Trial

SAT Math: Data Analysis

Average (arithmetic mean)

Each of four people were given a blank piece of paper on which they wrote a positive integer.  If the average (arithmetic mean) of these integers is 21, then what is the greatest possible integer that could be written on one of the pieces of paper?

Knowsys Method

Note: In the math section of the SAT, you will encounter questions that do not have answer choices.  Instead of bubbling in a letter, you will bubble in your answer.  These questions are called grid in questions, and you should always guess an answer for them because there is no penalty for getting the question wrong!

Read the problem carefully.  Make sure you understand the situation described in the question and take note of important details.  The integers written on the pieces of paper are positive, and they are NOT distinct (different), so there could be repeats of the same number. 

Identify the bottom line.  Greatest possible integer (out of these 4) = ?

Assess your options.  There is only one possible method for solving this problem, and it is demonstrated below.

Attack the problem.  Whenever a problem asks about average (arithmetic mean), the first thing you should do is write out the average formula.

Screen Shot 2014-01-07 at 9.40.00 AM.jpg

Now, plug in the information you know from the problem.  You were given the average and the number of people.

Screen Shot 2014-01-07 at 9.42.49 AM.jpg

Multiply both sides by 4 to find the sum, which is 84.  Now, think about it.  The four integers written on the pieces of paper all add up to 84.  What is the greatest possible number that could be included among those four?  Figure out how to make the other three integers as small as possible to leave the greatest possible number left over.  The integers must be positive, so each one must be at least 1.  Three of them can be 1 because they do not have to be distinct.  So, subtract 3 from 84 and get 81. 

Loop back.  Check to verify that you have solved for the bottom line.

The correct answer is 81.

This is a medium level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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SAT Writing: Identifying Sentence Errors

Identifying Sentence Errors

Read the sentence and select the portion of the sentence that contains an error.  If there is no error, select E.

Screen Shot 2014-01-06 at 4.29.30 PM.jpg

Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion(s) against the Big 8 grammar concepts.

A.  When you see a verb underlined, check to see whether it agrees with its subject and whether it is in the correct tense.  The verb "began" agrees with "competition," and it matches up with the past tense in the sentence.  This is not the error.

B.  There are many pronoun rules that are tested on the SAT, but only one applies to "I."  When you see "I" underlined in an SAT grammar question, check to see whether that pronoun should be in the objective case or subjective case.  If the pronoun follows a preposition (about, between, by, down, etc.), that pronoun should be objective (me, you, us, him/her, them).  If the pronoun follows a "being" verb like am, is, are was, etc., that pronoun should be subjective (I, you, we, he/she, they).  In this case, the pronoun follows the preposition "between," so it should be in objective case ("between my brother and me").  We have found an error, but let's review the rest of the choices to be sure.

C.  Check to make sure that this verb agrees with its subject and the tense of the sentence.  The verb "suggested" agrees with the noun "mother," and it matches up with the past tense of the sentence.  This is not an error.

D.  When you see a pronoun like who, whom, whoever, or whomever underlined, check to see whether the pronoun should be in objective case (whom, whomever) or subjective case (who, whoever).  Use objective case after a preposition, and use subjective case before a verb.  A good rule of thumb is to use "who" when you can substitute "he" and "whom" when you can substitute "him."  In this choice, we need to take that rule one step further because the pronoun applies to more than one person.  Split up the statement into two parts, like so:  "Give twenty dollars to him.  He collected the most seashells."  After you have done that, follow this rule: him + he = whoever; him + him = whomever.  In this case, whoever is correct.  This is not an error.

E.  We already found an error, so E is not correct.

The correct answer is B.

This is a medium level problem.

For more information about who/whom, click here.

For more information about whoever/whomever, click here.

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SAT Reading: Sentence Completions

Sentence Completions

Select the word(s) that best fit the meaning of the sentence as a whole.

The salesman offered the woman a lower interest rate to ------- her to purchase the car, but the woman remained -------, waffling over whether she could commit to such a large purchase without talking to her family first.

A. extol . . vicarious
B. incline . . ineffable
C. induce . . irresolute
D. discern . . prolific
E. baffle . . dubious

Knowsys Method

Start by covering up the answer choices so that they do not distract or bias you.  Then read the sentence and use context clues to determine what the answer should be.  In two-blank sentence completions, start with the easier blank first.  In this case, the second blank is easier because you have more contextual clues to use.  If this woman is waffling (unable to make a decision), then you would describe her as "uncertain."  Using that as our prediction, we will look at all of the second blanks first. 

A. "Vicarious" comes from the Latin "'vicarius," which means "substitute."  The word "vicarious" is used today to indicate that you are experiencing something through someone else.  For instance, if your friend is going on a tour of Europe, you might ask him or her to take lots of pictures so that you can experience the trip vicariously.  This word does not match our prediction, so eliminate this choice.


B. "Ineffable" comes from the Latin "ineffabilis," which means "unutterable."  Something "ineffable" is impossible to put into words.  This word does not match our prediction, so eliminate this choice.   


C. Did you make any New Year's resolutions this year?  If so, you are probably "resolute" about achieving them.  "Resolute" means "determined or certain," so "irresolute" means the opposite, "uncertain."  This choice matches our prediction, so keep it for now.


D. “Prolific” comes from the Latin word for “offspring,” and it means “fertile or highly productive.”  Think PROlific = PROductive.  This choice does not match our prediction, so eliminate it.


E. "Dubious" is easy to remember because it sounds like what it means.  If you are feeling "dubious," then you are feeling doubtful.  If something is "dubious," then it is suspicious and not to be trusted.  This choice matches our prediction fairly well, so keep it for now. 

Now look back at the sentence and predict what should belong in the first blank.  A salesman would want his customer to make a purchase, so he is probably offering the lower interest rate to persuade the customer.  Using "persuade" as our prediction, let's look at the choices we have not yet eliminated.

C. "Induce" comes from the Latin "inducere," which means "lead in or persuade."  "Induce" means much the same thing today; it means "to persuade, influence, or cause."  This choice matches our prediction, so C is most likely the correct answer, but we need to check E to be sure.

E. To "baffle" is "to confuse or to frustrate."  This is the opposite of what the salesman in the question would want to do, so eliminate this choice. 

The correct answer is C.


Words used in this SC:

extol: to praise highly
vicarious: learned, understood, or realized through second-hand experience
incline: 1) to persuade, or 2) to bow or bend
ineffable: indescribable or unspeakable
induce: to persuade, influence, or cause
irresolute: uncertain
discern: 1) to understand,2) to see, or 3) to recognize as different
prolific: fertile or highly productive
baffle: to confuse or to frustrate
dubious: doubtful or uncertain

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SAT Math: Geometry

Coordinate Geometry

In the xy-coordinate plane, line m is parallel to the x axis and passes through the point      (4, -7).  Which of the following is an equation for line m?

A. x = -4
B. x = -3
C. y = -7
D. y + 7 = x - 4
E.  y – 7 = x + 4

Knowsys Method

Read the problem carefully.  Take careful note that the line in the question is parallel to the x axis.  

Identify the bottom line.  equation for line m = ?

Assess your options.  We must solve this problem by plugging the line into the point-slope formula.  The point slope formula is:

Screen Shot 2014-01-03 at 4.28.28 PM.jpg

Attack the problem.  We need to use the point-slope formula, but to do so, we must determine the slope (m) and the y-intercept (b).  It makes it a little easier to explain this problem if we draw out the line on the coordinate grid, but you do not have to do this step.  

Screen Shot 2014-01-03 at 4.23.46 PM.jpg

As the illustration shows, line m is parallel to the x axis, which makes it is a completely horizontal line.  A horizontal line has a slope of 0.  Think about it: if the y value never changes, then the change in y is zero, and no matter what the change in x, 0 divided by anything is 0.  Since you know that the y value never changes, you also know the y-intercept will be (0,-7).  Plug these values into the point-slope formula.

y = mx + b
y = (0)x -7
y = -7

Loop back.  Verify that you solved for the bottom line.

The correct answer is C.
This is a medium level problem.

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Link of the Week: Technological Progress

Why do we talk about technology so often in our links of the week?  Because technology is such a popular topic for SAT prompts. 

Consider these prompts that have appeared within the past few years:   

     Does a strong commitment to technological progress cause a society to neglect other    
     values, such as education and the protection of the environment?
     Are there benefits to be gained from avoiding the use of modern technology, even when
     using it would make life easier?
     Is the most important purpose of technology today different from what it was in the
     past?
     Have modern advancements truly improved the quality of people's lives?

Because technology is integrated into most aspects of our lives, you probably have ample personal experience to draw upon in discussing the role of technology in society.  But then again, so does pretty much every other student, and if you merely write about tablets, smartphones, apps, etc., your essay probably will not stand out from the crowd.  What will make your essay shine is if you find ways to apply scholarly examples to the issue of modern technology.  

Isaac Asimov, one of the best known science fiction writers of all time, considered both the promise and the potential dangers of technological advancement in his works.  This week, his article “Visit to the World’s Fair of 2014,” published in The New York Times in 1964, has appeared in the news as journalists consider whether his predictions from 50 years ago ring true today.  Check out this article, which links to Asimov’s original work and discusses some of the eerily accurate forecasts he makes therein.  Judge for yourself whether life in 2014 comparable to Asimov’s vision, and consider adding this article to your current event examples.  

Check back here next week for a new link!

SAT Grammar: Improving Sentences

Improving Sentences

Select the choice that results in the best sentence – the sentence that follows the requirements of standard written English and communicates effectively.

Although genetic factors can predispose a person to develop heart disease, doctors say that in most cases proper diet and exercise reduces thier risk.

A. exercise reduces their
B. exercise has been reducing their
C. exercise, reducing one’s
D. exercise reduce one’s
E. exercise, it does reduce the


Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8 grammar concepts.  

The underlined part of this sentence contains a noun and a verb, so your first thought should be, do the subject and verb agree?  The tricky part of this question is that the verb “reduces” seems to agree with the noun “exercise” at first.  If you look again, however, you will notice that the subject is compound (“proper diet and regular exercise”), so the verb should be plural, and the sentence should read, “…proper diet and regular exercise reduce…”  

The other issue in the underlined portion is the pronoun “their.”  Who are “they”?  Earlier in the sentence, the writer referenced “a person,” so this pronoun should be singular, either “one’s” or “your.”

Look for an answer choice that resolves the subject verb issue and includes a singular pronoun.

A. Choice A is incorrect, so you can eliminate it without reading it.

B.  Choice B still includes the pronoun “they.”  Eliminate this choice.

C.  Choice C includes the pronoun “one,” which is good, but this choice does not resolve the subject verb error properly.  The comma cuts the verb off from the nouns and changes the verb to a participle (a verb that acts as an adjective) for no reason.  Eliminate this choice.

D.  Choice D resolves the subject verb issue and uses the pronoun “one.”  Keep this choice and check the last remaining option.

E.  This choice probably strikes you as incorrect immediately.  What is “it”?  Why did the verb tense change?  What is “the risk”?  Eliminate this incorrect choice.

The correct answer is D.

This is a hard level problem.

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Link of the Week: My College Quickstart

If you took the PSAT/NMSQT® in October of this year, you have most likely received your results (or will very soon).  Once you get your score report, you can use the access code thereupon to log in to My College Quickstart, a service provided for free by the College Board.  This site has a wealth of useful features including:

1.  Explanations of questions you answered incorrectly or omitted on the PSAT
2.  An individualized study plan for the SAT based on your PSAT results
3.  Practice SAT questions and a full-length practice SAT
4.  Express SAT sign up
5.  Additional information about your PSAT score, including your projected SAT score
6.  A personality test that can help you choose a college and/or a major

…and much more!

Happy exploring, and check back for a new link next week!

SAT Writing: Identifying Setnence Errors

Identifying Sentence Errors

Read the sentence and select the portion of the sentence that contains an error.  If there is no error, select E.

Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portions against the Big 8 grammar concepts.

A.  Whenever you see a preposition underlined, determine whether its usage is idiomatic.  The phrase “anywhere from x to y,” as in “the cost may be anywhere from $5 to $20” or “children grow anywhere from a couple of centimeters to a few inches a year,” is a common idiomatic expression.  Choice A is not the error in the sentence.

B.  This choice constitutes the second part of the idiomatic expression “anywhere from x to y.”  Choice B is not the error in the sentence.  

C.  Once you hit this part of the sentence, you will probably sense that something sounds wrong.  What did Rockwell spend weeks or months doing?  Painting.  There should be no “and” before “painting” because Rockwell spent time painting, he did not spend time and paint.  This is most likely the error in the sentence, but check the remaining choice to be sure.

D.  If you see an adverb underlined on an SAT grammar question, be sure that it clearly modifies a verb, an adjective, or another adverb.  The adverb “meticulously” modifies “painting” because it tells you how Rockwell painted.  Choice D does not contain an error.  

E.  Since you found an error, E cannot be the answer.

The correct answer is C.

This is a medium level problem.

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SAT Reading: Sentence Completions

Sentence Completions

Select the word(s) that best fit the meaning of the sentence as a whole. 

Percy was often perceived as haughty or arrogant, but his ------- exterior ------- his true kindness and gentleness.

A. convoluted . . deterred
B. prolific . . feigned
C. pretentious . . belied
D. candid . . alleviated
E. condescending . . evoked


Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  Start with the easier blank first.  We already know that Percy is seen by others as haughty and arrogant, so it is easy to predict what should belong in the first blank.  We are looking for something synonymous with arrogant.  Using that prediction, let’s look at each of the choices for the first blank.  

A.  “Convoluted” means “intricate or complicated.”  The meaning of this word is fairly easy to remember because it sounds like “complicated,” “complex,” and “confusing.”  This does not match our prediction, so eliminate this choice.  
 
B.   “Prolific” comes from the Latin word for “offspring,” and it means “fertile or highly productive.”  Think PROlific = PROductive.  This choice does not match our prediction, so eliminate it.

C.   “Pretentious” comes from the same root as “pretend.”  To be pretentious is to pretend to be more important, wealthy, worldly, intelligent, etc. than you actually are in order to impress others.  This matches our prediction, so keep this choice for now.

D.   To be “candid” is to be open and honest.  If you have read the popular Divergent series, you might recognize candid because it is closely related to the word candor (honesty, frankness).  If you are not familiar with this series of books, Candor is a sect of society that believes in honesty above all else.  This choice is basically the opposite of what we are looking for, so eliminate it.

E.  “Condescend” once meant “to willingly lower oneself to the level of one’s inferiors,” but that use is almost archaic (old, out of date) now.  Now, “condescending” is generally used to mean “patronizing or snobbish.”  This matches our prediction, so keep this choice and move on to the second blanks.  

Now look at the second blank and predict what the answer should be.  If Percy is arrogant on the surface but kind underneath, his appearance contradicts his true nature.  Using “contradict” as a prediction, check the second blanks of the two remaining answers (C and E).

C.   To “belie” is “to give a false impression or contradict.”  You can remember this word by noticing that it sounds a little like “lie.”  This choice matches our prediction, so keep it.  

E.  “Evoke” includes the Latin root “vox,” which gave rise to words like “vocal,” “vocalize,” and “vocabulary.”  You may remember from past posts that the root “e” means “out,” so “evoke” means, in the most literal sense, “to call forth.”  The term can also mean “to bring to mind” or “to bring out.”  This does not match our prediction, so eliminate this choice.  

The correct answer is C.  

This is a medium level question.  

Words used in this SC:

convoluted: intricate or complicated
deter: to discourage or prevent from taking action
prolific: fertile or highly productive
feign: to fake
pretentious: self-important
belie: to give a false impression or contradict
candid: open, honest, and sincere
alleviate: to relieve
condescend: to act superior
evoke: to bring to mind

SAT Reading: Sentence Completions

Sentence Completions

Select the word that best fits the meaning of the sentence as a whole.

Although she was faced with many obstacles, Ramona remained ------- in pursuit of her goals.  

A.   banal
B.   innocuous
C.   apathetic
D.   resolute
E.   overt

Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  If Ramona pursues her goals despite the obstacles she faces, then how would you describe her?  She is probably persistent and determined.  Using “determined” as our prediction, let’s look at the choices.  

A.   “Arduous” comes from the Latin word “arduus,” meaning high or steep.  The term can literally refer to something that is difficult to climb, but it can also figuratively refer to anything that is difficult to overcome.   Although the obstacles Ramona faces may be arduous, Ramona herself is not.   Eliminate this choice.  

B.   The Latin word “nocuus” means harmful, so you can probably guess what “innocuous” means.  Something “innocuous” is harmless.  This does not match our prediction, so eliminate this choice.  
 
C.   “Apathetic” comes from two Greek roots: “a,” which means without, and “pathos,” which means “emotion, feeling or suffering.”  Apathy is a lack of feeling or emotion.  This is nearly the opposite of our prediction (someone who is apathetic is probably not determined to achieve a goal), so eliminate this choice.  
 
D.   The word “resolute” means determined.  Here is a helpful way to remember the meaning of this word: when I make New Year’s resolutions, I am resolute that I will achieve these goals.  This choice matches our prediction, so keep it and check the last option.

E.   “Prudent” comes from the Latin word “prudens,” meaning “skilled, sagacious (wise) or cautious.”  This does not fit with our prediction, so eliminate this choice.  

The correct answer is D.

Words used in this SC:
arduous: difficult
innocuous: harmless
apathetic: lacking concern or interest
resolute: determined and steady
prudent: very careful

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Link of the Week: Successful People

Over the years, numerous SAT prompts have focused on the path to success.  Here are a few examples:

1.  Does being ethical make it hard to be successful?
2.  Is persistence more important than ability in determining a person's success?
3.  Do success and happiness depend on the choices people make rather than on factors beyond their control?
4.  Do highly accomplished people achieve more than others mainly because they expect more of themselves?
5.  Can people achieve success only if they aim to be perfect?

Because success comes up so frequently in SAT prompts, it is a good idea to find an example that addresses the topic.  This list from the Huffington Post is a great place to start: it includes the stories of fifteen individuals who overcame obstacles and tragedies to become highly successful.  

Check back next week for a new link, and thanks for reading!

SAT Writing: Identifying Sentence Errors

Identifying Sentence Errors

Read the sentence and select the portion of the sentence that contains an error.  If there is no error, select E.

Screen Shot 2013-12-11 at 5.37.50 PM.jpg

Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portions against the Big 8 grammar concepts.

A.  When you see a verb underlined, check to see whether it agrees with its subject.  In this case, the verb “gave” agrees with its subject, “orientation.”  Eliminate this choice.

B.  The phrase “chance + to + verb” is idiomatically correct.  You would say “I had the chance to win a prize,” not “I had the chance winning a prize,” or “I had the chance win a prize.”  Eliminate this choice.  

C.  You might notice once you reach this point in the sentence that a list has begun.  The freshmen have the chance “to tour” campus, and they also have the chance “to learn” about school rules.  Verbs in a list should be parallel, as these two are.  This is not the error, so eliminate this choice.  

D.  The first two items in the list are “to tour” and “to learn,” so the last item should be “to meet,” not “they met.”  This choice is not parallel, so it must be the error in the sentence.

E.  The sentence includes an error, so E cannot be correct.  

The correct answer is E.

This is a medium level problem.

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SAT Math: Arithmetic

Digits

X and Y are distinct integers less than 6.  Given the correctly worked addition problem below, which of the following could be equal to XY?

Screen Shot 2013-12-10 at 4.52.26 PM.jpg

A. 26
B. 33
C. 35
D. 42
E. 44

Knowsys Method

Read the problem carefully.  A very important word to note in this problem is “distinct.”  If x and y are distinct, they cannot be the same number.  That eliminates answers B and E already.  Also, notice that X and Y must be less than 6.  That eliminates A.

Identify the bottom line.  XY = ?

Assess your options.  You can either plug in the answers or think about the problem logically.  The latter method is quicker, so we will demonstrate that below.  

Attack the problem.  If you look at the addition problem, you will see that X and Y must add up to 8.  The numbers in choice A add up to 8, but we already eliminated choice A in step 1.  That leaves us with choice C.  3 and 5 add up to 8, and if you sub in 3 as X and 5 as Y, you get this:

Screen Shot 2013-12-10 at 4.22.48 PM.jpg

Loop back.  Did you solve for the bottom line?  Yes.

The correct answer is C
This is an easy level problem

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Sentence Completions

Sentence Completions

Select the word that best fits the meaning of the sentence as a whole.

The novel’s ------- conclusion is sure to cause some dissatisfaction among readers who prefer clear-cut endings.

A.   ambiguous
B.   didactic
C.   fallacious
D.   innate
E.   overt

Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  If readers who prefer clear-cut endings might feel dissatisfied after reading this book, then its ending must unclear or confusing.  With “unclear or confusing” as our prediction, let’s look at the choices.  

A.   You probably know that the Latin prefix “ambi” means “both” or “many” (ambidextrous, ambivalent, etc.).  The other Latin root in “ambiguous” is “agere,” which means “to drive or to lead.”  Put those roots together, and you get a sense of what “ambiguous” means.  Something “ambiguous” is unclear because it could have many possible meanings or lead you in many different directions.   This matches our prediction, so keep it and scan the other choices.  

B.   “Didactic” comes from the Greek word “didaktos,” meaning “taught.”  Something “didactic” is intended to or designed to teach.  Eliminate this choice because it does not match our prediction.

C.   “Fallacious” means “deceptive or misleading.”  A useful trick for remembering the meaning of “fallacious” is to think about the word “false” which sounds similar and means something similar.   This does not match our prediction, so eliminate this choice.

D.   If you have taken French or Spanish in school, you know that the words for "born" in those languages are “né” and “nacido,” respectively.  It makes sense, then that an “innate” characteristic or ability is something you were born with.  This does not match our prediction, so eliminate this choice.  

E.   “Overt” comes from the French word “ouvrir,” which means “to open.”  Something “overt” is out in the open or obvious.  This is the opposite of our prediction, so eliminate this choice.
 
The correct answer is A.

Words used in this SC:

ambiguous: having several possible meanings
didactic: designed to teach
fallacious: deceptive or misleading
innate: existing from birth
overt: not hidden, obvious

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SAT Writing: Improving Sentences

Improving Sentences. 

Select the choice that results in the best sentence - the sentence that follows the requirements of standard written English and communicates effectively.

Burdened by several heavy grocery bags, the stairs were difficult for the woman to climb.

A.  the stairs were difficult for the woman to climb.
B.  the stairs were difficult for the woman who is climbing.
C.  the woman climbed the stairs with difficulty.
D.  the woman difficultly climbed the stairs.
E.  the woman climbed the stairs, which were difficult.

Knowsys Method

Read the sentence carefully, listening for errors. If you do not find the error immediately, then check the underlined portion against the Big 8 grammar concepts.

What do you notice about the original sentence?  It sounds a little like the stairs—and not the woman—are carrying the grocery bags.  This confusion is created by a misplaced modifier, a describing phrase that is not placed next to the word it describes.  When a sentence begins with a modifier phrase followed by a comma, the very next independent noun should be the subject of that phrase.  The woman is carrying the grocery bags in this sentence, so “the woman” should follow the comma.  Now let’s go through each choice and see which one works best.  

A.  We already found an error in this choice, so eliminate it.

B.  This choice has the same issue with a misplaced modifier, and it introduces a verb tense change that makes no sense.  Eliminate it.

C.  This choice fixes the modifier issue and makes sense.  If the woman is weighed down by the heavy grocery bags, she is likely to climb up the stairs with difficulty.  Keep this choice and scan the remaining two choices.

D.  Although this choice resolves the original modifier issue, it introduces a new problem.  How does one “difficultly climb” something?  That wording does not make sense, so eliminate this choice.

E.  This choice looks okay until the end.  Stairs are difficult to climb or to descend, but they are not difficult in and of themselves.  Eliminate this choice.  

The correct answer is C.

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SAT Math: Geometry

Triangles

Screen Shot 2013-12-06 at 3.16.36 PM.jpg

In the figure above, what is the sum, in terms of a, of angles b, c, d, and e?

A.  a
B.  2a
C.  180 – a
D.  180 – 2a
E.   360 – a

Knowsys Method

Read the problem carefully.  Notice that the image is drawn to scale because it does not indicate otherwise.  

Identify the bottom line.  b + c + d + e = ?

Assess your options.  If you find yourself stumped on a triangle problem on the SAT, run through the facts and rules you know about triangles and determine whether any of this knowledge applies to the problem at hand.  This problem is categorized as a “hard” level problem, but knowing one simple fact about triangles makes this problem easy to solve.

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FACT: The exterior angle d equals the sum of the opposite interior angles a and b.

So, d = a + b.  

Attack the problem.
Angle a is an exterior angle to both triangles in the image.  That means:

a = b + c

AND

a = d + e

Therefore:

b + c + d + e = 2a

Loop back.  You found the solution to the bottom line. 

The correct answer is B.

This is a hard level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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Link of the Week: TED Talks

Are you having trouble thinking up unique historical topics or current events?  Do you want your essay to truly stand out?  Try watching some TED talks.  

TED, or Technology, Education, Design, is a nonprofit dedicated to spreading innovative ideas through yearly conferences and web videos.  On the TED talks website, you can search for videos by topic (business, science, global issues, etc.), you can see lists of videos tagged with terms like “jaw-dropping,” “courageous” or “funny,” or you can simply view the most recent talks.  While a single TED talk may not give you enough details to constitute a full SAT example, these videos can point you in the direction of topics you might want to research.  

At the very least, you are sure to find videos that will pique your curiosity, inspire you, and inform you.  Happy searching!  Check back here next week for a new link. 

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SAT Writing: Improving Sentences

Improving Sentences

Select the choice that results in the best sentence – the sentence that follows the requirements of standard written English and communicates effectively.

Since that resaturant requires for customers to pay in cash, we will have to stop by the ATM beforehand.

A. Since that restaurant requires for customers to pay in cash
B. Since that restaurant requires that customers should pay in cash
C. That restaurant has a requirement that customers pay in cash
D. When you go to that restaurant it is required for customers to pay in cash and therefore
E. Since that restaurant requires customers to pay in cash

Knowsys Method

Read the entire sentence carefully, listening for errors.  Then focus on the underlined part.  Evaluate it by checking it against the Big 8 Grammar Rules.  If you find an error, use that error to quickly eliminate any answer choices that do not fix the problem you found.

If you noticed that the underlined portion sounds “off,” then you have a good ear for idioms.  A restaurant does not “require for customers to pay in cash”, a restaurant “requires that customers pay in cash,” or it “requires customers to pay in cash.”  We need to find a choice that uses one of these idiomatically correct phrases.  

A.  Choice A is the same as the original sentence, which contains an error.  Eliminate this choice.

B.  This choice would work, except that it includes an unneeded word, “should.”  Eliminate this choice.

C.  There are two problems with this choice.  First, the wording of the phrase “has a requirement that customers pay in cash” is awkward and unnecessarily wordy.  Second, this choice creates a comma splice because it turns the sentence into two independent clauses joined by a comma alone.  Eliminate this choice.

D.  This choice is wordy, which you should always avoid.  Additionally, this choice results in an incorrectly punctuated sentence.  There needs to one comma after “restaurant” and another after “cash.”  Eliminate this choice.

E.  This choice uses an idiomatically correct expression, “requires customers to pay in cash,” and it does not introduce any new errors.  This must be the correct answer.  

The correct answer is (E).

This is an easy level question.

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SAT Math: Algebra

Exponents

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Read the question carefully.  This question requires you to know exponent rules.  It is important for you to note that a and b are positive integers and that you are asked for a in terms of b.

Identify the bottom line.  a = ?

Assess your options.  Unfortunately, this problem is going to be difficult for you to solve if you have not memorized exponent rules.  If the rules you need to solve this problem do not immediately pop into your head, go back and review the exponent rules.  

Attack the problem.  There are two rules that apply to this problem:

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The first thing you have to do is get all the bases to look the same.  Look back at the original equation:

Screen Shot 2013-11-06 at 3.28.13 PM.jpg

The number 9 is three squared, so you can rewrite the equation like this:

Screen Shot 2013-11-06 at 3.29.07 PM.jpg

Now apply the first exponent rule to the left side of the equation:

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Now you can apply the second rule.  If the base is 3 on both sides, then the exponents must be the same number.  Set them equal to one another and solve for the variable.

Screen Shot 2013-11-06 at 3.29.45 PM.jpg

Loop back.  You found a in terms of b, so now you just need to select the correct answer choice, which is (B).

Correct answer: (B)

This is a medium level question.

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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SAT Reading: Sentence Completions

Select the words that best fit the meaning of the sentence as a whole.

The man was completely ------- common sense, an unfortunate trait that caused him to make ------- decisions with alarming frequency.   

A. myopic about . . frivolous
B. wary of . . acrid
C. apathetic toward . . onerous
D. inclined toward . . supercilious
E. bereft of . . imprudent

Knowsys Method

Always start by covering up your answer choices so that they do not distract you.  Read the sentence carefully, and then predict what you think the answer should be.  This is a logic-based sentence completion, so the definitions of the words are not built into the sentence, but if you use your skills of deduction, you should be able to predict what belongs in the blanks.  Focus on the first blank first.  The sentence states that the trait this man possesses is “unfortunate,” so he is probably lacking in common sense.  Use “lacking” as your prediction and take a look at all the answers for the first blank.

A. If you do not know the term “myopic,” you might have heard of the eye condition “myopia,” or nearsightedness.  People who suffer from “myopia” can see objects that are close to them, but anything far away is blurred.  “Myopic” can be interpreted literally as the inability to see faraway objects, or it can be taken figuratively to mean that someone does not consider the long-reaching consequences of his or her actions.  This term does not match our prediction, so eliminate this choice.

B. The word “wary” dates back hundreds of years to the Old Norse word “varr,” which means attentive.  To be wary of something is to show caution about potential problems that might arise.  This does not match our prediction, so eliminate this choice.

C. “Apathetic” comes from two Greek roots: “a,” which means without, and “pathos,” which means “emotion, feeling or suffering.”  Apathy is a lack of feeling or emotion, which looks close to our prediction but is too specific. We are looking for “lacking,” not “lacking emotion.”  Eliminate this choice.

E. “Bereft,” a past participle of “bereave,” can mean that someone has been deprived of a loved one, often because that loved one has passed away.  However, “bereft” can also mean “lacking” in a general sense.  This is the only choice so far that matches our prediction, so this is probably the right answer, but we need to check the second word to be sure.  

“Imprudent” means rash or lacking foresight.  If this man lacks common sense, does it make sense that his decisions are frequently rash?  Yes.  Choice E is clearly the correct answer.

The correct answer is (E).
This is a medium level question.

Words used in this SC:
myopic: having defective vision or a narrow view
frivolous: silly or unimportant
wary: watchful and cautious
acrid: very sharp or bitter
apathetic: lacking concern or interest
onerous: burdensome or troublesome
inclined: having a tendency to do something
supercilious: excessively proud or arrogant
bereft: deprived of or lacking in
imprudent: unwise

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