If a + b = 18, b + c = 45, and a + c = 39, what is the average of a, b, and c?
The correct answer is 17
Explanation: Start by combining the three equations into one equation involving a, b, and c. Do this by adding up the equations:
a + b = 18
b + c = 45
a + c = 39
2a + 2b + 2c = 102
This means that 2(a + b + c) = 102, which means a + b + c = 51 (since 102/2 is 51). The question asks for the average of a, b, and c, and to find an average, you simply need to divide the sum of the terms by the number of terms. Thus, take 51 (the sum of a, b, and c) and divide it by 3 (the number of terms): 51/3 = 17.
In response to the SAT cheating scandal in Long Island, NY, the College Board has announced enhanced SAT security measures, effective with the 2012-2013 academic year. These changes intend to dissuade students from attempting to cheat, by ensuring that such students will be caught. It is crucial that all students planning to take the SAT next year are aware of these changes, so I'm providing a summary below.
Key changes include:
1. Students must submit a photo during registration.
This photo will be printed on your admission ticket, for comparison with your photo ID.
2. Students must provide the name of their high school during registration. It will no longer be an option for students to skip this step. Once registration opens for the 2012-2013 academic year, registrations submitted without students' attending high schools will not be processed.
3. Test center and/or test type changes no longer permitted on test day. Students who want to take the SAT at a different test center than the one they registered for will need to request this change prior to test day. Similarly, students who want to change the type of test they will take (for example, SAT rather than SAT II) will need to request this change in advance.
4. Standby testing no longer permitted. All test-takers will be required to register beforehand.
5. Students must bring their photo ID AND photo admission ticket to the test center on test day. Students who arrive without BOTH items will not be admitted to the test center.
6. Photo IDs & photo admission tickets will be checked throughout test day. Checks will occur upon entry to the test center, upon entry to the test room, upon reentry to the test room following breaks, and upon collection of answer sheets.
Because the director had yet to make his final decisions on the cast,
she had prematurely announced to all of her friends that she had been
(B) (C) (D)
cast in the lead role. No error
The correct answer is A
Explanation: The error in this sentence occurs at choice A where there is a word choice error. The transition word “because” is illogical in the context of the sentence, given that the second clause states that “she had prematurely announced” the casting decision. “Because” is used to indicate cause-and-effect relationships, but this sentence does not have such a relationship. If she had “prematurely” announced it, then the director could not have made “his final decisions on the cast” yet, meaning the first word in the sentence should indicate contrast between the clauses. This mistake could be corrected by changing “because” to “although.”
Triangles 1 and 2 are both equilateral triangles. If Triangle 1’s perimeter is ⅓ that of Triangle 2, and Triangle 1 has an area of 2√3 units, how long is one side of Triangle 2?
The correct answer is D
Explanation: Start by finding the length of one side of Triangle 1. Equilateral triangles divide into two 30°-60°-90° triangles, which have proportional sides of s:s√3:2s. However, this s is really ½ as long as the side of the equilateral triangle (since the 30-60-90 triangle is ½ the equilateral triangle), meaning that the sides are really ½s: ½s√3: s. Thus, if the height of Triangle 1 is 2√3, then the side length must be 4 (from ½s√3 = 2√3, and 2√3/ ½√3 = 4).
If the perimeter of Triangle 2 is 3 times as large as that of Triangle 1, that means that every side of Triangle 2 must be 3 times as large as every side of Triangle 1, meaning each side of Triangle 2 is just 4•3, or 12.
Instead of doing a brief skimming of the textbook, the teacher recommends doing ______, because most of the test questions will concern information presented in the book rather than that discussed in class.
(A) an expurgation
(B) a translation
(C) a perusal
(D) a glance
(E) a summary
The correct answer is C
Explanation: To predict the meaning of the missing words, look for keywords in the sentence. Here, the keywords are found in the first clause of the sentence, “instead of doing a brief skimming,” which suggests that the teacher has recommended the opposite of said skimming. Because the missing word describes what the teacher “recommends doing,” it must mean the “opposite of skimming.” Choice C is, therefore, the correct answer: a “perusal” is “a close reading or examination of something.”
Additionally, none of the other answer choices work:
Expurgation: the removal of objectionable materials from a book or other work (the prompt does not indicate that the textbook has objectionable material or needs to be censored or edited)
Translation: a written or spoken rendering of the meaning of a word, speech, book, or other text, in another language (a translation is not necessarily a close reading)
Glance: a brief look at something (this is the opposite of a correct answer)
Summary: a brief statement or account of the main points of something (this is the opposite of a correct answer)
A company has ten applicants for four positions. If each applicant is qualified for each vacancy, how many possible ways can the company fill the four openings?
The correct answer is C
Explanation: 4 positions to fill from 10 applicants means the question is looking for a combination: how many groups of four can be made from ten total? Therefore, the best approach to this is to use the combination formula: nCr = n!/(r!(n-r)!), where n is the number of objects available and r is the number taken at a time. Thus, here n = 10 and r = 4. Use these numbers in the formula to get:
10! or 10!
This equals 210.
Neither Patricia nor Paula are going to be in class on Friday because their basketball team is playing in the state tournament in Sacramento on Saturday night.
(A) are going to be in class on Friday because their basketball team is playing
(B) are going to be in class on Friday due to her basketball team playing
(C) is going to be in class on Friday due to her basketball team playing
(D) is going to be in class on Friday because their basketball team are playing
(E) is going to be in class on Friday because their basketball team is playing
The correct answer is E
Explanation: As written, this sentence contains a subject-verb agreement error. The plural verb “are” does not agree in number with its singular subject “neither Patricia nor Paula.” When two singular nouns are joined by any word other than “and,” the noun remains singular, so “are” is inappropriate here. Choice E corrects this mistake by changing “are” to the grammatically correct and singular verb “is.”
Everyone knows that the best way to prep for SAT verbal is to read more books. One reason for this is that it's about 1,000 x easier to retain vocabulary learned in context than through rote memorization. Think about it... Each word is a fiber in the fabric of communication. When you learn new vocab in context, you sense not only what individual words mean, but also how words connect to one another and how they are used. Come SAT Sentence Completions, memories of this context will act like a mnemonic: The context will conjure a word's definition.
But, what should I read to learn new words? There are many options! Below, I suggest a few.
1) Reading classical literature (like, The Scarlett Letter, Frankenstein, and Jayne Eyre) is best. Not only are these books rife with SAT vocabulary, but reading them will also hone your ability to work through complex sentence structures. Furthermore, scrambling through stories set in an unfamiliar time period or place will train you to work around confusing details to get a sense of the overall plot--a CRITICAL skill for approaching Passage Based Reading questions. Many of these books are available free online, through websites like Project Gutenberg.
2) If ya just can't mesh with Hardy, Austen and the Bronte Sisters, why not hang with a more modern crowd? The New York Times is SAT reading level, filled with luscious lexicon, and will inform you of important happenings throughout the world. You might also try stories and articles from The New Yorker, Vanity Fair, or Rolling Stone.
3) Although reading young adult literature won't help you prepare for Passage Based Reading questions, many YA books--like, The Hunger Games, Harry Potter (the spells will teach you Latin roots!) and Balzac and the Little Chinese Seamstress--incorporate SAT level vocabulary. Just make sure to look up EVERY new word encountered, even if you don't need to do this to understand the story. (Also check out this Hunger Games SAT vocab quiz, from dictionary.com!)
4) SparkNotes: SAT Vocabulary Novels sound pretty cheesy, but each book features 1,000 of the most frequently tested vocabulary words. Throughout each book, SAT words are printed in boldface and definitions appear on the same page, so students can easily access and digest the meanings as they read along.
--- If you have a smartphone, download the dictionary.com app! Not only will it feed you a word of the day, but you can also use it to look up new words as you read on the train, in a diner, or while you stand in line.
--- If you don't have a smartphone, read by a computer so you can define new words as needed. If you read mostly away from home, carry a pencil and paper to write down words for later review.
--- Reinforce & retain new vocab by incorporating it into your schoolwork, writing, and everyday conversation.
Happy reading! Please let us know if you find more excellent reading material for studying SAT vocab!
These Key SAT Words are Expertly Identified by Sentia Tutors
Rote: proceeding mechanically and repetitiously
Hone: to sharpen
Lexicon: the vocabulary of a specific language, field, or trade
Tuesday's blog post hinted that young adult literature is a surprisingly good place to pick up SAT vocabulary. As a follow up, I want to explore our most enchanting YA resource: J.K. Rowling's Harry Potter series. Brimming with Latin-based names and incantations, Harry Potter is a fun and helpful guide to Latin roots you’ll find on the SAT.
How many Latin roots can you find in Harry Potter? Here are the roots of 10 spells (with related SAT vocabulary!) to get you started:
1. Confundo (Confundus Charm) -- This spell, which causes the victim to become confused, comes from the Latin root, con, which means “with.” In this case, con implies a mixing up of sorts. All things are thrown together to become muddled, enmeshed, and indistinguishable… confused.
SAT Words with the Root con:
- contiguous: sharing an edge or boundary; touching
- consensus: agreement, accord
- conjecture: an inference based upon guesswork
2. Crucio (Cruciatus Curse) – This is a curse of torture or pain. Derived from the Latin root, cruci meaning “cross,” or “torture,” the Crucio curse should be avoided at all costs!
SAT Words with the Root cruci:
- excruciating: very painful; extreme
- crucible: a severe, searching test or trial
- crucify: to treat with gross injustice; persecute; torment; torture
3. Deletrius – A spell that makes things disappear or vanish. This spell has the Latin root, de, which means “away from,” “removing,” or “down."
SAT Words with the Root de:
- deleterious: harmful; injurious
- depreciation: a decrease in value
- destitute: abandoned; forsaken
4. Expecto Patronum (Patronus Charm) – This spell is used to repel dementors. Patronum is based on the Latin root, patr, which means father. By extension, we can also take patr to indicate protectiveness and high rank.
SAT Words with the Root patr:
- patrician: a person of noble rank; an aristocrat
- patricide: the act of killing one’s father
- patriarch: father
5. Expelliarmus (Disarming Charm) – A disarming spell; often used to force opponents to drop their wands. This spell contains the Latin roots ex, meaning, “off,” “away from,” or “out,” and arma, which means “weapons.”
SAT Words with the Root ex or arma:
- exonerate: to free from blame or guilt
- expunge: delete; remove
- armistice: a temporary suspension of hostilities; a truce
- armature: armor
6. Impedimenta (Impediment Jinx) – This jinx trips, freezes, binds, or otherwise blocks an opponent’s approach. Fittingly, this walk-stopping jinx contains the root, ped, Latin for “foot.”
SAT Words with the Root ped:
- Expedite: to speed up the progress of; to accelerate
- Pedestrian: Undistinguished; ordinary; conventional
- Impede: To hinder the progress of
7. Imperio (Imperius Curse) – One of the three “Unforgivable Curses,” the Imperius Curse places the subject in a dream-like state in which he/she is completely subject to the will of the caster. Using this curse can result in life imprisonment in Azkaban. Imperio comes from the root impero, which means “command.”
SAT Words with the Root impero:
- imperious: domineering and arrogant
- imperative: absolutely necessary or required
8. Lumos – A spell that produces a narrow beam of light that shines from the tip of a wand, Lumos derives from the Latin, lum or luc, meaning “light.”
SAT Words with the Root lum or luc:
- elucidate: to make clear or plain
- luminary: a famous, inspiring person
- pellucid: transparent; translucent
9. Morsmordre (Dark Mark) – Morsmorde is a spell that produces the Dark Mark—symbol of Lord Voldemort and the Death Eaters. It comes from the Latin root, mort, meaning death. Notice that mort is the root of Voldemort’s name, as well.
SAT Words with the Root mort:
- mortify: to humiliate
- remorse: sincere and deep regret
- moribund: approaching death
10. Wingardium Leviosa (Levitation/Hover Charm) – One of the first spells taught to Hogwarts students, Wingardium Leviosa lifts objects so they float in the air. Wingardium contains the Latin root arduus, meaning “high” or “difficult,” and Leviosa sprouts from lev, which means “lift” or “light.”
SAT Words with the Root arduus or lev:
- arduous: laborious; difficult; requiring great exertion
- alleviate: to relieve; to lessen
- levity: lightness of mind, character or behavior
If x is a one-digit integer, which of the following is NOT a possible value of 3 - x?
The correct answer is A
Explanation: The trick to this question is to define a "one-digit integer." That simply means that x must be an integer that is only one-digit long. An integer can be positive or negative (or zero!), so x, in this case, could be -9, -8, -7... 7, 8, or 9. Each of the answer choices can be created from 3 - x, except for choice A:
(A) 3 - 10 = -7, and 10 is not a one-digit integer
(B) 0 - 3 = -3
(C) 3 - 3 = 0
(D) 3 - -3 = 6
(E) 3 - -4 = 7