Let’s look at a GRE triangle question:

The first thing you want to do on a problem like this is ask yourself: What do I know? We know the lengths of sides AB, BD and BC.  We also know that angle BDC is a right (90^o) angle.

The next thing you should ask yourself is: What does the question ask me to find? The question above asks us to find the perimeter of triangle ABC.  The perimeter is the distance all the way around.

Finally, you should ask yourself: What do I need to know in order to answer the question? Before we can find the perimeter of triangle ABC, we need to find the missing length, AC. If we can’t find AC independently, we can determine the lengths of AD and DC and add those values together to find AC (this is the method we’ll use for this problem.)

Here is where it gets interesting—and easy. Trust me!

Since triangle BDC is a right triangle, we know that BDA is also a right triangle. (Remember the rule: two angles that form a straight line must add up to 180^o.)  When we have a right triangle and we know the length of any two sides, we can use the Pythagorean Theorem (a² + b² = c², where a and b are the two perpendicular sides and c is the hypotenuse, or longest side) to solve for the length of the missing side.

However, just because we can use the Pythagorean Theorem doesn’t mean we should. Really, who wants to deal with exponents and square roots if you don’t have to? If you know two magical ratios, you will seldom need the Pythagorean Theorem.

Often on GRE triangles, the lengths of the sides of a right triangle will occur in the ratio of 3:4:5 or 5:12:13. It’s important to remember that these ratios do not necessarily give the actual lengths of the sides—because the values are ratios, they represent the side lengths pared down to their simplest form. The actual lengths could be 6:8:10 or 10:24:26 or any other multiple of the basic ratios.

Now, when we look at triangle BDA, we see that we have a multiple of 5 for AB, the hypotenuse. That means we could have a 3:4:5 triangle. Dividing 30 by 5 gives a value of 6, which is going to be the number by which the entire ratio has been multiplied; 6 times 3:4:5 yields 18:24:30. Since 24 and 30 are accounted for, the length of AD must be 18. (If multiplying the ratio by 6 did not give 2 of the 3 lengths the test-maker provided, then we would have to use the Pythagorean Theorem, after all.)

Let’s do the same thing for triangle BDC. The hypotenuse, BC, measures 26, which is a multiple of 13 (13 x 2 = 26.) If we multiply the entire 5:12:13 ratio by 2, we get 10:24:26. Since 24 and 26 are accounted for, the length of DC must be 10. (Again, if multiplying the ratio by 2 did not give 2 of the 3 lengths the test-maker provided, then we would have to use the Pythagorean Theorem.)

If we add 18 and 10, we find that the length of AC is 28.

Now, we have enough information to answer the question: What is the perimeter of triangle ABC? The perimeter will be the length of AB + the length of BC + the length of AC. Adding up the actual numbers, we find that 30 + 26 + 28 = 84.

Be sure that the Pythagorean Theorem and these two classic ratios are in your GRE toolbox for Test Day!

The Kaplan New GRE Verbal Workbook includes a chapter devoted to Reading Comprehension, as well as sets of practice questions and additional resources. One of these resources is a list of additional tips for tackling the Reading Comprehension section, including Bolded Statements questions. These tips are found on pages 78-80, and I’m going to borrow from them here.

There are differences between real-world reading and reading GRE passages is that on the GRE:

• On Test Day, you don’t care about the facts in the passage — you only care about ideas. A passage might tell you that the character Superman first appeared in 1938. You don’t care what year Superman was introduced, but you care about WHY the author told you that. The passage may then go on to describe how the powers attributed to Superman have changed over time. In that case, knowing that Superman has been around for 70+ years might be important.
• Prior knowledge is not welcome on Test Day. Forget everything you might know about Superman — everything  you need to know will be contained within the passage. Wrong answer choices play on things that test-takers understand to be logically true, but if those facts aren’t mentioned in the passage, you don’t care.
• If a passage tells you Superman has a twin sister, then as far as you are concerned, he has a twin sister. The passage text is TRUE. Period. You may question texts as much as you like in real-world reading, but on the GRE, accept that whatever the passage is telling you is correct.

Bolded Statement questions should be tackled the same way as other Reading Comprehension question types. In these questions, you REALLY don’t care about the facts or details. You ONLY care about the purpose of the statements, and you consider each statement separately. Is it an opinion? An example? An argument? If it is an argument, is it the passage’s primary or secondary argument, or perhaps a counterargument? Is it evidence, and if so, of what? You care about the purpose of each statement in relation to the other sentences in the passage.

Let me repeat that. Just as with other question types, you must consider Bolded Statements in the context of the passage as a whole. Do not skip the un-bold statements; they are your context clues for figuring out the role the Bolded Statements play.

Have a question about grammar, punctuation, usage, or style? Email me at jennifer.land@kaplan.com and put “blog question” in your subject line. Then look for a response here!

But I’m not writing this to pat myself on the back or share yet another Kaplan success story. The most interesting feature of Becky’s email is that she didn’t even bother to mention her math score.

This isn’t because she did poorly, or because we didn’t work on the math section. As a matter of fact, Becky told me at our first tutoring session that she wanted to spend all 15 of her tutoring hours on math. She was an English major, so her confidence with the verbal section — and complementary fear of the math section — was hardly surprising. Well, we did spend the first session doing math, since that was what she wanted. I was skeptical, however, that English literature programs were all that interested in her math score.

“Do you know where you’re applying?” I asked her. She rattled off a list. “And have you contacted them to see what they want on the GRE?” Becky, it turned out, had no idea.

I smiled. “Great! That’s your first homework assignment,” I said. “Contact the programs you’re interested in and find out what they want on the math and verbal sections.” Becky did her homework that week, and that was how she discovered that none of her programs cared a rat’s butt about her math score. She also learned that what they did want was an extremely high verbal score — much higher than what she had scored on the diagnostic, even as an English major.

We proceeded to spend the entire remainder her tutoring package working on verbal.

Had we beaten down the math section as Becky initially wanted, the results would have been very hilarious but also very tragic. Since everyone takes the GRE, from French historians to theoretical physicists, there is no universal concept of a “good” performance — “good” varies drastically from program to program.

So now I ask you: have you contacted the schools you’re interested in? Do you know what they actually want you to get on the GRE?

If not, that’s your first homework assignment.

Don’t believe me? Ah, but you will.

Let’s consider a Quantitative Comparison problem that calls on our knowledge of circles. Many test-takers see circle problems and begin to hyperventilate, but you should not be one of those test-takers. Circles are often fantastically easy to work with once you learn a few tricks.

Of course, you will need to know the basic circle formulas such as area and circumference. However, another incredibly useful tool to add to your toolbox is the proportional relationship between the measures of a circle.

Let me share an example:

In this Quantitative Comparison problem, we are given the measure of the central angle O (45^o) and the length of arc XYZ (3). We are then asked to compare 6π to the circumference of the circle. At first glance, it may seem that we don’t have enough information to answer this question. After all, many of us have been taught that the radius is everything to a circle, and without it we can do nothing.

If the proportional relationship of circle measurements—the beautiful, and appropriately circular relationship that is true to all circles, everywhere—is in your toolbox, however, you can do this problem in under a minute.

Here is that relationship:

Arc length/circumference = central angle/360 degrees = area of sector/ area of circle

Notice how the three relationships are “anchored” by the relationship between the central angle and the full degree measure of the circle. If we know the fraction of the circle that the central angle represents, then we also know the fraction that the resulting arc length is of the circumference, and the fraction that the area of the sector (the “pie piece” of the circle determined by the central angle) is of the entire area of the circle.

Based on the information that we’re given for a particular circle question, we can use any two of the three proportions above to solve for a missing measurement. For example, to solve this particular problem, we can use these two proportions:

Arc length/circumference = central angle/360 degrees

When we plug in the values that we’re given for the central angle and arc length, we can solve for the circle’s circumference:

3/circumference = 45 degrees/ 360 degrees

Simplifying the second proportion, we get:

3/circumference = 1/8

Now we know that the arc length (3) is 1/8^th of the circle’s circumference (because the central angle is 1/8^th of the full degree measure of the circle). Continuing forward, we can cross-multiply to solve for the circumference of the circle:

3 x 8 = 1 (circumference)

24 = circumference

Let’s look back at the quantities we were asked to compare:

If we remember that π is slightly more than 3 (3.14159… to be more precise), then we can estimate that 6π is slightly more than 18, which is clearly less than 24. Thus, Quantity B is greater than Quantity A.

If the proportional relationship of circle measurements is not in your GRE toolbox, be sure to learn it (and practice using it often) before Test Day!

Since the new GRE launched in August, only score ranges have been available to test takers – and those ranges are based on the old 200-800 scoring scale.

Here’s how the new GRE scores will work:

• Starting November 8^th, new GRE test takers who took the exam in August and September will begin receiving their official scores on the new 130-170 scoring scale. Official scores will continue to roll out to test takers through November.
• The full score reporting schedule from ETS is available here, and breaks down as follows:

Here are the score concordance tables comparing old GRE scores and new GRE scores.  And here is the full breakdown of scaled scores to percentile scores on the new GRE.

Also – check out ETS’ new Excel tool where you can put in old or new GRE scores and calculate predicted GMAT scores. There’s also a Flash version. ETS continues to pursue business school admissions committees aggressively. 600+ business schools, included a majority of top programs now accept the GRE as an alternative to the GMAT.

Some observations on the new scores:

• The new scoring scales follow a normal distribution with 150 as the mean for both math and verbal. The old 200-800 GRE scores were really skewed as the mean drifted over time.
• On the old test, low verbal scaled scores matched with high percentile scores while high math scaled scores matched with low percentile scores. Before, ~620 on the math side and ~455 on the verbal side of the test were both 50^th%ile. ETS has realigned the scaled score-to-percent scores for the new GRE so that a 150 Quant and a 150 Verbal are the new 50^th percentile.
• An 800 on the quantitative section on the old GRE corresponds with a score of only 166 on the new test.  So, getting a perfect math score on the old test only puts you in the 94^th percentile on the new test. ETS has made the math content harder on the new GRE to allow for differentiation of high scoring candidates for quant-intensive programs like business school, engineering and the physical sciences.
• On the verbal side of the old GRE, you were already in the 99^th percentile with a 730.  With the new test and the new scores, 99^th percentile on the quant side is a 170, and on the verbal side a 169 or 170 puts you in the 99^th percentile.
• Getting just a couple more questions correct will lead to a big percentile increase on this test. A 155 is 69^th percentile on both the math and verbal sides of the new GRE; a 157 (getting another question or 2 correct) is 77^th percentile on both sides of the new GRE.

Our team will be attending a follow-up score interpretation session with ETS on November 15^th.  More information coming soon.  Please reach out us on Facebook or Twitter if you have questions about scoring on the new GRE.

There will be more to come in my next post relating to the order of operations, so let’s continue working with words as they relate to equations and expressions.  My last post delved into a specific word problem typically found on the GRE’s quantitative section, and we saw that some words are fairly routine in translation:  “sum” always means to add (+), “is” indicates an equal sign (=). But do you have the same automatic determination when faced with terms like “will be” (becomes “=”) or “per” (equates to “divided by”)?

The goal of practicing word problems is to create a proficient and accurate word-by-word translation of words into math operations and, in turn, the symbols that represent those operations.  If we gain the ability to make a literal translation of all of a given word problem’s expressions, then we have only to complete the calculations to arrive at the correct answer.

Let’s look at a few examples of word-for-word translating:

Anne is 7 years older than Bill was 5 years ago.

Typically, we use single letters to represent a person’s name:  Anne becomes A, Bill becomes B.  As we’ve already seen, “is” translates to “=” while “older than” signals addition.  Since the word “ago” refers to the past, we need to subtract that amount when relating our numbers back to the present, such that:

A= (B-5) +7

Too simple for you?  Let’s kick up the difficulty level:

If Mack’s salary (M) were to be increased by $5000 (+5000), then the combined salaries of Mack and Andrea (+A) would be equal (=) to 3 times (x3) what Mack’s salary would be if it were increased (+) by one-half of itself (1/2M).

Putting it all together, we arrive at:

M + 5000 + A = 3(M + 1/2M)

As you can see, the solution involves understanding the given scenario and then translating the information while carefully taking things one step at a time.  Come to think of it, that’s good advice for dealing with any of life’s challenges…

You were probably with me right up until the last two words of that sentence, right? “Prime factorization” is a highly unfortunate bit of math vocabulary, as it sounds really scary but is actually just a fancy phrase for “split apart the number until you can’t split it apart anymore.” Let’s use 75 as an example.

How can you split 75? Well, it has a 5 at the end, so it’s got to be divisible by 5. In fact, it’s 5 times 15. So:

75 = 5 * 15

5 is a prime number, so you can’t split that anymore. 15, however, is 5 * 3. Altogether, then:

75 = 5 * 5 * 3 = 5^2 * 3

That’s it — 5^2 * 3 is the “prime factorization” of 75. Not so scary. This extremely easy technique takes problems that look terrifying and makes them a snap. Here’s great example:

If 75^3 is a multiple of 5^m, what is the largest possible value of m?

A) 3

B) 4

C) 5

D) 6

E) 7

This is exactly the kind of problem that makes many GRE test-takers’ hearts freeze over — and possibly yours as well! But when you see it on Test Day, think: “Okay, there’s a really big number — 75 cubed. What should I do when I have big numbers? Prime factorization!”

We just found the prime factorization of 75 – it is 5^2 * 3 — so plug it into the problem in place of 75, and distribute the exponent of 3 to everything inside the parentheses:

75^3 = (5^2 * 3)^3 = 5^6 * 3^3

The question asks for the largest possible value of m in the expression 5^m. So m is a power of 5, and what power of 5 do we see in the problem? 6. Pick D and move on!

Recently a reader asked me to explain the appropriate uses of two relative pronouns: in which and when.  (I am adding where to the mix, as well, because it has some of the same issues as when.)

A relative pronoun is one that introduces a subordinate clause.  As with all pronouns, the relationship to the antecedent must be clear. This isn’t usually a problem; the tricky thing about these relatives is determining appropriateness.

The basic rule of thumb for written English is that you should NOT use when or where unless you are referring to a time or a place, respectively. Consider the following fragments:

• The shop where we ordered the invitations…
• The season when trees are bare…
• The episode in which Peter was cast as Benedict Arnold…

Because an episode of a television series is neither a place nor a time, it is not appropriate to use where or when. An episode is a setting in which something is portrayed. Other examples are as follows:

• Situations in which one party is at fault…
• Opportunities for which one is improperly dressed…
• Books in which there is an unnamed narrator…
• Theaters where Macbeth is performed… [in which would be OK here as well]
• Evenings when Macbeth is performed… [on which or during which could be OK here]

Sometimes either construction would work. In the Macbeth examples above, where or when are appropriate because they refer to a specific location or time; using a preposition with which would work, too, but most writers prefer the simple, concise where or when whenever permissible.

Keep in mind that the rules are not as stringent for informal spoken English. Peppering your conversations with “in which” would probably sound strange to your friends. The creators of the television series Friends noted this, and they named the episodes the way viewers would casually describe them: “The One Where They’re Going to a Party.”

Unless you are naming something as creative and hugely popular as episodes of Friends, stick to the formal and appropriate constructions when writing. GRE essay graders don’t award points for humor or creativity, but they do reward correct usage. Graduate and professional programs do, too!

Have a question about grammar, punctuation, usage, or style? Email me at jennifer.land@kaplan.com and put “blog question” in your subject line. Then look for a response here!

Let’s examine the following Quantitative Comparison question:

Dave is x years old and Phyllis is y years

older than Dave, where x>y>0.

Column A                                                                                                Column B

The sum of Phyllis’s                                                                                     3x

age and Dave’s age

As always with Quantitative Comparisons, the answer choices never change.  They are:

A – The quantity in Column A is larger than the quantity in Column B

B – The quantity in Column B is larger than the quantity in Column A

C – The quantities in Column A and Column B are equal

D – The relationship between the quantities in Column A and Column B cannot be determined

First, walk through a translation of the centered information step by step. Dave’s age is x years and Phyllis’s age is y years older than Dave, or x+y years.  Next, let’s look at Column A. The sum (adding them together) of their ages is x+x+y, or 2x+y years.  Now, subtract the 2x from both columns and we are left with a y remaining in Column A and an x remaining in Column B.  The centered information tells us that x>y, so Column B is greater.

Translation is many times the slippery part of an algebra problem.  Practice will make you better – using Kaplan methods will help you determine when you should bother with calculations or whether there is an easier route to finding the correct answer choice.

Next time, I will discuss some more convoluted wording found within GRE word problems…

“Expectations” may seem like a topic of meaningless corporate fluff-talk. But they matter. Equally intelligent, equally dedicated students can succeed wildly or fail horribly, all depending on the expectations they set. The story about appeasing customers may seem completely irrelevant to the GRE, but it’s actually completely analogous. In test prep, you are your own customer.

It’s October now. Let’s say that at the rate you’re studying for the GRE, you’ll be able to get your dream score in February. If you tell yourself you want to master the GRE by March, you’d be thrilled to achieve your goal score in February. If you tell yourself you want to master the GRE by January, you’ll be panicking and self-destructive if you haven’t hit the mark by then. It’s the same as the customer story, only the scale is in months, not days. Since you’re both the employee and the customer, bad expectations can actually cause the project to fail. Students who set arbitrary, pointless deadlines for their own success begin to self-destruct upon seeing that those deadlines won’t be met, and to what end?

When you hold your graduate degree in your hands several years from now, will it make any difference whether you mastered some concepts in January or in March? Will it make any difference at all? Sure, it would be nice to finish the GRE sooner, but your top priority is to get a good score, not to get the GRE over with. Focus on what actually counts.

This all seems perfectly obvious on paper, but it’s not how people actually behave. All the time I hear, “I should already know this,” and my heart breaks because I can hear the anger, worry, and frustration welling up in my student’s voice. “I should already know this.” No, you shouldn’t! You should know it by Test Day. Get your expectations right, and you’ll have an infinitely happier test prep experience.