Probability

Data Analysis: Probability

Read the following SAT test question and then select the correct answer.

Read each question carefully to avoid making any mistakes. Identify the bottom line (what the question is asking) and assess your options for reaching it by asking yourself “What could I do?” and “What should I do?” Choose the most efficient method to attack the problem and find an answer. Last, loop back to make sure that your answer addresses the bottom line.

If a number is chosen at random from the set {-10, -5, 0, 5, 10}, what is the probability that it is a member of the solution set of both 3x – 2 <10 and x + 2?

Bottom Line: Prb = ?

Assess Your Options: You cannot solve for a probability until you know whether each number in the set meets the requirements that you are given. You could plug numbers from the set into each inequality and see if they work, but it is much faster to simplify the inequalities before you begin working with them.

Attack the Problem: Simplify the inequalities by solving both for x.

3x – 2 < 10
3x < 12
x < 4

x + 2 > -8
x > -10

You now know that x must be less than 4, but greater than -10. The question asked you to find a number that fits both of these solution sets. Look at the original set that you were given. The only two answers that are between -10 and 4 are -5 and 0 (-10 does not work because it cannot be equal to negative -10; it has to be greater than -10). You found 2 numbers out of 5 that you were given that work. To write this as a probability, you must set the number of relevant outcomes over the number of total possible outcomes. Your answer is .

Loop Back: You found a probability matching the restrictions you were given. Look down at your answer choices.

(A) 0

(B)

(C)

(D)

(E)

The correct answer is (C).


On sat.collegeboard.org, 50% of the responses were correct.

For more help with SAT math, visitwww.myknowsys.com!

Pronouns

Link of the Day

Many SAT essay questions ask about decision making.  Should decisions be based on feelings?  On facts alone?  How do you decide what is relevant in decision making?  Take a look at this article about a wolf that has found its way to California.  Taking care of the planet by preserving a diverse array of species is important.  Keeping humans and their cattle safe is also important.  What is your opinion about this current event?  What themes do you see in this story that are likely to appear on an SAT essay question?

Writing: Improving Sentences

Part or all of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A.  

Read the original sentence to yourself, listening for errors.  Then evaluate the underlined portion of the sentence using the Big 8 Grammar Rules.  Focus on the first error that you find to quickly eliminate wrong answer choices.

Chilean novelist and short-story writer María Luisa Bombal wrote innovative and influential stories featuring heroines which create fantasy worlds in order to escape from unfulfilling love relationships and restricted social roles.

As you read this sentence, you should realize that the stories are not escaping from unfulfilling love relationships and unrestricted social roles; the heroines are creating fantasy worlds to escape.  Heroines are people.  To refer to people, always use “who” or “whom,” never “that” or “which.”  Replace the word “which,” with the word “who” and look down at your answer choices.

(A) heroines which create

(B) heroines, they create

(C) heroines, they created

(D) heroines who create

(E) heroines that were creating

(A) This answer matches the original sentence, so you can eliminate it.

(B) This answer creates a comma splice.  There are two complete sentences on either side of the comma that should be separated with a period.  Eliminate this choice.

(C) This answer creates a comma splice and is also in the wrong tense.  When speaking about literature, use the present tense.  You don’t have to match the tense used when speaking about the author.  Eliminate this choice.

(D) This answer matches the correction that you made.  Keep it and check the last choice.

(E) Never use the word “that” to refer to people.  Eliminate this choice.

The correct answer is (D).

On sat.collegeboard.org, 73% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

Always cover your answer choices so that you can read the sentence carefully with an unprejudiced mind.  Make a prediction to fill the blank, and then match your prediction to the correct answer choice, eliminating any words that do not match.  Make sure that you look at all the answer choices before selecting your answer.

The impoverished city lacked the financial means to update its ------- electrical infrastructure.

Paraphrase the sentence to clarify its meaning.  The city is in poverty and lacks money for an update.  If something needs an update that means that it is old and outdated.  Predict the word “old” and look down at your answer choices.

(A) despondent

(B) antiquated

(C) rejuvenated

(D) superlative

(E) esoteric

(A)  If you have heard this word used before, you have probably heard it applied to a person with a negative emotion.  You are not looking for an emotional word; you are looking for something that means “old.”  Eliminate this choice.  (B) Think of the related word, “antique.”  This matches your prediction perfectly.  Keep it.  (C)  The Latin root “re” means again while the Latin root “juven” means young.  The infrastructure cannot be young again because the city does not have any money to change it.  Eliminate this choice.  (D)   The Latin root “super” means “over” or “above.”  A poor city will not have an infrastructure that is better than another city’s infrastructure, so eliminate this choice.  (E) The Greek root “eso” means “within,” as in belonging to an inner circle.  Although the infrastructure is within the city, this word does not match your prediction and should be eliminated.

The correct answer is (B).

Words used in this SC:

Impoverished: reduced to poverty

Infrastructure: the underlying framework

Despondent: feeling or showing profound hopelessness

Antiquated: old-fashioned or obsolete

Rejuvinated: restored to youthfulness

Superlative: of the highest quality or order, surpassing others

Esoteric: requiring specialized knowledge to be understood (Knowsys vocab!)

On sat.collegeboard.org, 67% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!

Rates

Arithmetic: Rates

Read the following SAT test question and then click on a button to select your answer. 

Use the same method for every math problem on the SAT.  Read the problem carefully, identify the bottom line, and assess your options for solving the problem.  Choose the most efficient method to attack the problem.  Often there will be multiple steps to a single problem, so when you have an answer, be sure to loop back and verify that it matches the bottom line.

A machine can insert letters in envelopes at the rate of 120 per minute. Another machine can stamp the envelopes at the rate of 3 per second. How many such stamping machines are needed to keep up with 18 inserting machines of this kind?

Bottom Line:  # stamping machines = ?

Assess your Options:  You could try to work backwards from the answers, but there is no need.  It will be faster just to solve the problem.

Attack the Problem:  You have been given two different units of time: minutes and seconds.  There are 60 seconds in a minute.  Changing the minutes to seconds will be easiest, so the letter inserting machine works at a rate of 120 letters per 60 seconds.  120 divided by 60 is 2 letters in envelopes per second.  If there are 18 letter inserting machines, then together they will insert 36 letters in envelopes per second (2 × 18 = 36).

You don’t know how many stamping machines you need, so use x to represent that number.  Stamping machines have a rate of 3 envelopes per second, so each machine will finish 3 envelopes in a second.  You know that the stamping machines must keep pace with the 18 letter inserting machines that finish 36 envelopes per second, so the outcome must be 36.  Write 3x = 36.  When you solve for x,  x = 12.

Loop Back:  You used x to represent the number of stamping machines, your bottom line, so you are ready to look at the answer choices.

(A) 12

(B) 16

(C) 20

(D) 22

(E) 24

The correct answer is (A).

On sat.collegeboard.org, 58% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Idioms

Writing: Identifying Sentence Errors

The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E. 

Read the whole sentence to yourself, listening for errors.  Then check each underlined portion of the sentence against the Big 8 Grammar Rules.  When you think you have identified an error, mark it and quickly check the other answer choices.

Except for the phonograph, the performances Bof great musicians and the voices of famous people Cwould have been lost Dto history. ENo error

(A) Did the sentence sound strange to you when you read it?  Paraphrase it in your mind.  The sentence should convey the meaning that if there was no phonograph, we would not know how past musicians sounded.  However, there is an inappropriate word choice.  In order for the meaning of this sentence to be clear, the words “except for” must be replaced with the word “without.”  Mark this error and quickly check the other underlined portions.

(B) The preposition “of” is idiomatically correct following the word “performances.”  In addition, the modifier “great” is placed close to the word it modifies, “musicians.”  There is no error here.

(C) Many students incorrectly write “would of been” when the idiomatically correct phrase is “would have been.”  This sentence does not include that error.  There is no error here.

(D)  The words “lost to history” clearly and concisely convey the idea that these sounds would only have occurred in the past if the phonograph did not allow us to continue to hear them in the present.  There is no error here.

(E) This choice cannot be correct because you already identified an error.

The correct answer is (A).

On sat.collegeboard.org, 53% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Sentence Completions

Critical Reading: Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 

                         

Cover the answers so that wrong answer choices do not mislead your thoughts as you carefully read the sentence.  Focus on one blank, the one that seems easier, and make a prediction for that blank.  Eliminate any answer that does not match your prediction.  Then use the same method for the second blank.

The architect wanted to ------- his own initial vision and design but recognized the importance of ------- requests from his client; in the end, he had to make several concessions.

Look at the second blank because there are more contextual clues to help you find this blank.  The last portion of the sentence tells you that the architect had to make concessions.  In order to make concessions, he first had to recognize the importance of conceding to requests from his clients, which means he accepted or approved them.  Use these words as your prediction and look down at your answer choices.

(A)   maintain . . accommodating

(B)   develop . . submitting

(C)   protect . . excluding

(D)   refuse . . incorporating

(E)    preserve . . disregarding

(A) The word accommodating shows that he was willing to make changes.  Keep it.  (B)  The architect does not submit requests; the client does. Eliminate this choice.  (C)  "Excluding" is the opposite of your prediction.  Eliminate it.  (D)  If the architect incorporates his client’s requests, he accepts them and uses them to adapt his design.  Keep this option.   (E) "Disregarding" is the opposite of your prediction.  Eliminate it.

Now return to that first blank.  It is separate from the second part of the sentence by the word “but,” a word that indicates a contrast.  If the architect eventually has to make concessions or changes, a contrast to this idea would be that he wants to keep his initial vision and design without changes.  Use the word “keep” as your prediction and look down at the remaining choices.

(A) maintain . . accommodating

(D) refuse . . incorporating

(A) The word “maintain” matches the word “keep.”  Keep this answer choice.  (D)  It doesn’t make sense for the architect to refuse his own ideas; he wants to refuse the ideas of his client.  Eliminate this choice.

The correct answer is (A).

                                                         

Words used in this SC:

Concessions: changes as a result of yielded privilege or power

Maintain: keep up, preserve

Accommodating:

Develop: change, progress

Submitting: yielding authority

Protect: keep safe, defend

Excluding: shutting out

Refuse: reject

Incorporating: including

Preserve: protect, maintain

Disregarding: ignoring

On sat.collegeboard.org, 77% of the responses were correct.

For more help with SAT vocabulary, visit www.myknowsys.com!

Coordinate Geometry

Link of the Day:

A new year symbolizes a new start for many.  Although the world is essentially the same as it was before the clock struck midnight, there is a new optimism about the future.  People want to focus on goals such as peace and prosperity.  Read this current event about an unexpected gesture from North Korea, and then ask yourself what you can expect from 2013.  What themes can you identify in this article that are likely to be part of an SAT essay question?

Geometry: Coordinate Geometry

Read the following SAT test question and then select the correct answer. 

Always read the question carefully and identify the bottom line.  Assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to verify that it addresses the bottom line.

In the figure, the slope of the line through points P and Q is . What is the value of k?

Bottom Line: k = ?

Assess Your Options:  You could start from the point (1, 1) and use the slope to find new points, hoping that by adding 3 to the y value and 2 to the x value you will reach a point that contains a 7 y value.  Unfortunately, it is very easy to make a mistake using this method, such as adding the y change to the x value or vice versa.  Instead, use the information that you are given, the slope, to write an equation.

Attack the problem:  Although you are given the slope, you also know how the slope was obtained.  Think about it:  The slope is rise over run or the change in y over the change in x. 

You know two different y values, and two different x values, so you can plug in all the information that you know for the slope.

Now you need to set this formula for slope equal to the value for slope that you were given in the problem, isolate the variable k, and solve for it.

3(k – 1) = 6 × 2

3k – 3 = 12

3k = 15

k = 5

Loop Back: You solved for k, so you are ready to look at your answer choices.

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

The correct answer is (B).

On sat.collegeboard.org, 51% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!