Question of the Day's
People expect that their elected officials will not be __________ representatives; it is considered common knowledge that politicians always have their own bent. a. rationale b. competent c. flexible d. disinterested e. caring
Punctuation can serve as a road-sign. In this case, the semicolon indicates that the second sentence will mirror the sentiment of the first. The second sentence tells us that people expect politicians to have a bent, or be biased. Therefore, we might predict the first sentence to read 'officials will not be unbiased or impartial.' Now, find the word that best matches the prediction. We can see that choice (D) is best. Disinterested (or dispassionate) means unbiased, professional and composed. None of the other choices means unbiased.
If (a + 2b)⁄(17b - 2a) = 1, which of the following must be true about the relationship between a and b? a is 3 more than b b is 3 more than a a is 1/5 of b a is 5 times b a is 3/5 of b
a is 5 times b (pg. 17) a + 2b = 17b - 2a 3a = 15b a = 5b
There were streaks of both arrogance and ___________ in the artist's approach. Not only did she believe that she was by far the best contemporary painter, but she also constantly decried all conventional approaches to the medium. a. insolence b. esurient c. meekness d. egotism e. peremptoriness
a. insolence (disrespectful)
In contrast to instances where size is commensurate with potency of flavor, smaller peppers tend to be far more _________ than larger peppers. a. banal b. piquant c. acrid d. unique e. diverse
b. piquant (spicy)
The architecture in the town is anything but _____________; it draws its banal style from models already in use. a. trite b. revolutionary c. symmetrical d. uniform e. appropriate
b. revolutionary
A movie poster typically captures the essence of the film; however, the bright colors and smiling faces of the actors found on this poster belie the feature's ___________ tone. a. pedantic b. jovial c. morose d. caustic e. derisive
c. morose - gloomy pedantic-ostentatious learning jovial-heart, good-humored caustic-corrosive, severely critical derisive-contemptuous, mocking
A ride at Disneyland can hold 2 people in the front seat and 3 in the back seat. A group of 8 friends wish to go on the ride, but since the ride can only hold 5 people at a time, 5 of the friends will go first while the other 3 will wait for the next car. Alice and Stephen will both go in the first group: Alice must sit in the front left seat and Stephen must sit in the back middle seat. In how many ways can the group of 8 friends fill the 5 spots if Alice and Stephen are present in each arrangement? a. 30 b. 56 c. 90 d. 120 e. 336
d. 120 (pg.1) 8-2=6 5-2=3 6!/3!
The cost to rent a boat for a fishing trip is x dollars, which is to be shared equally among the people taking the trip. If 12 people go on the trip rather than 20, how many more dollars, in terms of x, will it cost per person? a. x/8 b. x/12 c. x/16 d. x/20 e. x/30
e. x/30 (pg. 12) pick a number (we'll go with 60) 60/20=$3 per person 60/12=$5 per person $2 additional cost, so now need to plug 60 into x to see what equation comes out with $2
Line A is perpendicular to the line with the equation y= -1/5 * x, and the point (3, -10) is on line A. What is the equation of line A?
y = 5x - 25 (pg. 5) *Any line perpendicular to this line has a slope of -1/m* slope of line A= 5 solve for b by plugging in coordinates y= 5x + b -10=5(3) + b b=-25 y=5x -25
A certain farmer planted x acres of corn at a cost of p dollars per acre. If y acres were destroyed by locusts and the farmer sold the rest of the crop for q dollars per acre, which of the following represents the farmer's gross profit on the sale of the corn?
(x-y)q - xp (pg. 8)
If 4x = -8, then 3x2 + 7x - 8 =
-10 (pg.19)
a = 4(3 - 5) + 2b = -4(5 - 3)What is the value of 2|a| - |2b|?
-4 (pg.19) solve for a and b then plug in numbers to equation
Each block in a certain bucket is either red, yellow, or blue. There are half as many red blocks as blue blocks and 3 times as many yellow blocks as red blocks. If a block is withdrawn from the bucket at random, what is the probability that the block is blue?
1/3 (pg. 13) red = 1/2(blue); 3(red) = yellow pick a number for red (3) blue=6 yellow= 9 probability of picking a blue = 6/18 = 1/3
How many different 6-digit positive integers are there, where 3 of the digits are each one of the digits 5 or 7, and the other 3 digits are each of one of the digits 1, 4, 6, or 8 ?
10, 240 (pg. 6) First, calculate number of ways to select 3 different objects from 6 different objects using nCk: n=3; k=6 6!/3!(6-3)! = 20 ways to specify which three digits will be 5 or 7 for 5 and 7: 2 x 2 x 2 = 8 different ways to specify if a digit will be 5 or 7 for 1, 4, 6, 8: 4 x 4 x 4 = 64 different ways to specify if a digit will be 1, 4, 6, or 8 20 x 8 x 64 = 10, 240
A certain jewelry store sells customized pendants in which three gemstones selected by the customer are set in a straight row down the center of the pendant. If exactly 5 different types of gemstone are available, and if at least two of the gemstones in any given pendant must be different, how many different pendants are possible?
120 (pg.10) 5C3 = 5!/ (5-3)! = 60 20 * 3 = 120
Jonna and Russell meet at a diner that is directly south of Jonna's house and directly west of Russell's house. If the diner is exactly 10 miles from Jonna's house and Russell's house is 2 miles closer to the diner than to Jonna's house, how far apart is Russell's house from the diner?
24 (pg. 14) Make a triangle for the distances. 10= distance from Jonna's house to diner x= distance from Jonna to Russell's house x-2: distance from Russell's house to diner 10^2 + (x-2)^2 = x^2 x = 26 26-2 = 24
If c + a = 20 and b - c = 8, then a + b =
28 (pg.15) c = 20 -a b - (20 - a) = 8 b - 20 + a = 8 b + a = 28
Country A and Country B will form a joint committee on economic policy. The committee is to have exactly 6 members. 5 candidates for the committee come from Country A and 6 from Country B. If at least 3 members of the committee must come from Country A, how many district committees are possible?
281 (pg. 7) First possibility: 5 from A, 1 from B 5C5= 1 6C1= 6 6 X 1 = 6 Second possibility: 4 from A, 2 from B 5C4=5 6C2=15 15 X 5 = 75 Third possibility: 3 from A, 3 from B 5C3=10 6C3=20 20 X 10 = 200 200 + 75 + 6 = 281
Ava, a peripatetic day laborer, never failed to make __________ decisions; she believed in neither deliberation nor prudence when confronted with various choices. a. paradoxical b. ignoble c. headlong d. undemonstrative e. unctuous
a. paradoxical In the sentence, the word 'peripatetic' - means wandering - is not vital to the blank. The final clause of the sentence is the clue that that Ava was not wise or careful when it came to making decisions. (C), headlong, fits the meaning of 'not wise'. (B) is too extreme and negative to fit in this sentence. (D) and (E) are out of scope since we know neither Ava's emotional state or interaction with others. Deliberate and prudent are similar - therefore, (A) is an opposite wrong answer choice since paradoxical would require opposing or conflicting events. ignoble-dishonorable headlong-without forethought; careless undemonstrative-emotionless unctuous-insincere flattering
x - y + z = 04x + y + 5z = 0If z ≠ 0, then in the system of equations given, what is the ratio of x to z equal to?
-6/5 (pg. 17) Add the two equations together and solve for x/z
If y = 2x and z = 4y, then in terms of x, y + z =
10x (pg. 16) We know that y = 2x and z = 4y.Since z = 4y we need to plug in what we know for y: z = 4(2x) = 8x.Plugging all of this into the equation, we get 2x +8x = 10x.
The 1999 hot dog eating champion averaged 25 bites every 20 seconds. At this rate approximately how many bites would she take in 90 seconds?
113 (pg. 15) set up ratio: 25 bites/20 sec = x bites/90 sec solve for x x = 112.5 --> 113
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?
12 (pg. 15) There are two pairs of jeans with different prices. Because the question asks for the greatest number of pairs of jeans that can be bought, Chris wants to buy as many of the cheaper pairs as he can. The most pairs that can be bought with $560 would be $560/45 = 12.44, so 12 is the most that can be bought. Notice that Chris could also buy 11 pairs of $45 jeans and 1 pair of $65 jeans, for a total of 12 pairs costing $560.
A student's score on the final test in a certain course was 60% greater than the average (arithmetic mean) score of the 2 other tests the student took in the course. The student's score on the final test was what percent of the student's average test score for the entire course?
133 1/3 % (pg. 13) pick random numbers, say that the person scored 100 both times on tests (100 + 100 + 160)/3 = 120 (mean of all three tests) 160/120 = 1.33% = 133 1/3 %
At a certain pet show, exactly 6 dogs are entered in the beagle division and exactly 6 are entered in the dalmatian division. If the top 3 dogs in each division receive first-, second-, and third-place ribbons respectively, with no other dogs receiving a prize, how many different ways can ribbons be awarded to winners in the two divisions together?
14, 400 (pg. 13) beagles: 6 * 5 * 4 = 120 dalmations: 6 * 5 * 4 = 120 120 * 120 = 14,400
The average (arithmetic mean) of 5 positive numbers is 8. If the average of 4 of these numbers is 5.5, what is the value of the other number?
18 (pg. 15) Use formula: sum of terms./number of terms = mean w + x + y + z/4 =5.5 w + x + y + z = 22 v + w + x + y + z/5 = 8 v + w + x + y + z = 40 40 - 22 = 18
An author received $540 in royalties for sales of her book during its first month of publication. If 200 more copies had been sold during this time, she would have received $60 more in royalties. How many copies of the book sold during its first month of publication?
1800 (pg. 12) royalty per book: 60/200 = .30 540/.30 = 1800
A promoter is organizing an opera concert. Ten singers are available for the program: 3 sopranos, 3 mezzos, 2 tenors and 2 baritones. If the promoter intends every segment to be a duet by performers with different vocal ranges, how many pairings of performers are possible?
37 (pg. 16) The correct answer is 37. The question asks us to figure out all the ways we can combine one singer with another singer who has a different vocal range. That means matching the sopranos with the mezzos, with the tenors, and with the baritones. Then we'd match the mezzos with the tenors and the baritones. Finally, we'd match the tenors with the baritones. So there are 3 sopranos and 3 mezzos, which makes 3 x 3 = 9 possible pairs of soprano/mezzo. 3 sopranos and 2 tenors = 6 pairs. 3 sopranos and 2 baritones = 6 pairs. 3 mezzos and 2 tenors = 6 pairs. 3 mezzos and 2 baritones = 6 pairs. 2 tenors and 2 baritones = 4 pairs. So that's 9 + 6 + 6 + 6 + 6 + 4 = 37. A quicker way to solve this would be to use the combinations formula to find the total number of ways to choose 2 singers from a group of 10 (10C2 = 10!/(2!8!) = (10 x 9)/(2 x 1) = 90/2 = 45) and then subtract the combinations included in that number that involve two singers from the same vocal range: there are 3 ways to combine 2 sopranos, 3 ways to combine 2 mezzos, 1 possible pair of baritones, and 1 possible pair of tenors. 45 - 3 - 3 - 1 - 1 = 37.
If w= -5, what is the value of the expression 12 - 3w + w^2 ?
52 (pg. 9) 12 - 3(-5) + (-5 * -5) = 52
The buyer of a certain robotic toy must choose 3 of 5 optional motions and 5 of 6 optional accessories. How many different combinations of motions and accessories are available to the buyer?
60 (pg. 14) Use combinations formula: 5C3 = 5!/(3! * (5-3)!) = 120/12 = 10 6C5 = 6!/(5! * (6-5)!) = 720/120 = 6 6 * 10 =60
In the figure, AD || BC. What is the perimeter of quadrilateral ABCD? (see pg. 10)
620 (see page 10, number 22) We're given the lengths of three of the four sides of ABCD; all we need to find is the length of side AD, and then we'll be able to find the perimeter. If we drop a perpendicular line segment from point C to side AD and call the point where this perpendicular line segment meets side AD point E, we divide the figure into rectangle ABCE and right triangle CDE. Since ABCE is a rectangle, AE has the same length as BC, 250. Similarly, EC has the same length as AB, 40. We can now find the length of ED: it is a leg of a right triangle with hypotenuse 50 and other leg 40. This is just 10 times as big as a 3:4:5 right triangle; therefore, ED must have a length of 10 3, or 30. So AD, which is AE + ED, is 250 + 30, or 280. Now we can find the perimeter: 280 + 40 + 250 + 50 = 620
Alice and David are two of the ten people in a group. In how many different ways can this group of 10 people be divided into a group of 7 people and a group of 3 people if Alice and David are to be in the same group?
64 (pg. 14) For the group of 3, David and Alice will take two of those spots, so only one more person can be in that group. Since there are 8 people left, each of the eight people could possibly be in the group, so there are 8 possibilities for the group of 3. For the group of 7, there are 5 spots left for the 8 people in the group to fill. Use 8C5 formula: 8C5 = 8!/(5!(8-3!)) = 40,320/720 = 56 Add the two combinations together: 56 + 8 = 64
A certain collector sold 5/8 of her paintings, including 2/3 of her Impressionist paintings. If 3/5 of her paintings were Impressionist, what fraction of the paintings that were not sold were Impressionist?
8/15 (pg.4) This question has an unknown quantity (the total number of paintings) and a number of different painting 'categories' (sold/not sold, Impressionist/not Impressionist) so picking numbers is the best approach. Using 120 (8 x 3 x 5 = 120) to represent the total number of paintings, we can get the following quantities from the question stem: Total paintings sold: 5/8 * 120 =75 Total Impressionist paintings: 3/5 * 120=72 Total Impressionist paintings sold: 2/3 * 72 =48 72-48= 24 Impressionist paintings not sold 120-75= 45 total paintings not sold 24/45 = 8/15
If (3x⁄4 - 2)^2 = 0, then x =
8/3 (pg.18) Solve for x
The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 50 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
80% (pg. 5) length of one side of square A= A length of one side of square B= 2A length of one side of square C= 2A + 1/2(2A) = 3A Area of Square A= A * A = A^2 Area of Square B= 2A * 2A = 4A^2 Area of Square C= 3A * 3A = 9A^2 A^2 + 4A^2 > 9A^2 5A^2 > 9A^2 5 > 9 (9-5)/5 * 100 = 80%
While the student considered biology an exciting subject, he found the lectures in his classes to be ____________. a. tedious b. exhilarating c. impassive d. erudite e. menacing
a. tedious (dull) impassive-not feeling erudite-learned menacing-threatening
A certain school has 50 students assigned randomly to 5 distinct classes, and each student is assigned to only one class. If the quantities of students in the 5 classes are consecutive numbers, what is the probability that a given student is in one of the two largest classes? a. 48% b. 46% c. 42% d. 38% e. 34%
b. 46% (pg. 4) The key to this problem is the fact that the numbers of students in the classes are consecutive. Whenever you see "consecutive" in a math problem, it's there for a specific reason. It tells you that each number in the series is separated from the next by a fixed amount. Consecutive integers are separated by 1, consecutive even integers by 2, etc. So here we know that if we add up all the classes, we'll get 50 students. We also know that the numbers of students in the classes are separated by 1. So, let's call the smallest class x. The next largest class would be x + 1, then x + 2, x + 3 and x + 4. If we added these up, we'd get 5x + 10 = 50. Now we can solve for x: subtract 10 from both sides to get 5x = 40; divide both sides by 5 to get x = 8. So the smallest class has 8 students and the two largest classes then will have 8 + 3 and 8 + 4 students respectively, which gives us a total of 23 students in the two largest classes. 23/50 x 100 = 46%
There are people at a dance, where x is an integer greater than 1. The number of different pairs of people who can be partnered up for the waltz is z. Which of the following could be the value of z? a. 2 b. 6 c. 9 d. 14 e. 20
b. 6 (pg.2) This is a combination question: apply the combinations formula
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word? a. 15 b. 60 c. 90 d. 120 e. 240
b. 60 (pg.2) 5!/(5-3)! 5!/2!=60
It seemed they were never in similar moods; when she was content, he was dissatisfied, and when she was sullen, he was _________. a. spiteful b. boisterous c. dour d. inquisitive e. ponderous
b. boisterous
Connoisseurs gather -------- knowledge on a single subject. a. scant b. copious c. spurious d. peculiar e. arcane
b. copious
The modern novel is not only the _____ of the epic, but it has also despoiled drama, the lyrics and the oration that are part of its inheritance. a. sister b. heir c. forerunner d. predecessor e. descendant
b. heir
If two integers between -5 and 3, inclusive, are chosen at random, which of the following is most likely to be true? a. The sum of the two integers is even b. The sum of the two integers is odd c. The product of the two integers is even d. The product of the two integers is odd e. The product of the two integers is negative
c. The product of the two integers is even (pg. 11) a. even sum: need either 2 even or 2 odd 2 even: 4/9 * 4/9 = 16/81 2 odd: 5/9 * 5/9 = 25/81 16/81 + 25/81 = 41/81 b. odd sum = 1 - 41/81 = 40/81 c. all we need is an even number 1- 25/81 = 56/81 d. two odds: 5/9 * 5/9 = 25/81 e. neg and pos or pos and negative 3/9 * 5/9 = 15/81 15/81 + 15/81 = 30/81 greatest value is C
Just as the Elizabethan _____ thought little of Shakespeare because he failed to follow in the footsteps of the great Greeks, some modern critics dislike the best work of the dramatists of our own time, because they are not cast in the Shakespearean mold. a. experts b. audiences c. reviewers d. directors e. pundits
c. reviewers pundits= experts
One business partner was parsimonious while the other was ________, but they were very successful in working together. a. prolix b. obstreperous c. spendthrift d. dictatorial e. energetic
c. spendthrift prolix=wordy obstreperous=uncontrollable spendthrift=irresponsible with money dictatorial=ruler energetic=lively
A coin is tossed and a six-sided die is rolled in a game. If Marie gets heads and an even number, she will advance to the second round. In the second round, she will again toss the coin and roll the die. If she gets tails and an odd number she will advance to the third round. What is the probability that she will not advance to the third round? a. 1/32 b. 1/16 c. 9/16 d. 15/16 e. cannot be determined
d. 15/16 (pg. 3) Let's look at each round. The probability of getting heads is 1/2 and the probability of rolling an even number is 1/2. Therefore the probability of advancing to the second round is: 1/2 * 1/2 = 1/4 For the second round, the probability will be the same even though the desired outcome is different (tails instead of heads and odds instead of evens), because there are only two sides to a coin, and the probability of rolling an odd number on a six-sided die is the same as rolling an even. Therefore the probability of advance to the third round is also: 1/2 * 1/2 = 1/4 To find the probability of advancing through the first round to the second and advancing from the second to the third, we multiply: 1/4 * 1/4 = 1/16 The probability that an event will not occur is the probability that it will occur subtracted from 1. 1 - 1/16 = 15/16
At an art gallery, there are 7 spaces to hang 14 paintings. The 14 paintings to choose from are: three by Cezanne, three by Monet, one by Renoir, two by Van Gogh, two by Pissarro, two by Degas, and one by Manet. The even-numbered spaces must hold either a Cezanne or a Monet. The first space must hold a Renoir. The fifth space must hold a Manet, and the remaining spaces must hold either a Van Gogh, a Pissarro, or a Degas. How many unique arrangements of paintings are possible? a.28 b.72 c.1200 d.3600 e.7776
d. 3600 (pg. 3) Space 1: must be the Renoir (one option) Space 2: must be either a Cezanne or Monet (two painters x three paintings each = 6 options) Space 3: must be a Van Gogh, Pissarro, or Degas (three painters x two paintings each = 6 options) Space 4: must be a Cezanne or Monet (only 5 options remain, since we used one for Space 2) Space 5: must be the Manet (one option) Space 6: must be either a Cezanne or Monet (only 4 options remain, since we used two options already for Spaces 2 and 4) Space 7: must be a Van Gogh, Pissarro, or Degas (only 5 options remains, since we used one for Space 3). To summarize our options: Space 1: 1 Space 2: 6 Space 3: 6 Space 4: 5 Space 5: 1 Space 6: 4 Space 7: 5 Now let's multiply all of the options for each space together to find the total number of options. 1 x 6 x 6 x 5 x 1 x 4 x 5=3600
In how many ways can the letters in the name BELLA be arranged? a. 5 b. 15 c. 30 d. 60 e. 120
d. 60 (pg.1) We would usually solve a question like this as we would any other permutation--by using factorial (!). However, we need to keep in mind that the letter "L" occurs twice in the word. If we consider L1 and L2 separately, we will have some overlap in our arrangements: B - E - L1 - L2 - A is considered the same arrangement as B - E - L2 - L1 - A. In a permutation question involving indistinguishable elements, we divide the factorial for the total number of letters in the word and then divide it by the product of the factorials of each of the indistinguishable elements. Therefore the answer is: 5!/2! = 60
He was constantly haunted by his own self-defeating impulses and tendency toward capriciousness, and could not escape his downward spiral into utter _______ as his time, energy, and resources were squandered on useless pursuits. a. guile b. encomium c. magnanimity d. dissipation e. deference
d. dissipation - wasteful spending a. guile - skillful deceit b. encomium - formal praise c. magnanimity - generosity e. deference - respectful submission
This hotel chain has a reputation of luxury, but despite its ____________ name, it offers fewer amenities than hotels that charge half its price. a. dubious b. bargaining c. questionable d. illustrious e. quintessential
d. illustrious
The three sides of a triangle measure x - 2, x + 1, and x + 2. Which of the following could x not equal? a. 19 b. 17 c. 8 d. 4 e. 3
e. 3 (pg. 8) In a triangle length of one side < sum of lengths of any 2 sides length of one side > posi diffs of lengths of other 2 sides sides of E. are 1, 4, 5 5-4= 1 = 1
If a square parking lot has an area of z, what is the longest distance on a straight line that a car could drive on the lot?
square root of 2z (pg. 6) length of one side of square is square root of z ratio of a 45:45:90 triangle is x:x:x * 2^1/2 multiply square root of z by square root of 2
