deviations are 2, 0, 2

We don’t need to worry about the arithmetic means (they just help us calculate the deviation of each element from the mean); our focus should be on the deviations. The SD formula squares the individual deviations and then adds them, then the sum is divided by the number of elements and finally, we find the square root of the whole term. So if a deviation is greater, its square will be even greater and that will increase the SD.

If the deviation increases and the number of elements increases, too, then we cannot be sure what the final effect will be – an increased deviation increases the SD but an increase in the number of elements increases the denominator and hence, actually decreases the SD. The overall effect as to whether the SD increases or decreases will vary from case to case.

First, we should note that answers C and E have identical deviations and numbers of elements, hence, their SDs will be identical. This means the answer is certainly not C or E, since Problem Solving questions have a single correct answer.

Let’s move on to the other three options:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2

For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2

For answer choice D, the mean = 2 and the deviations are 3, 0, 1, 2

Comparing answer choices A and D, we see that they both have the same deviations, but D has more elements. This means its denominator will be greater, and therefore, the SD of answer D is smaller than the SD of answer A. This leaves us with options A and B:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2

For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2

Now notice that although two deviations of answers A and B are the same, answer choice A has a higher deviation of 3 but fewer elements than answer choice B. This means the SD of A will be higher than the SD of B, so the SD of A will be the highest. Hence, our answer must be A.

Let’s try another one:

*Which of the following data sets has the third largest standard deviation?*

*(A) {1, 2, 3, 4, 5} *

*(B) {2, 3, 3, 3, 4} *

*(C) {2, 2, 2, 4, 5} *

*(D) {0, 2, 3, 4, 6} *

*(E) {-1, 1, 3, 5, 7}*

How would you answer this question without calculating the SDs? We need to arrange the sets in increasing SD order. Upon careful examination, you will see that the number of elements in each set is the same, and the mean of each set is 3.

Deviations of answer choice A: 2, 1, 0, 1, 2

Deviations of answer choice B: 1, 0, 0, 0, 1 (lowest SD)

Deviations of answer choice C: 1, 1, 1, 1, 2

Deviations of answer choice D: 3, 1, 0, 1, 3

Deviations of answer choice E: 4, 2, 0, 2, 4 (highest SD)

Obviously, option B has the lowest SD (the deviations are the smallest) and option E has the highest SD (the deviations are the greatest). This means we can automatically rule these answers out, as they cannot have the third largest SD.

Deviations of answer choice A: 2, 1, 0, 1, 2

Deviations of answer choice C: 1, 1, 1, 1, 2

Deviations of answer choice D: 3, 1, 0, 1, 3

Out of these options, answer choice D has a higher SD than answer choice A, since it has higher deviations of two 3s (whereas A has deviations of two 2s). Also, C is more tightly packed than A, with four deviations of 1. If you are not sure why, consider this:

The square of deviations for C will be 1 + 1+ 1 + 1 + 4 = 8

The square of deviations for A will be 4 + 1 + 0 + 1 + 4 = 10

So, A will have a higher SD than C but a lower SD than D. Arranging from lowest to highest SD’s, we get: B, C, A, D, E. Answer choice A has the third highest SD, and therefore, A is our answer

Although we didn’t need to calculate the actual SD, we used the concepts of the standard deviation formula to answer these questions.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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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]]>The post Breaking Down Changes in the New Official GMAT Practice Tests: Unit Conversions in Shapes appeared first on Veritas Prep Blog.

]]>In the Quant section of the first new test, there was one type of question that I’d rarely encountered in the past, but saw multiple times within a span of 20 problems. It involves unit conversions in two or three-dimensional shapes.

Like many GMAT topics, this concept isn’t difficult so much as it is tricky, lending itself to careless mistakes if we work too fast. If I were to draw a line that was one foot long, and I asked you how many inches it was, you wouldn’t have to think very hard to recognize that it would be 12 inches.

But what if I drew a box that had an area of 1 *square* foot, and I asked you how many *square* inches it was? If you’re on autopilot, you might think *that’s easy. It’s 12 square inches. *And you better believe that on the GMAT, that would be a trap answer. To see why it’s wrong, consider a picture of our square:

We see that each side is 1 foot in length. If each side is 1 foot in length, we can convert each side to 12 inches in length. Now we have the following:

Clearly, the area of this shape isn’t 12 square inches, it’s 144 square inches: 12 inches * 12 inches = 144 inches^2.

Another way to think about it is to put the unit conversion into equation form. We know that 1 foot = 12 inches, so if we wanted the unit conversion from feet^2 to inches^2, we’d have to square both sides of the equation in order to have the appropriate units. Now (1 foot)^2 = (12 inches)^2, or 1 foot^2 = 144 inches^2. So converting from square feet to square inches requires multiplying by a factor of 144, not 12.

Let’s see this concept in action. (I’m using an older official question to illustrate – I don’t want to rob anyone of the joy of encountering the recently released questions with a fresh pair of eyes.)

*If a rectangular room measures 10 meters by 6 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter = 100 centimeters)*

*A) **24,000*

*B) **240,000*

*C) **2,400,000*

*D) **24,000,000*

*E) **240,000,000*

First, we can find the volume of the room by multiplying the dimensions together: 10*6*4 = 240 cubic meters. Now we want to avoid the trap of thinking, *“Okay, 100 centimeters is 1 meter, so 240 cubic meters is 240*100 = 24,000 cubic centimeters.” * Remember, the conversion ratio we’re given is for converting meters to centimeters – if we’re dealing with 240 *cubic* meters, or 240 meters^3, and we want to find the volume in *cubic* centimeters, we’ll need to adjust our conversion ratio accordingly.

If 1 meter = 100 centimeters, then (1 meter)^3 = (100 centimeters)^3, and 1 meter^3 = 1,000,000 centimeters^3. [100 = 10^2 and (10^2)^3 = 10^6, or 1,000,000.] So if 1 cubic meter = 1,000,000 cubic centimeters, then 240 cubic meters = 240*1,000,000 cubic centimeters, or 240,000,000 cubic centimeters, and our answer is E.

Alternatively, we can do all of our conversions when we’re given the initial dimensions. 10 meters = 1000 centimeters. 6 meters = 600 centimeters. 4 meters = 400 centimeters. 1000 cm * 600 cm * 400 cm = 240,000,000 cm^3. (Notice that when we multiply 1000*600*400, we can simply count the zeroes. There are 7 total, so we know there will be 7 zeroes in the correct answer, E.)

Takeaway: Make sure you’re able to do unit conversions fluently, and that if you’re dealing with two or three-dimensional space, that you adjust your conversion ratios accordingly.** If you’re dealing with a two-dimensional shape, you’ll need to square your initial ratio. If you’re dealing with a three-dimensional shape, you’ll need to cube your initial ratio. **The GMAT is just as much about learning what traps to avoid as it is about relearning the elementary math that we’ve long forgotten.

**GMATPrep question courtesy of the Graduate Management Admissions Council.*

*Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.*

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]]>The post Quarter Wit, Quarter Wisdom: An Innovative Use of the Slope of a Line on the GMAT appeared first on Veritas Prep Blog.

]]>The concept of slope is extremely important on the GMAT – it is not sufficient to just know how to calculate it using (y2 – y1)/(x2 – x1).

In simple terms, the slope of a line specifies the units by which the y-coordinate changes and the direction in which it changes with each 1 unit increase in the x-coordinate. If the slope (m) is positive, the y-coordinate changes in the same direction as the x-coordinate. If m is negative, however, the y-coordinate changes in the opposite direction.

For example, if the slope of a line is 2, it means that every time the x-coordinate increases by 1 unit, the y-coordinate increases by 2 units. So if the point (3, 5) lies on a line with a slope of 2, the point (4, 7) will also lie on it. Here, when the x-coordinate increases from 3 to 4, the y-coordinate increases from 5 to 7 (by an increase of 2 units). Similarly, the point (2, 3) will also lie on this same line – if the x-coordinate decreases by 1 unit (from 3 to 2), the y-coordinate will decrease by 2 units (from 5 to 3). Since the slope is positive, the direction of change of the x-coordinate will be the same as the direction of change of the y-coordinate.

Now, if we have a line where the slope is -2 and the point (3, 5) lies on it, when the x-coordinate increases by 1 unit, the y-coordinate DECREASES by 2 units – the point (4, 3) will also lie on this line. Similarly, if the x-coordinate decreases by 1 unit, the y-coordinate will increase by 2 units. So, for example, the point (2, 7) will also lie on this line.

This understanding of the concept of slope can be very helpful, as we will see in this GMAT question:

*Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K? *

*(A) 5*

*(B) 10*

*(C) 5√(5)*

*(D) 15*

*(E) 10√(5)*

**Method 1: The Traditional Approach**

Traditionally, one would solve this question like this:

The equation of a line with slope m and constant c is given as y = mx + c. Therefore, the equations of lines L and K would be:

Line L: y = (-2)x + a

and

Line K: y = (1/2)x + b

As both these lines pass through (6,8), we would substitute x=6 and y=8 to get the values of a and b.

Line L: 8 = (-2)*6 + a

a = 20

Line K: 8 = (1/2)*6 + b

b = 5

Thus, the equations of the 2 lines become:

Line L: y = (-2)x + 20

and

Line K: y = (1/2)x + 5

The x-intercept of a line is given by the point where y = 0. So, the x-intercept of line L is given by:

0 = (-2)x + 20

x = 10

This means line L intersects the x-axis at the point (10, 0).

Similarly, the y-intercept of a line is given by the point where x = 0. So, y-intercept of line K is given by:

y = (1/2)*0 + 5

y = 5

This means that line K intersects the y-axis at the point (0, 5).

Looking back at our original question, the distance between these two points is given by √((10 – 0)^2 + (0 – 5)^2) = 5√(5). Therefore, our answer is C.

**Method 2: Using the Slope Concept**

Although the using the traditional method is effective, we can answer this question much quicker using the concept we discussed above.

Line L has a slope of -2, which means that for every 1 unit the x-coordinate increases, the y-coordinate decreases by 2. Line L also passes through the point (6, 8). We know the line must intersect the x-axis at y = 0, which is a decrease of 8 y-coordinates from the given point (6,8). If y increases by 8, according to our slope concept, x will increase by 4 to give 6 + 4 = 10. So the x-intercept of line L is at (10, 0).

Line K has slope of 1/2 and also passes through (6, 8). We know the this line must intersect the y-axis at x = 0, which is a decrease of 6 x-coordinates from the given point (6,8). This means y will decrease by 1/2 of that (6*1/2 = 3) and will become 8 – 3 = 5. So the y-intercept of line K is at (0, 5).

The distance between the two points can now be found using the Pythagorean Theorem – √(10^2 + 5^2) = 5√(5), therefore our answer is, again, C.

Using the slope concept makes solving this question much less tedious and saves us a lot of precious time. That is the advantage of using holistic approaches over the more traditional approaches in tackling GMAT questions.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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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]]>The post Coordinate Geometry: Solving GMAT Problems With Lines Crossing Either the X-Axis or the Y-Axis appeared first on Veritas Prep Blog.

]]>*Does the line with equation ax+by = c, where a,b and c are real constants, cross the x-axis?*

What concepts will you use here? How will you find whether or not a line crosses the x-axis? What conditions should it meet? Think about this a little before you move ahead.

We know that most lines on the XY plane cross the x-axis as well as the y-axis. Even if it looks like a given line doesn’t cross either of these axes, eventually, it will if it has a slope other than 0 or infinity.

Note that by definition, a line extends infinitely in both directions – it has no end points (otherwise it would be a line “segment”). We cannot depict a line extending infinitely, which is why we will only show a small section of it. Ideally, a line on the XY plane should be shown with arrowheads to depict that it extends infinitely on both sides, but we often omit them for our convenience. For instance, if we try to extend the example line above, we see that it does, in fact, cross the x-axis:

So what kind of lines do not cross either the x-axis or the y-xis? We know that the equation of a line on the XY plane is given by ax + by + c = 0. We also know that if we want to find the slope of a line, we can use the equation y = (-a/b)x – c/b, where the slope of the line is -a/b.

A line with a slope of 0 is parallel to the x-axis. For the slope (i.e. -a/b) to be 0, a must equal 0. So if a = 0, the line will not cross the x-axis – it is parallel to the x-axis. The equation of the line, in this case, will become y = k. In all other cases, a line will cross the x-axis at some point.

Similarly, it might appear that a line doesn’t cross the y-axis but it does at some point if its slope is anything other than infinity. A line with a slope of infinity is parallel to the y-axis. For -a/b to be infinity, b must equal 0. So if b = 0, the line will not cross the y-axis. The equation of the line in this case will become x = k. In all other cases, a line will cross the y-axis at some point.

Now, we can easily solve this official question:

*Does the line with equation ax+by = c, where a, b and c are real constants, cross the x-axis?*

*Statement 1: b not equal to 0*

*Statement 2: ab > 0*

As we discussed earlier, all lines cross the x-axis except lines which have a slope of 0, i.e. a = 0.

*Statement 1: b not equal to 0*

This tells statement us that b is not 0 – which means the line is not parallel to y-axis – but it doesn’t tell us whether or not a is 0, so we don’t know whether the line is parallel to the x-axis or crosses it. Therefore, this statement alone is not sufficient.

*Statement 2: ab>0*

If ab > 0, it means that neither a nor b is 0 (since any number times 0 will equal 0). This means the line is parallel to neither x-axis nor the y-xis, and therefore must cross the x-axis. This statement alone is sufficient and our answer is B.

Hopefully this has helped clear up some coordinate geometry concepts today.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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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]]>The post GMAT Tip of the Week: Death, Taxes, and the GMAT Items You Know For Certain appeared first on Veritas Prep Blog.

]]>On the GMAT, several things are certain. Here’s a list of items you will certainly see on the GMAT, as you attempt to raise your score and therefore your potential income, thereby raising your future tax bills in Franklin’s honor:

**Integrated Reasoning**

You **will struggle** with pacing on the Integrated Reasoning section. 12 prompts in 30 minutes (with multiple problems per prompt) is an extremely aggressive pace and very few people finish comfortably. Be willing to guess on a problem that you know could sap your time: not only will that help you finish the section and protect your score, it will also help save your stamina and energy for the all-important Quant Section to follow.

**Word Problems**

On the Quantitative Section, you **will certainly** see at least one Work/Rate problem, one Weighted Average problem, and one Min/Max problem. This is good news! Word problems reward repetition and preparation – if you’ve put in the work, there should be no surprises.

**Level of Difficulty**

If you’re scoring above average on either the Quant or Verbal sections, you **will see** at least one problem markedly below your ability level. Because each section contains several unscored, experimental problems, and those problems are delivered randomly, probability dictates that every 700+ scorer will see at least one problem designed for the 200-500 crowd (and probably more than that). Do not try to read in to your performance based on the difficulty level of any one problem! It’s easy to fear that such a problem was delivered to you because you’re struggling, but the much more logical explanation is that it was either random or difficult-but-sneakily-so, so stay confident and move on.

**Data Sufficiency**

You **will see** at least one Data Sufficiency problem that seems way too easy to be true. And it’s probably not true: make sure that you think critically any time the testmaker is directly baiting you into a particular answer.

**Sentence Correction**

You **will have to** pick an answer that you don’t like, that doesn’t catch the ear the way you’d write or say it. Make sure that you prioritize the major errors that you know you can routinely catch and correct, and not let the GMAT bait you into a decision you’re just not qualified to make.

**Reading Comprehension**

You **will see** a passage that takes you a few re-reads to even get your mind to process it. Remember to be question-driven and not passage-driven – get enough out of the passage to know where to look when they ask you a specific question, but don’t worry about becoming a subject-matter expert on the topic. GMAT passages are designed to be difficult to read (particularly toward the end of a long test), so know that your competitive advantage is that you’ll be more efficient than your competition.

**Critical Reasoning**

You **will have the opportunity** to make quick work of several Critical Reasoning problems if you notice the tiny gaps in logic that each argument provides, and if you’re able to notice the subtle-but-significant words that make conclusions extra specific (and therefore harder to prove).

Few things are certain in life, but as you approach the GMAT there are plenty of certainties that you can prepare for so that you eliminate surprises and proceed throughout your test day confidently. On this Tax Day, take inventory of the things you know to be certain about the GMAT so that your test day isn’t so taxing.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post Quarter Wit, Quarter Wisdom: Be Tolerant Towards Pronoun Ambiguity on the GMAT appeared first on Veritas Prep Blog.

]]>**Using a pronoun without an antecedent.** For example, the sentence, “Although Jack is very rich, he makes poor use of it,” is incorrect because “it” has no antecedent. The antecedent should instead be “money” or “wealth.”

**Error in matching the pronoun to its antecedent in number and gender.** For example, the sentence, “Pack away the unused packets, and save it for the next game,” is incorrect because the antecedent of “it” is referring to “unused packets,” which is plural.

**Using a nominative/objective case pronoun when the antecedent is possessive. **For example, the sentence, “The client called the lawyer’s office, but he did not answer,” is incorrect because the antecedent of “he” should be referring to “lawyer,” but it appears only in the possessive case. Official GMAT questions will not give you this rule as the only decision point between two options.

But note that the rules governing pronoun ambiguity are not as strict as other rules! Pronoun ambiguity should be the last decision point for eliminating an option after we have taken care of SV agreements, tenses, modifiers, parallelism etc.

Every sentence that has two nouns before a pronoun does not fall under the “pronoun ambiguity error” category. If the pronoun agrees with two nouns in number and gender, and both nouns could be the antecedent of the pronoun, then there is a possibility of pronoun ambiguity. But in other cases, logic can dictate that only one of the nouns can really perform (or receive) an action, and so it is logically clear to which noun the pronoun refers.

For example, “Take the bag out of the car and get it fixed.”

What needs to get fixed? The bag or the car? Either is possible. Here we have a pronoun ambiguity, but it is highly unlikely you will see something like this on the GMAT.

A special mention should be made here about the role nouns play in the sentence. Often, a pronoun which acts as the subject of a clause refers to the noun which acts as a subject of the previous clause. In such sentences, you will often find that the antecedent is unambiguous. Similarly, if the pronoun acts as the direct object of a clause, it could refer to the direct object of the previous clause. If the pronoun and its antecedent play parallel roles, a lot of clarity is added to the sentence. But it is not necessary that the pronoun and its antecedent will play parallel roles.

Let’s look at a different example, “The car needs to be taken out of the driveway and its brakes need to get fixed.”

Here, obviously the antecedent of “its” must be the car since only it has brakes, not the driveway. Besides, the car is the subject of the previous clause and “its” refers to the subject. Hence, this sentence would be acceptable.

A good rule of thumb would be to look at the options. If no options sort out the pronoun issue by replacing it with the relevant noun, just forget about pronoun ambiguity. If there are options that clarify the pronoun issue by replacing it with the relevant noun, consider all other grammatical issues first and then finally zero in on pronoun ambiguity.

Let’s take a quick look at some official GMAT questions involving pronouns now:

*Congress is debating a bill requiring certain employers **provide workers with unpaid leave so as to** care for sick or newborn children. *

*(A) provide workers with unpaid leave so as to *

*(B) to provide workers with unpaid leave so as to *

*(C) provide workers with unpaid leave in order that they *

*(D) to provide workers with unpaid leave so that they can *

*(E) provide workers with unpaid leave and *

The answer is (D). Why? The correct sentence would use “to provide” (not “provide”) and “so that” (not “so as to”), and should read, “Congress is debating a bill requiring certain employers to provide workers with unpaid leave so that they can care for sick or newborn children.” In this sentence, “they” logically refers to “workers.” Even though “they” could refer to employers, too, after you sort out the rest of the errors, you are left with (D) only, hence answer must be (D).

Let’s look at another question:

*While depressed property values can hurt some large investors, **they are potentially devastating for homeowners, whose **equity – in many cases representing a life’s savings – can plunge or even disappear.*

*(A) they are potentially devastating for homeowners, whose*

*(B) they can potentially devastate homeowners in that their*

*(C) for homeowners they are potentially devastating, because their*

*(D) for homeowners, it is potentially devastating in that their*

*(E) it can potentially devastate homeowners, whose*

The correct answer is (A). The correct sentence should read, “While depressed property values can hurt some large investors, they are potentially devastating for homeowners, whose equity – in many cases representing a life’s savings – can plunge or even disappear.” The pronoun “they” logically refers to “depressed property values.” Both the pronoun and its antecedent serve as subjects in their respective clauses, so the pronoun antecedent is quite clear.

One more question:

*Although Napoleon’s army entered Russia with far more supplies than **they had in their previous campaigns**, it had provisions for only twenty-four days. *

*(A) they had in their previous campaigns *

*(B) their previous campaigns had had *

*(C) they had for any previous campaign *

*(D) in their previous campaigns *

*(E) for any previous campaign*

The correct answer is (E). The correct sentence should read, “Although Napoleon’s army entered Russia with far more supplies than for any previous campaign, it had provisions for only twenty-four days.”

The pronoun “it” logically refers to “Napolean’s army” and not Russia. Both the pronoun and its antecedent serve as subjects in their respective clauses, so the pronoun antecedent is quite clear. Note that the pronoun and its antecedent are a part of the non-underlined portion of the sentence so we don’t need to worry about the usage here but it strengthens our understanding of pronoun ambiguity.

**free online GMAT seminars** running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!

*GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

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]]>The post GMAT Tip of the Week: Ernie Els, The Masters, and the First Ten GMAT Questions appeared first on Veritas Prep Blog.

]]>With 18 holes each day for 4 days (Quick mental math! 18×4 is the same as 9×8 – halve the first number and double the second to make it a calculation you know well – so that’s 72 holes), any one hole shouldn’t matter. So why was Els’ first hole such a catastrophe?

*It forces him to be nearly perfect the rest of the tournament, because he’s playing at such a disadvantage.*

Meanwhile, Day 1 leader Jordan Spieth shot par (“average”) his first few holes and Rory McElroy, in second place at the end of the day, bogeyed (one stroke worse than average) a total of four holes on day one. The leaders were far from perfect themselves – another important lesson for the GMAT – but by avoiding a disastrous start, they allowed themselves plenty of opportunities to make up for mistakes.

And that brings us to the GMAT. Everyone makes mistakes on the GMAT, and that often happens regardless of difficulty level. So if you’re shooting for a top score and you miss half of the first ten questions, you have a few problems to contend with.

For starters, you have to “get hot” here soon and go on a run of correct answers. Secondly, you now have a lot fewer problems available to go on that hot streak (there are only 27 more Quant or 31 more Verbal questions after the first ten). And finally, the scoring/delivery algorithm doesn’t see you as “elite” yet so the questions are going to be a little easier and less “valuable,” meaning that you’ll need to “get hot” both to prove to the computer that you belong at the top level and then to demonstrate that you can stay there.

That’s the Ernie Els problem – regardless of how good you are, you’re probably going to make mistakes, so when you force yourself to be nearly perfect on the “easier” problems you end up with a tricky standard to live up to. Even if you really should be scoring at the 700-level, you don’t have a 100% probability of answering every 500-level problem correctly. That may well be in the 90%+ range, and maybe your likelihood at the 600 level is 75 or 80%. Getting 7, 8, 9 problems right in a row is a tall order as you dig your way out of that hole.

So the first 10 problems ARE important, but not because they have that much more power over the rest of the test – it’s because the more of them you miss, the more unrealistically perfect you have to be. The key is to “not blow it” on the first 10, rather than to “do everything you can to get them all right,” which is the mindset that holds back plenty of test-takers.

Again take the Masters: the leaderboard on Thursday night is never that close to the leaderboard on Sunday evening. Very often it’s someone who starts well, but is a few strokes off the lead the first few days, who wins. The GMAT is similar: a lot can happen from questions 11 through 37 (or 41), so by no means can you celebrate victory a quarter of the way through. Your goal shouldn’t be to be perfect, but rather to get off to a good start. Getting 7 questions right and having sufficient time to complete the rest of the section is much, much better than getting 9 right but forcing yourself to rush later on.

Essentially, as Ernie Els and thousands of GMAT test-takers have learned the hard way, you won’t win it in the first quarter, but you can certainly lose it there. As you budget your time for the first 10 questions of each section, take a few extra seconds to double-check your work and make sure you’re not making egregious mistakes, but don’t over-invest at the expense of the critical problems to come.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

The post GMAT Tip of the Week: Ernie Els, The Masters, and the First Ten GMAT Questions appeared first on Veritas Prep Blog.

]]>The post Use This Tip to Avoid Critical Reasoning Traps on the GMAT appeared first on Veritas Prep Blog.

]]>Here is a problem I knew I’d be asked about often the moment I saw it:

*W, X, Y, and Z represent distinct digits such that **WX * YZ = 1995. **What is the value of W?*

*X is a prime number**Z is not a prime number*

The first instinct for most students I work with is, “I’m told nothing about W in either statement*.* There have to be many possibilities, so each statement alone is not sufficient.” When this thought occurs to you during the test, it’s important to resist it. By this, I don’t mean that you should simply assume that you’re wrong – there likely will be times when your first instincts are correct. Instead, what I mean is that you should take a bit more time to prove your assumptions to yourself. If there really are many workable scenarios, it won’t take much time to find them.

First, whenever there is an unusually large number and we’re dealing with multiplication, we want to take the prime factorization of that large number so that we can work with that figure’s basic building blocks and make it more manageable. In this case, the prime factorization of 1995 is 3 * 5 * 7 * 19. (First we see that five is a factor of 1995 because 1995 = 5*399. Next, we see that 3 is a factor of 399, because the digits of 399 sum to a multiple of 3. Now we have 5 * 3 * 133. Last, we know that 133 = 7 * 19, because if there are twenty 7’s in 140, there must be nineteen 7’s in 133.)

Now we can use these building blocks to form two-digit numbers that multiply to 1995. Here is a list of two-digit numbers we can assemble from those prime factors:

3 * 5 = 15

3 * 7 = 21

3 * 19 = 57

5 * 7 = 35

5 * 19 = 95

These are our candidates for WX and YZ. There aren’t many possibilities for multiplying two of these two-digit numbers and still getting a product of 1995. In fact, there are only two: 95*21 = 1995 and 35*57 = 1995. But we’re told that each digit must be unique, so 35*57 can’t work, as two of our variables would equal 5. This means that we know, before we even look at the statements, that our two two-digit numbers are 95 and 21 – we just need to know which is which.

It’s possible that WX = 95 and YZ = 21, or WX = 21 and YZ = 95. That’s it. What at first appeared to be a very open-ended question actually has very few workable solutions. Now that we’ve established our sample space of possibilities, let’s examine the statements:

Statement 1: If we know X is prime, we know that WX cannot be 21, as X would be 1 in this scenario and 1 is not a prime number. This means that WX has to be 95, and thus we know for a fact that W = 9. This statement alone is sufficient to answer the question.

Statement 2: If we know that Z is not prime, we know that YZ cannot be 95, as Z would be 5 in this scenario and 5 is, of course, prime. Thus, YZ is 21 and WX is 95, and again, we know for a fact that W is 9, so this statement alone is also sufficient.

The answer is D, either statement alone is sufficient to answer the question, a result very much at odds with most test-taker’s initial instincts.

Takeaway: the GMAT is engineered to wrong-foot test-takers, using our instincts against us. Rather than simply assuming our instincts are wrong – they won’t always be – we want to be methodical about proving our intuitions one way or another by confirming them in some instances, refuting them in others. By being thorough and methodical, we reduce the odds that we’ll step into one of the traps the question-writer has set for us and increase the odds that we’ll answer the question correctly.

*Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him, here.*

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]]>The post Are There Set Rules for Answering GMAT Sentence Correction Questions? appeared first on Veritas Prep Blog.

]]>Was there a way, she wondered, to view Sentence Correction with the same unwavering consistency with which we view Quantitative questions? While I understand her frustration, the answer is, alas, an unqualified “no.” English is far too complex for us to boil down Sentence Correction to a series of stimulus-response reflexes. Context and logic always matter.

To see why we can’t go on autopilot during Sentence Correction questions, consider the following problem:

__Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also__* caused erosion and very q**uic**kly deforested whole regions. *

*A) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also*

* B) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast), which gave consumers relatively inexpensive houses and furniture, but also*

* C) The systematic clearing of forests in the United States, creating farmland (especially in the Northeast) and giving consumers relatively inexpensive houses and furniture, but also*

* D) The systematic clearing of forests in the United States created farmland **(especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also*

* E) The systematic clearing of forests in the United States not only created farmland (especially in the Northeast), giving consumers relatively inexpensive houses and furniture, but it*

If you fully absorbed the class discussion about the importance of parallel construction, you probably noticed an indelible parallel marker here: “not only.” Okay, you think. Any time I see *not only x*, I know *but also y* should show up later in the sentence.

This isn’t wrong, per se, but the construction “not only/but also” is only applicable in certain circumstances. So before we jump to the erroneous conclusion that this is the construction that is called for in this sentence, let’s examine its underlying logic in more detail.

Take the simple example, “On the way to work, I not only got stuck in traffic, but also….” Think about your expectations for what should come next in this sentence – getting stuck in traffic was the first unfortunate thing to happen to this hapless subject, and we’re expecting a second unfortunate event in the latter part of the sentence. Not only/but also is appropriate when we’re talking about *similar* things.

Now consider the construction. “On the way to work, I got stuck in traffic, but…” Now our expectations are markedly different – the second half of the sentence is going to contrast with the first. We’re expecting something *different*.

Let’s go back to our GMAT sentence. We’re comparing the consequences of the clearing of forests. First, the clearing “created farmland and gave consumers inexpensive houses” (good things). However, it also “caused erosion and deforested the region” (bad things). Because we’re comparing two very *different* consequences, the construction “not only/but also” – which is used to compare similar things – is inappropriate. Now we can safely eliminate answers A, B and E.

That leaves us with C and D. First, let’s examine C. Notice there’s a participial modifier in the middle of the sentence set off by commas, and a sentence should still be logical if we remove these modifiers. We would then be left with, “The systematic clearing of forests in the United States, but also caused erosion and very quickly deforested whole regions.” This clearly doesn’t work – the initial subject (the systematic clearing) has no verb, so C is wrong. This leaves us with answer choice D, which is the correct answer.

Takeaway: though noticing common constructions on Sentence Correction problems can be helpful, we can never go on autopilot. Ultimately, context, logic, and meaning will always come into play. Before you select any answer, always ask yourself if the sentence is logically coherent before you select it. If you want to ace the GMAT, turning off your brain is not an option.

**GMATPrep question courtesy of the Graduate Management Admissions Council.*

*Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can read more articles by him here.*

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]]>The post Quarter Wit, Quarter Wisdom: Using a Venn Diagram vs. a Double Set Matrix on the GMAT appeared first on Veritas Prep Blog.

]]>Venn diagrams are like Superman – all powerful. They can help you solve almost all questions involving either 2 or 3 overlapping sets. But then, there are some situations in which double set matrix method (aka Batman with his amazing weaponry) might be easier to use. It is possible to solve these questions using Venn diagrams, too, but it is more convenient to solve them using a Double Set Matrix.

We have discussed solving three overlapping sets using Venn diagrams here.

Today, we will look at the case in which using a Double Set Matrix is easier than using a Venn diagram – in instances where we have two sets of variables, such as English/Math and Middle School/High School, or Cake/Ice cream and Boys/Girls, etc.

Eventually, we will solve our question again using a Venn diagram, for those who like to use a single method for all similar questions. First, take a look at our question:

*A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?*

*(A) 18*

*(B) 27*

*(C) 36*

*(D) 72*

*(E) 180*

To solve this problem using a Double Set Matrix, first jot down one set of variables as the row headings and the other as the column headings, as well as a row and column for “totals.” Now all you need to do is add in the information line by line as you read through the question.

“…*male graduate students outnumber male undergraduates by a ratio of 7 to 2…*”

“…*females constitute 70% of the group.*”

Female students make up 70% of the group, which implies that male students (total of 9x) make up 30% of the group.

9x = (30/100)*Total Students

Total Students = 30x

Since 9x is the total number of male students while 30x is the total number of all students, the total number of female students must be 30x – 9x = 21x.

“*If undergraduate students make up 1/6 of the group…*”

Undergrad students make 1/6 of the group, i.e. (1/6)*30x = 5x

If the total number of undergrad students is 5x and the number of male undergrad students is 2x, the number of female undergrad students must be 5x – 2x = 3x.

This implies that the number of graduate females must be 18x, since the total number of females is 21x.

Therefore, the number of graduate females must be a multiple of 18. 27 is the only answer choice that is not a multiple of 18, so it cannot be the number of graduate females – therefore, our answer must be B.

Now, here is how Superman can rescue us in this question. An analysis similar to the one above will give us a Venn diagram which looks like this:

Of course, we will get the same answer: the number of graduate females must be a multiple of 18. We know 27 is not a multiple of 18, so it cannot be the number of graduate females and therefore, our answer is still B.

Hopefully, next time you come across an overlapping sets question, you will know exactly who your superhero is!

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