Erroneas 2

B ojo, x no puede ser 0 NI 1 Por lo tanto sólo puede ser -1.

(1-x)/(x-1)=(1/x) Column A x Column B -1/2

D

(x+3)(y-4)=0 A xy B -12

D

0<x<y<1 A 1-y B y-x

120

30 ipods were up for sale at the local electronic store. The store owner sold the first 20 ipods for at least $15 and he sold the next 9 ipods for at least $20. If the owner made a total revenue of $600 by selling these 30 ipods, how much must he have sold the last ipod for?

B Ojo que 950 es casi 10^3 (estas aproximaciones sirven)

A 950^2000 B 10^6000

C amount of concentration 3 weight 5 barium chloride % grams grams original 30% x 0.30x water 0% 10 0 new 20% 10 1 x 0.30x Let x 5 number of grams of original solution. Total weight and amounts of barium chloride may be added by column. (20%) 3 (10 1 x) 5 0.30x, so 10 1 x 5 1.50x, x 5 20.

A 30% solution of barium chloride is mixed with 10 grams of water to form a 20% solution. How many grams were in the original solution? (A) 10 (B) 15 (C) 20 (D) 25 (E) 30

D Let r 5 loaded rate; then 2r 5 empty rate. Total time 5 r r 8 20 3 + 1 +10 = hours. Multiplying by 3r on both sides, we get 90 5 23r, so r 5 90 4 23, or about 3.9 miles per hour. However, the problem asks for the speed when empty, which is 2r, or 7.8. This is less than 8 mph, but not less than 6 mph.

A barge travels twice as fast when it is empty as when it is full. If it travels 20 miles north with a cargo, spends 20 minutes unloading, and returns to its original port empty, taking 8 hours to complete the entire trip, what is the speed of the barge when it is empty? (A) less than 3 mph (B) less than 4 mph but not less than 3 mph (C) less than 6 mph but not less than 4 mph (D) less than 8 mph but not less than 6 mph (E) 8 mph or more

R= 18 If the beggar can make a whole cigarette from 8 butts then he can make 16 cigarettes from the 128 he found. But it doesn't end here. That is the trick in this problem. We've been asked to find the 'maximum' number. Once he smokes those 16, he will in turn have another 16 butts, which gives him enough to make another 2 cigarettes. Hence, he smokes a total of 18 cigarettes. The correct answer choice is C.

A beggar on the street can make one cigarette out of every 8 cigarette butts he finds on the streets. At the end of the day, the beggar manages to find a total of 128 cigarette butts. What is the maximum number of cigarettes that he can make and smoke from all the butts he found? 12 16 18 20 24

C Let h 5 time to travel downstream. Let r 5 speed of the boat in still water. Since the two trips cover the same distance, we can write the equation: h(r 1 3) 5 2h(r 2 3). Dividing by h, r 1 3 5 2r 2 6, so r 5 9.

A certain river has a current of 3 miles per hour. A boat takes twice as long to travel upstream between two points as it does to travel downstream between the same two points. What is the speed of the boat in still water? (A) 3 miles per hour (B) 6 miles per hour (C) 9 miles per hour (D) 12 miles per hour (E) The speed cannot be determined from the given information.

35

A desert outpost has a water supply that is sufficient to last 21 days for 15 people. How many days will it last for 9 people? 28 32.5 35 37.5 42

6 el área del marco es el area grande menos el área de la picture

A flat rectangular picture, represented by the unshaded region in the figure, is mounted in a flat rectangular frame, represented by the shaded regions. The frame is 1 inche wide on all sides. For what value of x, in inches, is the area of the frame equal to the area of the picture? 4 5 6 7 8

B Recordar que en una distr. normal, el 95% de la proba se encuentra a +-2 desviaciones estandar

A random variable Y is normally distributed with a mean of 200 and a standard deviation of 10. Quantity A The probability of the event that the value of Y is greater than 220 Quantity B 1/6

115 Hay que considerar 3 casos: 4 biographies and no novels; 3 biographies and 1 novel; 2 biographies and 2 novels. a) sòlo una forma (4C4)=1 b) 4C3 x 6C1= 24 c) 4C2 x 6x2= 90

A reading list for a huminaties course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How may selections of 4 books satisfy the requirements? 90 115 130 144 195

A, C si es rectangulo no sabes cual es la hip

AB = 8, BC=6 Which of the following statements individually provide sufficient information to calculate the area of triangle ABC? The perimeter of the triangle is 24 ABC is a right triangle Angle C is 90 degrees

E recordar que t porciento se escribe como t/100

Alice earns d dollarsa and has t percent of what she earns deducted for taxes. How much of what she earns does Alice have left after taxes? d(1-100t) dollars d(1-10t) dollars d(1-t) dollars d(1-.1t) dollars d(1-.01t)dollars

C Ojo! no me dice que 9000 son estudiantes. Sea z el numero de pesonas que van al juego que NO son estudiantes.

Among the 9000 people attending a football game at college C, there were x students from college C and y students who were not from college C. A the number of people attending the game who were not students B 9000-x-y

A, B, E Dice que Py Q pueden ser iguales... no me convence tanto.

Both P and Q are positive numbers, and S is a negative number. Which of the following fractions could be undefined? P/(Q + S) Q/(P + S) S/(P + Q) Q/(S − P) S/(P − Q)

A para cada opcion tengo 2 opciones (sí o no) entonces tendría 2^6=32

Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control. Column A Number of different combinations possible Column B 25

B

Column A 45/3^4 x 4^3/5^2 x 27/8^2 Column B 3^2/4^3 x 48/5^2 x 75/3^3

D Standard deviation is a measure of how far or near the data in a set is spread around its mean. Though the sets in Quantity A and Quantity B have the same range, they may or may not have the same spread. The tricky in this question is to notice that the number of elements in the set in Quantity B is defined. We can find the standard deviation of the set because we know there are 7 elements and each element in 2 points away from each other. Whereas, the set in Quantity A can have just 2 elements or can have 100 elements to. The standard deviation therefore could be as close to its mean or as far from it as it could be.

Column A The standard deviation of a set of numbers whose range is 12 Column B The standard deviation of a set of numbers which consists of 7 consecutive multiples of 2

25 This is a tricky question. On the chart, male students are represented by the light gray bars. To answer this question, you will need to find the total number of student enrolled in each program. 500 male students are enrolled in civil engineering program. 250 male students are enrolled in chemical engineering program. 400 male students are enrolled in computers engineering program. 300 male students are enrolled in electronics engineering program. 375 male students are enrolled in mechanical engineering program. 50 male students are enrolled in nuclear energy engineering program. The total number of student enrolled is therefore, 500+250+400+300+375+50=1875 male students enrolled at Medwin University. But the total number of male students given in the question is 1850 which is 25 less than what we just found by counting students enrolled at individual programs. The reason for this difference is due to the dual degree program. The students who enrolled for the dual degree program are in the list of both students at mechanical engineering and chemical engineering. They are essentially counted twice. So, the number of male students enrolled on the mechanical and civil dual degree program is 25. The correct answer is B.

Each student belong to only one of the departments at Medwin University EXCEPT those who enrolled for a dual degree program in both mechanical and civil engineering. If there are a total of 1850 male students at Medwin University, how many male students are enrolled on both mechanical and civil engineering dual degree program? 0 25 75 125 Cannot be determined

1/35 si tengo 8 puntos y escojo 4 para hacer un cuadrilátero, entonces todos los cuadrílateros posibles son 8C4 =70. De esos 70, sólo 2 son cuadrados, por lo tanto 2/70 = 1/35 (ojo! la clave es que ya estamos hablando de cuadrados)

Eight points are equally spaced on a circle. If 4 of the 8 points are to be chosen at random, what is the probability that a quadrilateral havin the 4 points chose as vertices will be a square? 1/70 1/35 1/7 1/4 1/2

72

Eustace is three years older than Muriel. When they got married 40 years ago, the difference of twice of Eustace's age from thrice of Muriel's age was 16. How old will Muriel be when they celebrate their 50th anniversary? 66 70 72 75 78

B,C Question 1 of 1 If -1 < x < 1 and x is non-zero, which of the following inequalities must be true? Indicate two such statements. C'mon, champ! You can do better! Solution: Since x lies between -1 and 1, and x≠0 , clearly x must be a fractional value and x must be either a positive or a negative number but not a zero. Knowing this, let's solve each answer choice one at a time. x5<x . Remember that when a positive fractional number is raised to a positive exponent, its value decreases. For example, (12)5=132, which is less than ½. But when the fractional number is negative and is raised to a positive odd exponent, its value increases. For example, (−12)5=−132 which is in fact greater than -1/2. So, we cannot say if x5<x and hence answer choice A is incorrect. x2<|x| . This statement removes negative signs altogether and it is pretty easy. If a fractional number is raised to an even power, then it will always be less than its absolute value. For example, (12)2=14 which is less than ∣∣12∣∣ which is just 12. But (−12)2=14 as well. Therefore, answer choice B is correct. x10−x11>x9−x8 . To solve this, it is better if you don't pick numbers because if you do, then you will need to raise those numbers to their 11th power. It will be much quicker to solve this algebraically. First, we need to rearrange the terms in the inequality by getting like terms on the same side i.e. even exponents with even exponents and odds with odds which gives us x10+x8>x9+x11. By factoring out the common terms, we get x8(x2+1)>x9(1+x2). Since x2 is positive, x2+1 must be positive too and so we can cancel them out. We now have x8>x9. By factoring out x6 on both sides, we get x6×x2>x6×x3. Again, since x6 has an even exponent, we can cancel it out to give us x2>x3. This is indeed true, because if x is negative, then x2 would be larger than x3 as x2 would be positive and x3 would be negative. If x is positive, then it is more evident. The x3 would be much smaller than x2 , as x is a fractional value. Therefore, B and C are correct.

If -1 < x < 1 and x is non-zero, which of the following inequalities must be true? Indicate two such statements. x^5<x x^2<|x| x^10-x^11>x^9-x^8

15x

If 1+x+x2+x3=60, then the average (arithmetic mean) of x, x2, x3 and x4 is equal to which of the following? 12x 15x 20x 30x 60x

two! Convertir todo en (algo/10^x)

If 1/[(2^11)(5^17)] is expressed as a terminating decimal, how many nonzero digits will the decimal have? one two four six eleven

840 si K es divisible entonces debe incluir 1 2 3 4=2x2 (ya teníamos un 2, sólo falta otro dos) 5 6= 2x3 (ya tenemos un 2 y un 3) 7 8=2x2x2 (nos falta un 2) Al final 1x2x3x2x5x7x2

If K is the least positive integer that is divisible by every integer from 1 to 8 inclusive, then K = 840 2,520 6,720 20,160 40,320

21, 56

If X and Y are two positive integers each with atmost two-digits and both have the same digits, but in reverse order, then which of the following CANNOT be the difference between X and Y? 9 21 27 56 72

13/30

If a two digit number is chosen at random out of all possible positive two digit numbers, what is the probability that either the number or one of its neighbors is divisible by 7? 1/7 13/90 26/90 3/7 13/30

-pq Esa raíz tiene que ser positiva. Entonces se parece al valor absoluto This is a tricky question. Since the given expression is the square root of a positive number, we must be looking for a positive number, something similar to |pq| and the usual tendency here is to choose pq as the correct answer because we want a positive number and pq appears to be positive. BUT it is incorrect to assume that pq is a positive number and that -pq is a negative number. In fact, if p < 0 and q > 0, then -p will be positive. (since p is a negative number, -(negative number) = positive number) Therefore, in this case, -p > 0 and q > 0. So, -pq > 0 and the correct answer is B. Note to understand why the other answer choices are incorrect: We can directly eliminate answer choices A, C and D as they are all negative. A. -|pq| is negative because it can be written as -1 x |pq| and |pq| is always positive. Negative times positive is negative. C. pq is negative too because p < 0 and q > 0. Again the same rule applies here: Negative times positive is negative. D. p|q| is negative too because p < 0 and |q| is positive. Same rule here as well.

If p < 0 and q > 0, then what is the value of sqrt(p2q2)−−−−−√? -|pq| -pq pq p|q| Cannot be determined

30%

If the box pictured to the right is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C? 10% 20% 30% 40% 50%

x+2y

If x and y are integers and x=50y+69 which of the following must be odd xy x+y x+2y 3x-1 3x+1

B, C; D

If x, y and z are positive numbers such that 3x<2y< 4z, which of the following statements could be true? x=y y=z y>z x>z

E

If x<y<0, which of the following inequalities must be true? y+1<x y-1<x xy2<x xy<y2 xy<x2

B triángulo 30-60-90

In a triangle, BC = 2AB Quantity A Length of side AB Quantity B Length of side AC

231 The number of ways in which 5 vehicles can be chosen from a total of (7+3=10) vehicles is: 10C5=10!5!5!=(10)(9)(8)(7)(6)5!=252 . The number of ways in which NO truck is chosen (that is, all chosen vehicles are buses) is: 7C5 = 7!/5!2! = ((7)(6))/2 = 21 ways. So the number of ways in which the 5 vehicles can be chosen such that at least one vehicle is a truck is 252 − 21 = 231.

In how many ways can a convoy of 5 buses and trucks be formed such that at least one truck is chosen out of 7 buses and 3 trucks available?

18 The 3 vowels and 3 consonants are to be placed together. So treat the 3 vowels as one block and the 3 consonants as one block. There are 3! ways to arrange the 3 vowels, but as there are 2 O's, the actual number of different ways of arranging the 3 vowels is 3!2!=3 . Likewise, because there are 2 T's, the actual number of ways of arranging the 3 consonants is 3!2!=3 . The two blocks of consonants and vowels can be arranged in 2! = 2 ways.Thus, there are a total of(3)(3)(2) = 18 ways to arrange the letters such that the vowels and consonants are placed next to each other. The correct answer is B.

In how many ways can the word TOYOTA be arranged such that all vowels and all consonants are together? 12 18 36 72 144

B Ojo, todo son radios!

In the figure, O and P are the centers of two circles. If each circle has radius r, what is the area of the shaded region? sq(2)r^2/2 sq(3)r^2/2 sq(2)r^2 sq(3)r^2 2sq(3)r^2

90

In the first half of last year, a team won 60 percent of the games it played. In the second half of the year, the team played 20 games winning 3 of them. If the team won 50% of the games it played last year, what was the total number of games the team played? 60 70 80 90 100

100/101

In the sequence a1, a2,....,a100, the kth therm is defined by ak=1/k - (1/k+1) for all integers k from 1 to 100. What is the sum of the 100 terms of this sequence? 1/10,100 1/101 1/100 100/101 1

19

In the sequence a1,a2,a3,....an,... each term after the first term is equal to the preceding term plus the constant c. If a1+a3+a5=27, what is the value of a2+a4?

A, B, C

In the xy-plane, line k is aline that does NOT pass through the origin. Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line k is negative? Indicate all such statements A) the x intercept of linke k is twice the y intercept of line k B) the product of the x intercept and the y intercept of line k is positive C) line k passes through the points (a,b) and (r,s), where (a-r)(b-s)<0

32/3 The problem asks for the time for Noreen to finish the job alone. If we let N be the time for Noreen to finish the job, then it will take Dayle 3N to finish the job. Given that they can finish the job in 8 hours if they work together, we can write the equation: 1N+13N=18 Solving for N, we have: 3+13N=18 43N=18 N=323 Therefore, Noreen can do the job in323 hours if she works alone. The correct answer is A.

It takes Dayle thrice as long as Noreen to do a certain piece of work. Working together, they can finish the work in 8 hours. How long would it take Noreen to do it alone? 32/3 32 24 3/32 16

200

Jennifer has $400 more than Brian has. If she were to give Brian 20% of her money, then Brian would have 2/3 of the amount of money that Jennifer would then have. How much money does Brian currently have (before exchanging money)?

6.25% Leer bien exactly on the hour

Jim's dog, Tucker, eats every hour on the hour (when the time on the clock reads an exact hour) and eats exactly half of the number of dog food pellets in his bowl. If Jim fills Tucker's bowl at 7:30 a.m. with 80 dog food pellets, what percent of the original 80 pellets will there be in Tucker's bowl at 11:30 a.m. of the same day? 2.75% 3.125% 6.25% 12.5% 20%

52 Perhaps the easiest way to solve this problem is to create variables (say, J, K and L) to represent the ages of the birthday celebrants, then express the combined age of the celebrants (J + K + L) in terms of one variable only. Since Joan is 2 years younger than Kylie, J = K - 2. Also, since Kylie is 3 years older than Lillian, K = L + 3. Next, solve for each celebrant's age in terms of one variable: J = K - 2 K = J + 2 K = L + 3 (J + 2) = L + 3 L = J - 1 Therefore, the expression for the sum of the celebrants' ages (J + K + L) can be written as J + (J + 2) + (J - 1). This simplifies to 3J + 1. How does this help? Well, since J must be an integer, the correct answer must be one greater than a multiple of 3. Only choice C, 52, fits this description, since 52 = 17 × 3 + 1. As a double-check, you can confirm that if Joan is 17, then Kylie is 19 and Lillian is 16. 17 + 19 + 16 = 52. The correct answer is thus C.

Joan, Kylie and Lillian all celebrate their birthdays today. Joan is 2 years younger than Kylie, and Kylie is 3 years older than Lillian. Which of the following could be the combined age of all three birthday celebrants today? 50 51 52 53 54

12 y 36 Ojo que me piden los divisores de n, pero estoy sacando el mcm de las n^2 (entonces al 2^3*3^3, sacarle la raíz para tener 2^2* 3^2)

Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S? 12 24 36 72

306/380

Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2lightbulbs simultaneously and at random from the box. Wha t is the probability that neither of the lightbubls selected will be defective? Give your answer as a fraction

0.7 (580/700)(579/699)

Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that NEITHER of the members selected will be a lawyer? 0.5 0.6 0.7 0.8 0.9

22.5 (ojo con el 1/10!)

One pipe can fill a pool 0.25 times faster than another pipe. But when both pipes are used, they fill the pool in ten hours. How long would it take to fill the pool if only the slower pipe is used?

5

Points W, X, Y and Z are on a line, not nec. in that order. The distance between W and X is 2, the distance between X and Y is 4, and the distance between Y and Z is 9. Which of the following could be the distance between X and Z 3 5 7 9 11

C

Quantity A (0.25)-3 Quantity B 1/(2^-6)

A Let p 5 number of pennies n 5 number of nickels d 5 number of dimes q 5 number of quarters Total number of coins 5 p 1 n 1 d 1 q 5 12. Total value 5 p 1 5n 1 10d 1 25q 5 145. Now, if q 5 1, then p 1 n 1 d 5 11, p 1 5n 1 10d 5 120. But in this case, the greatest possible value of the other eleven coins would be the value of eleven dimes, or 110 cents, which falls short of the amount necessary to give a total of 145 cents for the twelve coins put together. Therefore, Robert cannot have only one quarter.

Robert has 12 coins totaling $1.45. None of his coins is larger than a quarter. Which of the following cannot be the number of quarters he has? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

C!

Set S consist of all positive integers less than 81 that are NOT equal to the square of a integer A the number of integeres in set S B 72

A igualar distancias!

Steve is running a marathon from point A to point B. 30 minutes after he starts running, his friend Barney who runs 1 mile per hour slower than twice Steve's rate, starts from the same point and follows the same path. Barney overtakes Steve in 3 hours. Column A Distance covered by Barney before overtaking Steve. Column B 4 miles

A y B If v is the square of an integer, then sq(v) is an integer. You can use this fact, togheter with the fact that the product and the sum of integers are also integers to examine the first two choices: Choice A: the square root of 81v is 9sq(v), which is an integer. So 81v is the square of an integer. ... y así.

The integer v is greater than 1. If v is the square of an integer, which of the following numbers must also be the square of an integer? indicate all 81v 25v+10sqrt(v)+1 4v^2+4sqr(v)+1

50 Un INSCRIBED square tiene que tocar todos los lados del otro cuadrado.

The perimeter of square S is 40. Square T is inscribed in square S. What is the least possible area of square T 45 48 49 50 52

A

The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches. Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class? A) the tallest male student in the clasee is 5.8 inches taller than the tallest female student in the class B) the median height of the male studnets in the class is 1.1 inches grater than the median height of the female students in the class. C) the average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.

B Hacer los primeros y luego llegar a una formaula con el patròn que se forma

The sequence of numbers a1,a2,a3,...an,... is defined by an=1/n-1/(n+2), for each integer n>=1. What is the sum of the first 20 terms of this sequence? (1+1/2)-1/20 (1+1/2)-(1/21+1/22) 1-(1/20+1/22) 1-1/22 1/20-1/22

C only Ojo, llegar a la ecuación 7.00<1.04x<100

The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3. Which of the following statements MUST be true? Select all that apply A) The price of the book was less than 9.50 B) The price of the book was greater than 6.90 C) The sales tax was less than 0.45

It should be clear that this is a permutations problem with repetitions. With 13 elements to arrange, the number of permutations would be 13! If there were no repetitions. As Hank cannot tell the difference between one horse and another and one cow and another, we may treat the cows and horses as repeated elements. We will call the cows all c and since there are 10 cows, c = 10. There are 3 horses and hence h = 3. Now, the number of permutations is n!c!×h! Substituting our values we get 13!10!×3! which can be written as 13×12×113×2×1=13×2×11=286

There are thirteen animals in Bob's possession of which 10 are cows and three are horses. How many ways can Hank, Bob's best friend, arrange these animals provided that Hank cannot tell the difference between any two cows or any two horses but he can tell the difference between a cow and a horse? 13 30 286 1716 21772880

C

Three circles with their centers on line segment PQ are tangent at points P, R and Q, where point R lies on line segment PQ A The circumference of the largest circle B The sum of the circumference of the two smaller circles

B (30 segundos)

Tom and Bill agreed to race across a 50-foot pool and back again. They started together, but Tom finished 10 feet ahead of Bill. If their rates were constant, and Tom finished the race in 27 seconds, how long did Bill take to finish it? (A) 28 seconds (B) 30 seconds (C) 33 3 1 seconds (D) 35 seconds (E) 37 seconds

1

What is the 26th digit to the right of the decimal point in the decimal form of 1/99? 0 1 3 5 7 9

58 26 sí es un factor de 25 porque se puede escribir como 13x2. 28= 14x2 36=9x4 56=8x7 58=2x29 (esta es!)

What is the least positive integer that is NOT a factor of 25! and is not a primer number? 26 28 36 56 58

5/16 64 outcomes 6C3 heads= 20

When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads? 1/4 1/3 5/16 31/64 1/2

A y B Ojo que tambièn la pendiente infinita es positiva

Which of the following could be the x-intercept of a certain line if its slope is positive and its y-intercept is 3? -3 0 3

B, D poner todo en 2^x

Which of the following is equal to 8^24? Indicate all possible values. 2^96 4^36 12^12 16^18 24^8 32^15

3/(b-b^2) 5b-15 2+1/(2-b) Probar cada uno!

Which of the following must increase as b increases from 234 to 235? 3/(b-b^2) 5b-15 2+1/(2-b)

162 Cuando la distancia es la misma, lo màs fàcil es igualar la distancia (porque es igual, y sólo hago el tiempo total la diferencia de uno y otro)

While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town? 138 148 150 162 168

C

X is the set of all integers n that satisfy the inequality 2<=|n|<=5 A The absolute value of the greatest integer in X B The absolute value of the least integer in X

D

XXXXXb and c are positive integers. Column A 1/a+1/b+1/c Column B abc/(ab+bc+ac)

B

column A lenght of segment AC Columb B 3

D

n5 - n3 < 0 Quantity A n Quantity B n2

B

paralelogramo lados 6 y 4 A The area of ABCD B 24

D This problem requires a bit of awareness to answer correctly. The trick is that, since we don't know the length of the third side of either triangle, we cannot accurately solve for the area of either triangle! One possibility is that both triangles have two sides with a length of 4, the third side has a length 6, and, therefore, the areas are equal. Another possibility is that one triangle has two sides with a length 4 and the third side with a length of 6, while the other triangle has two sides with a length of 6 and one side with a length of 4. In this case, the 6-6-4 triangle would have a greater area. Since we are not given any angle measures or other clues, we have no way of knowing. The correct answer is D.

riangle ABC is an isosceles triangle with side lengths of 4 and 6. Triangle LMN is an isosceles triangle with side lengths of 6 and 4. (Figures not drawn to scale) Quantity A The area of triangle ABC Quantity B The area of triangle LMN

C

s is any non-positive integer Column A The maximum value of 2s3+2 Column B The maximum value of 3s3+2

B We can apply the Average Law to both quantities: Quantity A Quantity B Multiplying both sides by 15 (which is the common denominator of 5 and 3) simplifies the comparison: Quantity A Quantity B 9 x + 6 y 10 x + 5 y We can then subtract the common terms 9 x and 5 y from both sides: Quantity A Quantity B y x x is greater than y, so Quantity B is greater. The correct answer is B.

x > y Quantity A The average (arithmetic mean) of x, x, x, y, and y Quantity B The average (arithmetic mean) of x, x, and y

E The problem states that when x is divided by y the remainder is 6. In general, the divisor (y in this case) will always be greater than the remainder. To illustrate this concept, let's look at a few examples: 15/4 gives 3 remainder 3 (the divisor 4 is greater than the remainder 3) 25/3 gives 8 remainder 1 (the divisor 3 is greater than the remainder 1) 46/7 gives 6 remainder 4 (the divisor 7 is greater than the remainder 4) In the case at hand, we can therefore conclude that y must be greater than 6. The problem also states that when a is divided by b the remainder is 9. Therefore, we can conclude that b must be greater than 9. If y > 6 and b > 9, then y + b > 6 + 9 > 15. Thus, 15 cannot be the sum of y and b. The correct answer is E.

x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? 24 21 20 17 15

D

x<1 and x<>0 A x2+1 B x3+1