• Courses:
  • GRE
  • GMAT
  • SAT
  • ACT
  • PSAT
  • Sign in
    • GRE
    • GMAT
    • SAT
    • ACT
    • PSAT
  • Register
    • GRE
    • GMAT
    • SAT
    • ACT
    • PSAT

Barron's TestPrep Blog

Latest articles, news, discussions, etc. Subscribe to blog feeds.

  • All Posts
  • ACT
    • Math
    • Reading
    • English
    • Science
    • Writing
  • GMAT
    • Quant
    • Verbal
  • GRE
    • Quant
    • Verbal
  • SAT
    • Math
    • Reading
    • Writing

Invisible Gorillas: Prime Factors

Posted on May 20, 2013 by Bryce

In the last few blog posts we’ve explored “Invisible Gorillas”. As mentioned in the original post, Invisible Gorillas are patterns that recur on standardized tests that you can easily miss if you’re not looking for them. However, they’re simple to spot if you’re on the lookout for where they might show themselves.

 

I am not old. Granted, I didn’t get my first cell phone until I was in college. And yes, the first music I ever bought was on cassette tape. And sure, Google didn’t exist when I was born, but still. I am not being old. So why didn’t my teachers cover prime factorization when I was in school?

 

It’s not like the concept of prime factors is anything new. I would give you some historical evidence of this, but this newfangled Google thing gives me some trouble sometimes. But still, why wasn’t prime factorization more prevalent in schools when I was growing up?

 

For those of you as old as I am (or at least as disadvantaged as I was in not getting this information in school) prime factorization says that we can break any number down to smaller pieces—it’s prime bits—and make it easier to handle. We do that by first taking any factor pair and then seeing whether the factors are prime, or whether they are non-prime, in which case we repeat the process until we have all primes. Take the following example:

 

 

Our analysis shows us that 84=2*2*3*7. This in itself seems pretty simple, but making things simple is often the major step that you need to take in order to solve what looks like a complex problem. Take the following for example:

 

 is a factor of 540. What is the greatest possible value of x+y?

 

Although the form makes this look daunting, it’s simply an exercise in prime factoring. Watch what happens when we re-write the information in that form:

 

 

So, 540= 2*2*3*3*3*5. All that’s left to do is re-write that in a form that more closely resembles the form in which the problem was given.

 

 

Once the number has been broken into its prime factors, it’s plain to see that we can only squeeze two twos and three threes out of this number. There’s no different way we could break it down to get more twos or threes. Prime factoring figures out how many pieces of each type we have and allows us to re-assemble them in any way we see fit. So the greatest possible x is 2 and the greatest possible y is 3. Thus, 2+3 is equal to our answer of five.

 

Whether you’re old or young or somewhere in between, jump on board with prime factorization because taking numbers and breaking them into their component prime parts is a great way to solve problems and a recurring pattern on your test that you’ll be sure to recognize if you look for it!

  • Read more
  • Leave a comment

Why Anchoring (Predicting an Answer) is Important

Posted on May 17, 2013 by Kevin

 

I recently read an article in The New York Times, “Sometimes We Want Prices to Fool Us,” about how J.C. Penny’s ex-CEO Ron Johnson who tried to simplify pricing and improve business at the stores. It made it worse, though. But the failure might have been due to human psychology, not a management style.

Johnson wanted to always keep prices low and eliminate coupons and mailings. But profits fell over the course of 17 months and Johnson was let go. But that is not why I wanted to share this with all of you preparing for a test. The article brought up and interesting point about consumers and the idea of “anchoring.”

The importance of anchoring for consumers seems to parallel the importance of predicting for test takers. Here is an excerpt:

“Just having a generically fair or low price, as Penney did, said Alexander Chernev, a marketing professor at the Kellogg School of Management at Northwestern University, assumes that consumers have some context for how much items should cost. But they don’t.

“‘J. C. Penney might say it’s a fair price, but why should consumers trust J. C. Penney?’ he asked. ‘At the end of the day, people don’t want a fair price. They want a great deal.’

“Consumers infer that they get a great deal based on the reference point provided by the higher, presale price. Social scientists refer to this idea as anchoring, and it applies to all sorts of consumer behavior and expectations. Without that anchor, consumers have trouble determining whether the store is actually giving them a good price.”

This passage could easily apply to you, the test taker. With a couple changes, this is justification and evidence for predicting—a crucial and necessary way to identify wrong answers and increase your chances on each question:

“Just having answer choices, as standardized tests do, assumes that test takers have some context for knowing how correct an answer is. But they don’t.

“‘Test makers might say it’s a fair choice of answers, but why would test takers trust test makers?’

“Test takers infer that they have a great answer choice based on the reference point provide by their prediction. Social scientists refer to this idea as predicting, and it applies to all sorts of test taking behavior and expectations. Without that prediction, test takers have trouble determining whether the test is actually giving them a good answer choice.”

The key here is establishing a point of reference for each question. You need to establish the context for the question and infer what the answer will “smell” like and “taste” like, that is, deciding what kind of words will be in the answer choice: Will the words be positive or negative? Or should they be neutral? Should it be information found directly in the passage or in the sentence? Or is it information that should be supported by some idea? How big is the number going to find? Is it a positive or negative number?

These types of questions establish a foundation that you anchor to when wading into the answer choices. Without being tethered to something firm, you will easily be swept away by attractive wrong answer traps. And trust me. They will be attractive. The test makers are really good at making them attractive.

So, before you look at the answer choices, take a moment to predict what the answer will look like and smell like. Then you are ready to eliminate wrong answers and find the one correct answer.

  • Read more
  • Leave a comment

Invisible Gorillas: Answer Choices in Different Forms

Posted on May 16, 2013 by Bryce

In the last few blog posts we’ve explored “Invisible Gorillas”. As mentioned in the original post, Invisible Gorillas are patterns that recur on standardized tests that you can easily miss if you’re not looking for them. However, they’re simple to spot if you’re on the lookout for where they might show themselves.

 

Today we’re looking at the form of the answer choices. It’s a frustrating experience to feel that you’ve done every step correctly in a math problem and to reach the end only to realize that your choice isn’t there. Self-doubt can quickly creep in leading to thoughts of “Where did I mess up?”, “Do I need to start over?” or “Whyyyyy is this test sooo harrrrrrrd?”

 

Avoid the whininess of that last question and realize that having the value you reached at the end of your work not line up with the values in the answer choices is a common experience, and it doesn’t mean that you did anything wrong. Often by slightly transforming the answer choices the testmaker can take a simple question and make it one capable of separating the unprepared student and the test-taking superstar (that’s about to be you!).

 

Here are three common transformations that you’re likely to see.

 

  1. The answer is a combination of variables- Perhaps there’s a fact pattern that’s set up to have you solve for x. After going through all the math you’re confident that you’ve correctly solved for x, but you don’t see the value that you got. Double check to make sure that the question doesn’t ask for some form of x, such as 2x or x+y. It’s hard to get the right answer when you’re answering the wrong question!

 

  1. The answer is a reduced fraction- This is perhaps the simplest one on the list, but the correct answer to the problem will be the fraction reduced to it’s simplest form. If your answer is 18/51 and you don’t see that in the choices, don’t worry. The testmaker’s version—6/17—is likely just a reduced form of the fraction that you didn’t initially see.

 

  1. Your answer has a radical at the bottom of a fraction- For some reason many students fail to see that the following is true:

 

 

If you’re left with a square root in the denominator of a fraction, simply multiply both the top and bottom of your fraction by the same square root in order to simplify. Remember, that by the definition of a square root when you have this:

 

 

You can re-write it as:

 

And cancelling will leave you with:

For example:

 

 

Keep these examples in mind as you practice and you’ll realize that some of those times when you start to worry that you’ve gotten the wrong answer are just situations where you haven’t recognized your correct answer in another form!

  • Read more
  • Leave a comment

Using Hyphens

Posted on May 15, 2013 by Kevin

 

 

The hyphen is for punctuating words, either for joining or separating them. Hyphens form compound words, connect prefixes to words, or create linked adjectives. Using hyphens to separate words is only necessary when formatting justified text for readability. So we’ll only look at hyphens as linkers.

Unlike the rules for using periods, the rules for hyphens are fluid. As such, most recommendations are based on what produces a readable sentence. Different style guides will recommend similar and different ways to use the hyphen, so the best way to know whether a word needs a hyphen is to consult an up‐to‐date dictionary (differences exist among British, Australian, and American dictionaries).

But sometimes the dictionary won’t provide the answer you need. For example, ‘up‐to‐date’ is in the New Oxford American Dictionary. But the unhyphenated form—‘up to date’—is also listed. So, how do you know which to use? How did I know to use the hyphenated form in the previous paragraph?

Test for Hyphen Usage

  1. If you can’t reverse the order, use a hyphen.
  2. If you can’t remove one of the words, use a hyphen.

‘Up‐to‐date’ met both of these criteria. It would sound strange, or can mean something else entirely, if a word were removed, e.g. ‘up to dictionary’ or ‘up date dictionary.’ Also changing the order of the words (to‐date‐up) causes a readability problem. Ergo, hyphenate ‘up‐to‐date.’

 

COMMON WAYS TO USE A HYPHEN

I. Use to join words that together are a single unit of meaning

This is the most common way to use a hyphen. When a group of words modifies a noun, link them together with hyphens. The test above applies to this usage.

“ultra-modern sofa”

“love-sick dog”

 

II. Suspended Hyphens

When more than one item modifies a noun, and you want to be concise, suspended hyphens save the day.

“nineteenth‐ and twentieth‐century political movements”

“single‐ or multiple‐blank sentences”

 

III. With compound Object-Verbal Noun

Sometimes an object and a verb need to be linked with a hyphen to avoid misreading and confusion:

“man eating shark”

means that a person is consuming a shark. Whereas:

“man-eating shark”

means that a shark likes the taste of human flesh.

 

IV. Use with some prefixes and suffix

More often than not, use a hyphen with the following prefixes and suffix: all-, ex-, self-, half-, quasi-, or -elect.

“the president-elect”

“quasi-real”

“all-powerful”

 

V. Use when a prefix is attached to a proper noun

When you place a prefix on a proper noun, it is best to use a hyphen. Again, this ensures that no one misreads what you have written.

“pre-Google”

“post-Facebook”

“anti-Wal Mart”

 

VI. Use with fractions and compound numbers

Maybe the second-most popular usage, numbers and fractions need a hyphen.

“twenty-nine years old”

“two-thirds of ice cream cones”

 

  • Read more
  • Leave a comment
← Older posts
Newer posts →

Connect with us

  • fans
  • followers
  • 42 subscribers
Subscribe to Barron's Test Prep Newsletter

Popular Tags

Tags

ACT ACT Question of the Day ACT Sentence Correction Argument Analysis Essay Challenge Problem Circles comma ebooks Geometry GMAT GMAT Essay GMAT Question of the Day GMAT Questions of the Day GMAT Sentence Correction grammar grammar tuesday GRE GRE ebooks GRE Essay GRE Issue Essay GRE Question of the Day GRE Verbal independent clause Invisible Gorillas learning vocabulary Math Probability punctuation Quantitative Comparison Question of the Day quotation marks quotes SAT SAT essay SAT Identifying Sentence Errors SAT Improving Sentences SAT Question of the Day semicolon Sentence Completion Sentence Completions Sentence Equivalence Sentence Equivalence Questions Vocabulary Weekend funnies Word of the Week

Dig our articles

  • Popular
  • New
  • Comments

Invisible Gorillas: Prime Factors

Posted on May 20, 2013 by Bryce

Why Anchoring (Predicting an Answer) is Important

Posted on May 17, 2013 by Kevin

Invisible Gorillas: Answer Choices in Different Forms

Posted on May 16, 2013 by Bryce

Using Hyphens

Posted on May 15, 2013 by Kevin

New

  • May 2013
  • April 2013
  • March 2013
  • February 2013
  • January 2013
  • December 2012
  • November 2012
  • October 2012
  • September 2012
  • August 2012
  • July 2012
  • June 2012
  • May 2012
  • April 2012
  • March 2012
  • February 2012
  • January 2012
  • December 2011
  • November 2011
  • October 2011
  • September 2011
  • August 2011
  • Recent Comments

    • agen pulsa murah on Invisible Gorillas: Difference of Squares
    • Bryce on Invisible Gorillas: Difference of Squares
    • Sean Stephenson on Single or Double Quotation Marks?
    • Borse Louis Vuitton Outlet Roma on Forget a formula? Just derive it!
    • Frank on Comma Usage: Administrative Tasks

    GRE

    • Course Tour
    • Technology
    • Practice
    • Lessons
    • Solution Videos
    • Resources
    • Compare
    • Blog
    • Pricing

    GMAT

    • Course Tour
    • Technology
    • Practice
    • Lessons
    • Solution Videos
    • Resources
    • Blog
    • Pricing

    SAT

    • Course Features
    • Why Barron's
    • FAQ's
    • Test Dates
    • Pricing

    ACT

    • Course Features
    • Why Barron's
    • FAQ's
    • Test Dates
    • Subscribe

    PSAT

    • Course Features
    • Why Barron's
    • FAQ's
    • Test Dates
    • Subscribe

    School and Library Licenses

    Connect with Barron's Prep

    • Home
    • |
    • About us
    • |
    • Why Barron's
    • |
    • Blog
    • |
    • Support
    • |
    • Contact us
    • |
    • Privacy Policy
    • |
    • User Agreement
    • |
    • Sitemap

    Copyright © 2012 Barrons Educational Series Inc.

    All rights reserved.

     

    250 Wireless Blvd, Hauppauge, NY 11788, USA.

    Phone: 1-800-645-3476 | (631) 434-3311


    • Visit out NY Regents Review site at
      www.BarronsRegents.com

    • Visit out book site at
      www.BarronsEduc.com

    • Technology for this site is
      provided by Snapwiz Inc.