Extra Hard SAT Math Question – Combinations

Surely, with all those fencing lesson they didn't have time for math...
Surely, with all those fencing lesson they didn’t have time for math…

At the end of every SAT Math section, the test makers try to come up with an extremely difficult problem that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game. Continue reading “Extra Hard SAT Math Question – Combinations” »

What to Expect on the Revised SAT: Reading

Feel like you have to translate SAT passages? We can help!
Feel like you have to translate SAT passages? We can help!

The Revised SAT Evidence-Based Reading (that’s a mouthful) will include five(ish) passages: one Literature based passage, two History/Social Studies passages, and two Science passages. Similar to some passages on the current SAT, one of the passages in the Science and/or Social Studies fields may be replaced with a pairing of shorter, related passages, and both topics will include one or two related graphics that a few questions will refer back to. All in all, you’ll have 65 minutes to do fifty-two passage-based questions and ZERO sentence completion problems. There will still be vocabulary-based questions in the passages, but they’ll focus more on your ability to define a word in the context of the passage. Additionally, a new type of question will test your command of evidence. Continue reading “What to Expect on the Revised SAT: Reading” »

The SAT Shape-Shifts Again!

We can help with your questions about the SAT's new mutations!
We can help with your questions about the SAT’s new mutations!

OK, since the revision of the SAT is a pretty major topic in college admissions right now, I probably didn’t have to use a crazy title to get you to read about the New SAT, but how else was I going to fit Mystique into a blog post?

YES! If you hadn’t heard, the SAT is changing March of 2016. We know what you’re thinking, Class of ’17: “Why me? WHY NOW?!” But don’t get too stressed out! You might even like some of the changes they’re making. For instance, you’ll no longer be penalized for wrong answers, and they’re doing away with that pesky sentence completion. And never fear! We here at Test Masters are here to help guide you through the transition! In this post, we’ll get our feet wet with some of the overall format changes. Continue reading “The SAT Shape-Shifts Again!” »

ISEE Exam Reading Passage Example

Heinrich Zille kleiner Junge
“Little Boy” by Heinrich Zille (1858-1929). Courtesy of Wikimedia Commons.

The following passage is based on comparable Critical Reading passages found on the Independent School Entrance Exam (ISEE). The ISEE is used nationally for admission to private high schools. This passage was prepared by a Test Masters critical reading instructor for the purpose of familiarizing ISEE parents and students with the type of material they can expect to see on test day.

Continue reading “ISEE Exam Reading Passage Example” »

College Admissions Essay “Do”s and “Don’t”s

We're here to help tips and tricks throughout the college admissions process!
Learn more valuable admissions tips and tricks!

I can still remember sitting down at the computer the weekend before college apps were due to write my admissions essay. I had sufficiently procrastinated to the point where my parents might actually take disciplinary action if I didn’t write my essays. I sat down, scrolled through the Common App, and hoped one of the prompts would read, “Tell a moderately humorous story about something that happened during your charmed, suburban childhood,” but no such luck. All the questions about “a time when you struggled” or “when you experienced a major failure” made me feel like I lacked depth. As I ruminated on the “write about whatever you want” prompt, Dr. Seuss suddenly popped into my head; hours later, I had 650 words about how The Sneetches had taught me a valuable lesson about tolerance. It wasn’t a bad essay, but, given the schools I was applying to, it could have been better.

Continue reading “College Admissions Essay “Do”s and “Don’t”s” »

Ask Test Masters: International Student Applying to the Ivy League

Ask-Test-Masters
Have a question? Ask the college admission experts at Test Masters!

Ask Test Masters is a free educational service offered by the college admission experts at Test Masters. College Compass readers Arman and Mandy have a question about applying to competitive US schools as an international student. They write,

“We are from Sydney Australia and my goal/dream is for my son to be accepted to a very good US university, preferably with a bit of scholarship if possible. My son is 16 turning 17 in October, and currently in Year 10 and will start Year 11 in Term 4. He will graduate in Year 12 in 2015 and we are hoping to go to university in the US in August 2016. He goes to a Government Selective School and is currently their number 1 player in Division 1 Tennis. I need some guidance, please, on how do I go about it for him to have a better chance? Thank you in advance.” Continue reading “Ask Test Masters: International Student Applying to the Ivy League” »

Improve Your SAT Score – Multiple Choice Writing

GrammarMany students struggle with the SAT Multiple Choice Writing section, which is surprising given how coachable this section of the exam really is. The SAT Multiple Choice Writing section is nothing more than a basic test of your English grammar comprehension. In an effort to elucidate this theory, we have compiled a list of 14 example problems that highlight some of the more common grammatical mistakes students are expected to recognize on test day. Join us over the next several weeks as we review these fourteen questions, one-by-one, to help you improve your SAT score. Continue reading “Improve Your SAT Score – Multiple Choice Writing” »

7th Grade Duke University Talent Identification Program

Duke TIPFounded in 1980, the Duke University Talent Identification Program, or Duke TIP, identifies and supports academically gifted elementary, middle, and high school students. Today we will focus specifically on the Duke Talent Identification Program for 7th graders. The purpose of Duke TIP is to “work with students, their families, and educators to identify, recognize, challenge, engage, and help students reach their highest potential.” This is accomplished, of course, by first identifying these students and then encouraging their development with academic resources and activities.

Continue reading “7th Grade Duke University Talent Identification Program” »

Extra Hard SAT Math Question – Mean Means

The human race will tremble before my unstoppable math problem!

At the end of every SAT Math section, the test makers try to come up with an extremely difficult problem that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following problem:

If the average (arithmetic mean) of four different positive integers is 5, then the least possible product of the four integers is:

A) 20

B) 84

C) 104

D) 480

E) 504

This one might seem like a hard nut to crack. After all, there are many possible sets of four distinct positive integers that have an average of 5. We could not possibly test them all one by one given the time constraints of the SAT. So how are we going to figure out which four integers are the ones that yield the smallest possible product?

Well, if we want the smallest product, then we want as many of the integers to be as small as possible. If the smallest of the three integers were equal to 1, then that would be great, since multiplying by one simply produces the same number and would thus not increase the product of the three numbers. Since the four integers must be distinct, we can make the second integer 2 so that it is also as small as possible, and by the same logic the third integer would be 3. All that remains is to determine the fourth integer, which we can find using algebra:

The fourth integer is 14, and the product is:

Logically, the answer must be 84, or choice B. If you are still feeling unsure, you could try a few other sets of four integers to see if their products are less than 84. What happens, for instance, when we increase the 3 to 4 and decrease the 14 to 13?

No, Magneto! We have to educate humanity, not destroy it!
No, Magneto! We have to educate humanity, not destroy it!

Already, the product begins to increase. Try any other set and you will see that its product is greater than 84. It doesn’t matter that we decreased 14 to 13, because what controls the outcome in this problem is how small we can make the smallest numbers in the set. Thus, our original reasoning was correct.

If you know what to do, it takes only about 30 seconds to solve this problem. So you see, with practice, even the hardest problems on the SAT become easy. Check back here each week for more extra hard problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until  then, keep up the good work and happy studying!