The post How Does Scoring Differ Between the GMAT and the GRE? appeared first on Veritas Prep Blog.

]]>It’s a new year, and thus a good time to undertake a new intellectual challenge. For me, this challenge will take the form of teaching new classes on GRE preparation. Because the test has changed so much over the years, I thought it might be interesting to delineate my impressions of the newer incarnation, both in terms of how the GRE differs from the GMAT and in terms of how the GRE has evolved over time.

** **The GRE has two Quantitative sections and two Verbal sections of 30 minutes each, while the GMAT has a single Quantitative section and a single Verbal section of 75 minutes each. Moreover, while the GMAT is adaptive by the question, the GRE is adaptive by *section*. Do well on the first GRE Quantitative section and the entire next section will escalate in difficulty. (My impression: while the GRE does adjust from section to section, it does so in a way that feels significantly subtler than the GMAT exam.)

This is typically the most conspicuous difference test-takers notice. In our GMAT courses, we have a skill-builder section that allows students to re-master the basics before delving into a discussion about the types of higher-order thinking the GMAT will require. In other words, it’s not enough to simply recall the various rules, axioms, and equations we’ve forgotten from high school – those foundational elements will need to be applied in creative ways. While the GRE does require some higher-order thinking, on many quantitative questions simply having the foundational skills is enough to arrive at the correct answer. The strategic element is more about how to arrive at these answers in a timely manner and how to avoid panicking on the few hairier questions that will likely come your way.

Moreover, in lieu of the GMAT’s dreaded Data Sufficiency questions, the GRE has Quantitative Comparison questions, in which a test-taker is asked to compare the relative magnitude of two quantities – it’s possible that one quantity is larger than the other, that the two quantities are equal, or that it’s not possible to determine which quantity is larger. After grappling with knotty Data Sufficiency questions, a test-taker is likely to find Quantitative Comparison to be blessedly straightforward. Better yet, the GRE will allow you to return to questions once you’ve answered them, granting test-takers more opportunities to weed out careless mistakes. If that weren’t enough, on the GRE, you’ll have access to an on-screen calculator. So there are perks.

Of course, there’s a rub. The GRE’s Quantitative section might be easier in terms of the difficulty level of the questions, but that doesn’t necessarily mean that it’s easier to score well. If you’re able to ascend to the more difficult question levels on the GMAT, you can miss many of them and still do well. Not so on the GRE, where you need to be pretty close to perfect to achieve an elite score.

Like the GMAT, the GRE has a Reading Comprehension component. But unlike the GMAT, the GRE questions will often ask you to select “all that apply,” meaning that you may need to select as many as three correct assertions in order to receive credit for a question. Select two of the three? You get the question wrong. No partial credit. And while the GRE doesn’t have any Sentence Correction questions, it does have Sentence *Completion* questions, and these questions often come down to either recognizing somewhat obscure vocabulary words or utilizing more familiar words in less familiar ways.

Ultimately, in my experience, most test-takers will score at comparable percentile levels if they were to take both exams. Choosing which test is better for you might be a question of fit or comfort more than anything else. And while there’s a fair amount of overlap between the two exams, they feel different enough that you wouldn’t want to prepare for one and simply assume that you’re ready for the other. Each test has its own strategic texture and its own idiosyncrasies, so you want to be sure that you’ve worked through a curriculum specifically designed for the test in question before you sit for the exam.

Regardless of whether you take the GMAT or GRE, Veritas Prep is committed to helping you prepare to do your best on test day! Jump start your prep by taking advantage of Veritas Prep’s various free GMAT resources and free GRE resources to determine which test is right for you.

*This article was written by Veritas Prep instructor David Goldstein. Be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter** for more helpful articles like these! *

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]]>The post Complexities of Parallelism – Part I appeared first on Veritas Prep Blog.

]]>We see parallelism in many cases in GMAT. Some of them are:

- A list of elements
- Co-ordinating and correlative conjunctions such as “and”, “but”, “both … and…”, “either … or…” etc
- Stating a comparison such as “compared to A, B”
- Idioms involving elements in parallel such as “consider A B”

On the face of it, it seems quite simple and straight forward – all acting verbs or all nouns etc, but if a GMAT question focusses on it, it is bound to be more complicated than that. Parallelism depends on both, the form and the function of the words. Also, it is important to decipher the logic of the sentence – should the elements be in parallel in the first place? If yes, then which elements should be in parallel?

We also need to worry about when to repeat a particular word in all parallel elements and when not to. We know the thumb rule – either repeat in all or use only once in the beginning. But when is it a good idea to repeat the word in all elements?

Yes, it isn’t that simple after all!

But let’s answer all these questions using a couple of examples.

*Question 1: It is no surprise that Riyadh, the Saudi capital where people revere birds of prey and ride camels regularly, is home to the world’s largest hospital for falcons, a place where falcons from all over the world are treated in operating rooms, an ophthalmology department, and a pox area, and to the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for. *

*(A) an ophthalmology department, and a pox area, and to the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for. *

*(B) an ophthalmology department, a pox area, and the largest veterinary clinic for desert mammals, where camels and other desert species are expertly cared for. *

*(C) an ophthalmology department, to a pox area, and to the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for. *

*(D) to an ophthalmology department, and to a pox area and the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for. *

*(E) an ophthalmology department and a pox area, and the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for.*

Solution: There are lots of commas and lots of different elements in the sentence.

Logically, we see that Riyadh is home to the largest hospital for falcons and to the veterinary clinic for desert mammals. It can’t be home to operating rooms, an ophthalmology department, and a pox area! These are places inside a hospital!

So then, here is the structure of the sentence:

It is no surprise that Riyadh, …, is home to A and to B.

A and B should be in parallel.

Within A, we have a list of elements too.

A – the world’s largest hospital for falcons, a place where falcons from all over the world are treated in X, Y and Z

X – operating rooms

Y – an ophthalmology department

Z – a pox area

B – the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for

Therefore, to show parallelism between A and B, we have used “to” with both to show the beginning of the parallel elements. This separates them from the other set of parallel elements – X, Y and Z.

Note that only option (A) satisfies these conditions and hence is the correct answer here.

Takeaways

- The first thing to do is to figure out the logic of the sentence to see which elements should be in parallel and which shouldn’t.
- After that, put those that need to be in parallel. We might need to repeat certain words to signal the start of parallel elements when we have other intertwined lists too.

We will leave you with a question now. We will discuss it in detail in our next post.

Question 2: Geologists believe that the warning signs for a major earthquake may include sudden fluctuations in local seismic activity, tilting and other deformations of the Earth’s crust, changing the measured strain across a fault zone, and varying the electrical properties of underground rocks.

(A) changing the measured strain across a fault zone, and varying

(B) changing measurements of the strain across a fault zone, and varying

(C) changing the strain as measured across a fault zone, and variations of

(D) changes in the measured strain across a fault zone, and variations in

(E) changes in measurements of the strain across a fault zone, and variations among

*Getting ready to take the GMAT? Check out one of our many free GMAT resources to get a jump start on your GMAT prep. And as always, be sure to follow us on Facebook, YouTube, Google+, and Twitter for more helpful tips like this one!*

*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 Why We Need to Redraw GMAT Geometry Figures appeared first on Veritas Prep Blog.

]]>In Problem Solving questions, our target is to find just one solution. For example, when we have questions involving percentages, we assume some values and get the answer. No matter what values we assume, we will always get the same answer as long as the integrity of the data is maintained.

In Data Sufficiency questions, our target is to find multiple possible solutions after using all the given data and arrive at answer (E). If we are unable to find more than 1 solution using either statement (1) and/or statement (2), we arrive at answers (A), (B), (C) or (D).

The aim is diametrically opposite in the two cases. Therefore, our strategies in the two cases would also be different and they are. Consider Geometry questions with figures in them. In Problem Solving questions, we try to make the figures as symmetrical as possible under the given constraints. With symmetrical figures, it is easier to get an answer. One answer is all we need.

In Data Sufficiency questions, we try to make the figures as extreme as possible. Only the given data should hold in such a figure and no symmetry should exist in the other dimensions. Only then will we be able to really figure out whether the given information is enough to arrive at a unique answer.

Let’s explain this using two examples:

Problem Solving Question

PSvsDSQuesPS1.jpg ********************************

*In the figure above, the area of square PQRS is 64. What is the area of triangle QRT?*

*(A) 48*

* (B) 32*

* (C) 24*

* (D) 16*

* (E) 8*

This is a Problem Solving question.

All we are given is that PQRS is a square. Note that the location of point T is not defined. It is just any point on side PS. We can place it anywhere we like as long as it is on PS. At what point will it be easy for us to calculate the area of triangle QRT? Of course, T could be the middle point of PS (bringing in symmetry) and we could calculate the area of the triangle or we could make it coincide with S so that QRT is a right triangle half of square PQRS. Then, the area of triangle QRT will simply be half of 64, i.e. 32.

Note that we don’t necessarily need to do this. We can assume T to be a random point, drop an altitude from T to QR, find that the length of the altitude will be same as the side of the square, find that side of the square will be √(64) = 8 and area of triangle QRT will be (1/2)*8*8 = 32

We will arrive at the same answer of course! But, assuming a better position for point T (but only because it is not defined) will cut the calculations and help us arrive directly at 32 from 64.

Data Sufficiency Question

PSvsDSQuesDS1.jpg ********************************

*If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?*

*Statement 1: Angle ABD = 60°*

* Statement 2: AC = 12*

Looking at the figure, many test takers are tempted to think that the altitude AD will bisect BC. Note that that may not be the case.

According to the data given in the question stem alone, the figure could very well look something like this:

PSvsDSQuesDS2.jpg ********************************

All we know is that ADC is a right angle and the length of the altitude is 6. We don’t know whether any of the sides are equal, etc. Hence, it is a good idea to redraw the figure with extreme proportions – one side much greater than the other.

Now we can use the given statements to re-adjust the proportions.

Area of triangle ABC = (1/2)*AD*BC

We know that AD is 6. But we don’t know BC. Let’s examine each of the statements separately.

*Statement 1: Angle ABD = 60°*

This statement tells us that triangle ABD is a 30-60-90 triangle. Knowing the length of AD will give us the length of the other two sides too. But here is the problem – to know BC, we need to know length of CD too. That we cannot find from this statement alone. This statement alone is not sufficient to answer the question.

*Statement 2: AC = 12*

We know that ADC is a right angled triangle. Knowing AC and AD, we can find the length of CD using Pythagorean Theorem. But we cannot find BD using this statement and that is needed to get the length of BC. This statement alone is also not sufficient to answer the question.

Using both statements, we can find the lengths of both BD and CD, and hence, can find the length of BC. This will give us the area of the triangle. Therefore, our answer is C.

Note here that if we mistakenly assume that D is the mid point of BC, we might come to the conclusion that each statement alone is sufficient and might mark the answer as D, instead of C. Hence, it is a good idea to redraw the given figure in a Data Sufficiency question to ensure that it has as little symmetry as possible.

*Getting ready to take the GMAT? Check out one of our many free GMAT resources to get a jump start on your GMAT prep. And as always, be sure to follow us on Facebook, YouTube, Google+, and Twitter for more helpful tips like this one!*

*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 Quarter Wit, Quarter Wisdom: To Learn To-Infinitives appeared first on Veritas Prep Blog.

]]>Note that the infinitive is the base form of a verb. The infinitive has two forms:

** • the to-infinitive** = to + base

** • the zero infinitive** = base

We will discuss the to-infinitive form, a verbal. It can work as a noun, an adjective, or an adverb

The to-infinitive form is used in many sentence constructions, often expressing the purpose of something or someone’s opinion about something. The to-infinitive is used following a large collection of different verbs as well such as afford, offer, refuse, prepare, undertake, proceed, propose, promise etc

The function of a to-infinitive in a sentence could be any of the following:

I. To show the purpose of an action: In this case “*to”* has the same meaning as “*in order to”* or “*so as to”*. It follows a verb in this case.

For Example: She has gone to complete her homework.

II. To indicate what something can or will be used for: It follows a noun or a pronoun in this case.

For Example: I don’t have anything to wear. This is the right thing to do.

III. After adjectives

For Example: I am happy to be here.

IV. The subject of the sentence

For Example: To visit Paris is my lifelong dream.

V. With adverbs: It is used with the adverbs *too* and *enough* to express the reasoning behind our satisfaction or dissatisfaction. The pattern is that *too* and *enough* are placed before or after the adjective, adverb, or noun that they modify in the same way they would be without the to-infinitive. We then follow them by the to-infinitive to explain the reason why the quantity is excessive, sufficient, or insufficient.

For Example: He has too many books to carry on his own.

VI. With question words: The verbs ask, decide, explain, forget, know, show, tell, & understand can be followed by a question word such as where, how, what, who, & when + the to-infinitive.

For Example: I am not sure how to use the new washing machine.

We are likely to see infinitive phrases in GMAT sentence correction questions. An infinitive phrase is made up of the infinitive verb with its object and modifiers.

Let’s take a look at how we could see an infinitive in a GMAT question.

*Question: Twenty-two feet long and 10 feet in diameter, the AM-1 is one of the many new satellites that is a part of 15 years effort of subjecting the interactions of Earth’s atmosphere, oceans, and land surfaces to detailed scrutiny from space.*

*(A) satellites that is a part of 15 years effort of subjecting the interactions of Earth’s atmosphere, oceans, and land surfaces*

*(B) satellites, which is a part of a 15-year effort to subject how Earth’s atmosphere, oceans, and land surfaces interact*

*(C) satellites, part of 15 years effort of subjecting how Earth’s atmosphere, oceans, and land surfaces are interacting*

*(D) satellites that are part of an effort for 15 years that has subjected the interactions of Earth’s atmosphere, oceans, and land surfaces*

*(E) satellites that are part of a 15-year effort to subject the interactions of Earth’s atmosphere, ocean, and land surfaces*

Solution:

First let’s try to understand the basic structure of the sentence.

… AM-1 is one of the many new satellites “that/which clause”

“that/which clause” modifies the noun “satellites” in four of the given five options. Note that “satellites” is plural so we need to use the verb “are”. So options (A) and (B) are out.

(C) is also incorrect. It looks like “part of 15 years … from space” is a bad attempt at writing an absolute phrase. Absolute phrases modify the entire clause but here we need to modify “satellites” only. Satellites are a part of a 15 year effort to subject A to detailed scrutiny and hence we should use a that/which clause.

(D) is incorrect too. It uses another “that clause” – that has subjected the interactions …

This “that clause” modifies the noun “effort”, not “15 years”. The effort has subjected A to detailed scrutiny.

There is a better way of writing this sentence such that the “that clause” comes immediately after “effort”

(E) is correct. Note how it uses the infinitive form immediately after the noun “effort” to indicate how the effort is being used. It is being used to subject A to detailed scrutiny.

Hope now you will be able to recognise the different verbals and use them correctly.

*Getting ready to take the GMAT? Check out one of our many free GMAT resources to get a jump start on your GMAT prep. And as always, be sure to follow us on Facebook, YouTube, Google+, and Twitter for more helpful tips like this one!*

*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 All About “That” on the GMAT appeared first on Veritas Prep Blog.

]]>- Demonstrative Determiner
- Demonstrative Pronoun
- Relative Pronoun

**Demonstrative Determiner** – In this role, “that” specifies the specific person/thing about which we are talking. It is followed by a noun.

Can I have some of that cake, please?

I have never been to that part of Italy.

When we are talking about a plural noun, “that” becomes “those”.

**Demonstrative Pronoun** – In this role, “that” replaces a noun.

That is beautiful.

Look at that!

When we replace a plural noun, “that” becomes “those”.

**Relative Pronoun** – “that” introduces a defining/restrictive clause. This clause is essential to the sentence.

Loki is on the team that lost.

The produce that is sourced locally is environment-friendly.

There is no “that”/“those” distinction in this case. The clause is always introduced by “that”.

Hope these simple examples clarified the various roles “that” can play in a sentence. Not understanding this distinction could lead to a lot of confusion. The words around “that” will help you understand exactly what role it is playing in each case.

Let’s take a look at one of our own questions in which knowing this distinction comes in handy.

*Question: In nests across North America, the host mother tries to identify their own eggs and weed out the fakes, but the brown-headed cowbird – a brood parasite that sneaks its eggs into other birds’ nests – produces eggs that look very similar to those of the host, making that task surprisingly difficult.*

*(A) the host mother tries to identify their own eggs and weed out the fakes, but the brown-headed cowbird – a brood parasite that sneaks its eggs into other birds’ nests – produces eggs that look very similar to those of the host, making that task surprisingly difficult*

*B) the host mother tries to identify its own eggs and weed out the fakes, but the brown-headed cowbird – a brood parasite that sneaks its eggs into other birds’ nests – produces eggs that look very similar to that of the host, making it surprisingly difficult*

*C) host mothers try to identify their own eggs and weed out the fakes, but the brown-headed cowbird – a brood parasite that sneaks its eggs into other birds’ nests – produces eggs that look very similar to the host’s, making that task surprisingly difficult*

*D) host mothers try to identify their own eggs and weed out the fakes, but the brown-headed cowbird – a brood parasite that sneaks its eggs into other birds’ nests – produces eggs that look very similar to that of the host’s, making it surprisingly difficult*

*E) host mothers try to identify its own eggs and weed out the fakes, but the brown-headed cowbird – a brood parasite that sneaks its eggs into other birds’ nests – produces eggs that look very similar to those of the host’s, making that task surprisingly difficult*

Solution:

This is a complicated sentence and unfortunately, almost the entire sentence is underlined. That just makes it harder and more time consuming.

- … the host mother tries to identify their own eggs…

In the beginning itself, we see that the subject is “host mother” which is singular and the pronoun that refers back to it – “those” – is plural. Hence this sentence is incorrect. We just move on.

(B) … produces eggs that look very similar to that of the host …

We have two instances of the use of “that” here. The first “that” is used as a relative pronoun to introduce the clause “that look very similar to ….”

The second “that” is used as a placeholder for “eggs” hence we need to use “those” – the plural form – here.

(C) All correct

(D) … produces eggs that look very similar to that of the host’s…

The explanation is the same as that of (B). The second “that” is used as a placeholder for “eggs” hence we need to use “those” – the plural form – here.

Also, the correct comparison is:

either

“A’s eggs look very similar to those of B” (where “those” stands for eggs)

or

“A’s eggs look very similar to B’s” (where eggs is implied at the end).

But “A’s eggs look very similar to those of B’s” is incorrect since it implies

“A’s eggs look very similar to eggs of B’s eggs”

(E) … host mothers try to identify its own eggs…

The subject is “host mothers”, which is plural, but the pronoun is “its”, which is singular.

Hope this clarifies the various ways in which “that” can be used.

**free GMAT resources** to get a jump start on your GMAT prep. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter **for more helpful tips like this one!

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

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]]>The post Is It Incorrect to Use Multiple Verb Tenses in a Sentence? appeared first on Veritas Prep Blog.

]]>Take a look at this example sentence:

*I have heard that Mona left Manchester this morning, and has already arrived in London, where she will be for the next three weeks.*

Here, we have present perfect tense, simple past tense and simple future tense all in the same sentence, but they all make sense together to create a logical sequence of events.

The confusion over using multiple verb tenses in one sentence probably arises because we have heard that we need to maintain verb tense consistency. These two things are different.

Tense Consistency – We do not switch one tense to another unless the timing of the action demands that we do. We do not switch tenses when there is no time change for the actions.

Let’s take a look at some examples to understand this:

Example 1: During the match, my dad **stood** up and **waved** at me.

These two actions (“stood” and “waved”) happen at the same time and hence, need to have the same tense. This sentence could take place in the present or future tense too, but both verbs will still need to take on the same tense. For example:

Example 2: During my matches, my dad **stands** up and **waves** at me.

Example 3: During the match tomorrow, my dad **will stand** up and **wave** at me.

On the other hand, a sentence such as…

Example 4: During the match, my dad **stood** up and **waves** at me.

This sentence is grammatically incorrect. Since both actions (“stood” and “waves”) happen at the same time, we need them to be in the same tense, as shown in the variations of this sentence above. Consider this case, however:

Example 5: My dad **reached** for the sandwich after he had already **eaten** a whole pizza.

Here, the two actions (“reached” and “eaten”) happen at different times in the past, so we use both the simple past and past perfect tenses. The shift in tense is correct in this context.

**Takeaway: The tenses of verbs in a sentence must be consistent when the actions happen at the same time. When dealing with actions that occur at different points in time, however, we can use multiple tenses in the same sentence.**

Let’s look at an official GMAT question now to see how multiple tenses can be a part of the same sentence:

*For the farmer who takes care to keep them cool, providing them with high-energy feed, and milking them regularly, Holstein cows are producing an average of 2,275 gallons of milk each per year.*

*(A) providing them with high-energy feed, and milking them regularly, Holstein cows are producing*

*(B) providing them with high-energy feed, and milked regularly, the Holstein cow produces*

*(C) provided with high-energy feed, and milking them regularly, Holstein cows are producing*

*(D) provided with high-energy feed, and milked regularly, the Holstein cow produces*

*(E) provided with high-energy feed, and milked regularly, Holstein cows will produce*

This is a very tricky question. Let’s first shortlist our options based on the obvious errors.

The non-underlined part of the sentence uses the pronoun “them” to refer to the cows, so using “the Holstein cow” (singular) as the antecedent will be incorrect. The antecedent must be “Holstein cows” (plural) – this means answer choices B and D are out.

Also, we know for sure that “provide” and “milk” are parallel elements in the sentence, so they should take the same verb tense. Hence, answer choice C is also out.

Let’s look at A now. If we assume this option is correct, “providing” and “milking” act as modifiers to “keep them cool”. That certainly does not make sense since “providing with high energy feed” and “milking regularly” are not ways of keeping cows cool.

This means the correct answer is E, but we need to see how.

*For the farmer who takes care to keep them cool, provided with high-energy feed, and milked regularly, Holstein cows will produce an average of 2,275 gallons of milk each per year.*

Let’s break down the sentence:

*For the farmer who takes care to keep them…*

- cool,
- provided with high-energy feed,
- milked regularly,

*…Holstein cows will produce an average of 2,275 gallons of milk each per year.*

Note that we use two different tenses here: “For the farmer who takes care…” and “cows will produce…”. The word “takes” is the present tense while “will produce” is the future, but that does not make this sentence incorrect. The context of the author could very well justify the use of the future tense. Perhaps the farmers have obtained Holstein cows recently, and hence, will see the produce of 2,275 gallons in the future, only.

A shift in the tense certainly doesn’t make the sentence incorrect. When you’re presented with multiple verbs in various tenses in a problem, check to determine whether the verbs convey a logical sequence of events.

**free GMAT resources** to get a jump start on your GMAT prep. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter **for more helpful tips like this one!

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

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]]>The post Dreaded Data Sufficiency Questions That Will Test Your Knowledge of Number Properties appeared first on Veritas Prep Blog.

]]>Here is our advice – when solving number properties questions, imagine a number line. It reminds us that numbers behave differently “between 0 and 1”, “between -1 and 0”, “less than -1”, and “more than 1”, and that integers occur only at regular intervals and that there are infinite numbers in between them. The integers are, in turn, even and odd. Also, 0, 1 and -1 are special numbers, hence it is always a good idea to consider cases with them.

Let’s see how thinking along these lines can help us on a practice Data Sufficiency question:

*If a and b are non-zero integers, is a^b an integer?*

*Statement 1: b^a is negative*

*Statement 2: a^b is negative*

The answer to this problem does not lie in actually drawing a number line. The point is that we need to think along these lines: -1, 0, 1, ranges between them, integers, negatives-positives, even-odd, decimals and how each of these comes into play in this case.

What we know from the question stem is that *a* and *b* are non-zero integers, which means they occur at regular intervals on the number line. To answer the question, “Is *a*^*b* an integer?”, let’s first look at Statement 1:

*Statement 1: b^a is negative*

For a number to be negative, its base must be negative. But that is not enough – the exponent should not be an even integer. If the exponent is an even integer, the negative signs will cancel out. Since *a* and *b* are integers, if *a* is not an even integer, it must be an odd integer.

We know that the sign of the exponent is immaterial as far as the sign of the result is concerned (since *a*^(-*n*) is just 1/*a*^*n*). For *b*^*a* to be negative, then we know that *b* must be a negative integer and *a* must be an odd integer. Does this help us in deducing whether *a*^*b* is an integer? Not necessarily!

If *b* is negative, say -2, *a*^(-2) = 1/*a*^2. *a* could be 1, in which case 1/*a*^2 = 1 (an integer), or *a* could be 3, in which case 1/*a*^2 = 1/9 (not an integer). Because there are two possible answers, this statement alone is not sufficient.

Let’s look at Statement 2:

*Statement 2: a^b is negative*

Again, the logic remains the same – for *a* number to be negative, its base must also be negative and the exponent should not be an even integer. If the exponent is an even integer, the negative signs will cancel out. Since *a* and *b* are integers, if *b* is not an even integer, it must be an odd integer. Again, we know that the sign of the exponent is immaterial as far as the sign of the result is concerned (since *a*^(-*n*) is just 1/*a*^*n*).

For *a*^*b* to be negative, then we know that a must be a negative integer and* b* must be an odd integer. *a* could be -1/-2/-3/-4… etc, and* b* could be 1/3/5… or -1/-3/-5.

If *a* = -1 and *b* = 1, then *a*^*b* = -1 (an integer). If* a* = -2 and *b* = -3, then *a*^*b* = (-2)^(-3) = 1/(-2)^3 = -1/8 (not an integer). This statement alone is also not sufficient.

We hope you see how we are using values of 1 and -1 to enumerate our cases. Now, let’s consider using both statements together:

*a* is a negative, odd integer, so it can take values such as -1, -3, -5, -7, …

*b* is a negative, odd integer too, so it can also take values such as -1, -3, -5, -7, …

If *a* = -1 and* b* = -1, then *a*^*b* = -1 (an integer)

If* a* = -3 and *b* = -3, then *a*^*b* = (-3)^(-3) = -1/27 (not an integer)

Even using both statements together, we do not know whether *a*^*b* is an integer or not. therefore, our answer is E.

Thinking of a number line and knowing what it represents will help you tackle many Data Sufficiency questions that are about number properties.

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]]>The post 3 Ways to Solve a 750+ Level GMAT Question About Irregular Polygons appeared first on Veritas Prep Blog.

]]>*The hexagon above has interior angles whose measures are all equal. As shown, only five of the six side lengths are known: 10, 15, 4, 18, and 7. What is the unknown side length?*

*(A) **7*

*(B)**10*

*(C) 12*

*(D) 15*

*(E) 16*

There are various ways to solve this question, but each takes a bit of effort. Note that the polygon we are given is not a regular polygon, since the side lengths are not all equal. The angles, however, are all equal. Let’s first find the measure of each one of those angles using the formula discussed in this previous post.

(n – 2)*180 = sum of all interior angles

(6 – 2)*180 = 720

Each of the 6 angles = 720/6 = 120 degrees

Though we would like to point out here that if you see a question such as this one on the actual GMAT exam, you should already know that if each angle of a hexagon is equal, each angle must be 120 degrees, so performing the above calculation would not be necessary.

**Method 1: Visualization**

This is a very valid approach to obtaining the correct answer on this GMAT question since we don’t need to explain the reasoning or show our steps, however it may be hard to comprehend for the beginners. We will try to explain it anyway, since it requires virtually no work and will help build your math instinct.

Note that in the given hexagon, each angle is 120 degrees – this means that each pair of opposite sides are parallel. Think of it this way: Side 4 turns on Side 18 by 120 degrees. Then Side 15 turns on Side 4 by another 120 degrees. And finally, Side 10 turns on Side 15 by another 120 degrees. So Side 10 has, in effect, turned by 360 degrees on Side 18.

This means Side 10 is parallel to Side 18.

Now, think of the 120 degree angle between Side 4 and Side 15 – it has to be kept constant. Plus, the angles of the legs must also stay constant at 120 degrees with Sides 10 and 18. Since the slopes of each leg of that angle are negatives of each other (√3 and -√3), when one leg gets shorter, the other gets longer by the same length (use the image below as a visual of what we’re talking about).

Hence, the sum of the sides will always be 15 + 4 = 19. This means 7 + Unknown = 19, so Unknown = 12. Our answer is C.

If you struggled to understand the approach above, you’re not alone. This method involves a lot of intuition, and struggling to figure it out may not be the best use of your time on the GMAT, so let’s examine a couple of more tangible solutions!

**Method 2: Using Right Triangles**

As we saw in Method 1 above, AB and DE are parallel lines. Since each of the angles A, B, C, D, E and F are 120 degrees, the four triangles we have made are all 30-60-90 triangles. The sides of a 30-60-90 triangle can be written using the ratio 1:√(3):2.

AT = 7.5*√3 and ME = 2*√3, so the distance between the sides of length 10 and 18 is 9.5*√3. We know that DN = 3.5*√3, so BP = (9.5*√3) – (3.5*√3) = 6*√3.

Since the ratios of our sides should be 1:√(3):2, side BC = 2*6 = 12. Again, the answer is C. Let’s look at our third and final method for solving this problem:

**Method 3: Using Equilateral Triangles**

First, extend the sides of the hexagon as shown to form a triangle:

Since each internal angle of the hexagon is 120 degrees, each external angle will be 60 degrees. In that case, each angle between the dotted lines will become 60 degrees too, and hence, triangle PAB becomes an equilateral triangle. This means PA = PB = 10. Triangle QFE and triangle RDC also become equilateral triangles, so QF = QE = 4, and RD = RC = 7.

Now note that since angles P, Q, and R are all 60 degrees, triangle PQR is also equilateral, and hence, PQ = PR.

PQ = 10 + 15 + 4 = 29

PR = 10 + BC + 7 = 29

BC = 12 (again, answer choice C)

Note the geometry concepts that we used to solve this problem: regular polygon, parallel lines, angles, 30-60-90 right triangles, and equilateral triangles. We know all of these concepts very well individually, but applying them to a GMAT question can take some ingenuity!

*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!*

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

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]]>The post Quarter Wit, Quarter Wisdom: Using Ingenuity on GMAT Remainder Questions appeared first on Veritas Prep Blog.

]]>Say** “x” gives you a remainder of 2 when divided by 6**. What will be the remainder when x + 1 is divided by 6?

Go back to the divisibility concepts discussed above. When x balls are split into groups of 6, we will have 2 balls leftover. If we are given 1 more ball, it will join the 2 balls and now we will have 3 balls leftover. The remainder will be 3.

What happens in the case of** x + 6** – what will be the remainder when this is divided by 6? This additional 6 balls will just make an extra group of 6, so we will still have 2 balls leftover.

What about the case of** x + 9**? Now, of the extra 9 balls, we will make one group of 6 and will have 3 balls leftover. These 3 balls will join the 2 balls leftover from x, giving us a remainder of 5.

Now, what about the case of** 2x**? Recall that 2x = x + x. The number of groups will double and so will the remainder, so 2x will give us a remainder of 2*2 = 4.

On the other hand, if x gives us a remainder of 4 when divided by 6, then 2x divided by 6 will have a remainder of 2*4 = 8, which gives us a remainder of 2 (since another group of 6 will be formed from the 8 balls).

Let’s consider the tricky case of** x^2** now. If x gives us a remainder of 2 when it is divided by 6, it means:

x = 6Q + 2

x^2 = (6Q + 2)*(6Q + 2) = 36Q^2 + 24Q + 4

Note here that the first and the second terms are divisible by 6. The remainder when you divide this by 6 will be 4.

We hope you understand how to deal with these various cases of remainders. Let’s take a look at a GMAT sample question now:

*If z is a positive integer and r is the remainder when z^2 + 2z + 4 is divided by 8, what is the value of r?*

*Statement 1: When (z−3)^2 is divided by 8, the remainder is 4.*

*Statement 2: When 2z is divided by 8, the remainder is 2.*

This is not our typical, “When z is divided by 8, r is the remainder” type of question. Instead, we are given a quadratic equation in the form of z that, when divided by 8, gives us a remainder of r. We need to find r. This question might feel complicated, but look at the statements – at least one of them gives us data on a quadratic! Looks promising!

*Statement 1: When (z−3)^2 is divided by 8, the remainder is 4*

(z – 3)^2 = z^2 – 6z + 9

We know that when z^2 – 6z + 9 is divided by 8, the remainder is 4. So no matter what z is, z^2 – 6z + 9 + 8z, when divided by 8, will *only* give us a remainder of 4 (8z is a multiple of 8, so will give remainder 0).

z^2 – 6z + 9 + 8z = z^2 + 2z + 9

z^2 + 2z + 9 when divided by 8, gives remainder 4. This means z^2 + 2z + 5 is divisible by 8 and would give remainder 0, further implying that z^2 + 2z + 4 would be 1 less than a multiple of 8, and hence, would give us a remainder of 7 when divided by 8. This statement alone is sufficient.

Let’s look at the second statement:

*Statement 2: When 2z is divided by 8, the remainder is 2*

2z = 8a + 2

z = 4a + 1

z^2 = (4a + 1)^2 = 16a^2 + 8a + 1

When z^2 is divided by 8, the remainder is 1. When 2z is divided by 8, the remainder is 2. So when z^2 + 2z is divided by 8 the remainder will be 1+2 = 3.

When z^2 + 2z + 4 is divided by 8, remainder will be 3 + 4 = 7. This statement alone is also sufficient. Because both statements alone are sufficient, our answer is D.

*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!*

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

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]]>The post Using Parallel Lines and Transversals to Your Advantage on the GMAT appeared first on Veritas Prep Blog.

]]>**The ratios of the intercepts of two transversals on parallel lines is the same.**

Consider the diagram below:

Here, we can see that:

- “a” is the intercept of the first transversal between L1 and L2.
- “b” is the intercept of the first transversal between L2 and L3.
- “c” is the intercept of the second transversal between L1 and L2.
- “d” is the intercept of the second transversal between L2 and L3.

Therefore, the ratios of a/b = c/d. Let’s see how knowing this property could be useful to us on a GMAT question. Take a look at the following example problem:

*In triangle ABC below, D is the mid-point of BC and E is the mid-point of AD. BF passes through E. What is the ratio of AF:FC ?*

*(A) 1:1*

* (B) 1:2*

* (C) 1:3*

* (D) 2:3*

* (E) 3:4*

Here, the given triangle is neither a right triangle, nor is it an equilateral triangle. We don’t really know many properties of such triangles, so that will probably not help us. We do know, however, that AD is the median and E is its mid-point, but again, we don’t know any properties of mid-points of medians.

Instead, we need to think outside the box – parallel lines will come to our rescue. Let’s draw lines parallel to BF passing through the points A, D, and C, as shown in the diagram below:

Now we have four lines parallel to each other and two transversals, AD and AC, passing through them.

Consider the three parallel lines, “line passing through A”, “BF”, and “line passing through D”. The ratio of the intercepts of the two transversals on them will be the same.

AE/ED = AF/FP

We know that AE = ED since E is the mid point of AD. Hence, AE/ED = 1/1. This means we can say:

AE/ED = 1/1 = AF/FP

AF = FP

Now consider these three parallel lines: “BF”, “line passing through D”, and “line passing through C”. The ratio of the intercepts of the two transversals on them will also be the same.

BD/DC = FP/PC

We know that BD = DC since D is the mid point of BC. Hence, BD/DC = 1/1. This means we can also say:

BD/DC = 1/1 = FP/PC

FP = PC

From these two calculations, we will get AF = FP = PC, and hence, AF:FC = 1:(1+1) = 1:2.

Therefore, the answer is B. We hope you see that Geometry questions on the GMAT can be easily resolved once we bring in parallel lines.

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