Preguntas Erroneas

D, 24 Factorizar. Y para contar, saber cuántos 2, 5 y 13 puede haber.... Ojo que 2^0, 5^0 y 13^0 también cuentan!

2600 has how many positive divisors? 6 12 18 24 48

R=12

A biker needs to finish a 40 km race with 4 laps of 10 km each. If the biker started at 60 kmph in the first lap, and on each lap he went 20% faster than the previous lap, how much earlier would he reach the finish line, than when he maintains a uniform speed of 80 kmph throughout the race? 21 18 15 12 9

R= 11 igualar las dos ecuaciones. La redacciòn noe stà tan clara.

A company wants to spend equal amounts of money on the purchase of two types of machines. The cost of one is $320 and the cost of the other is $560. What is the minimum number of total machines the company can purchase? 4 7 11 12 13

R= A (97,656,240) Ojo! las prohibidas son 10 combinaciones (10x1x1x1x1x1)

A country issues license plates that consist of just one number (0 through 9, inclusive) and five letters, selected from a 25-letter alphabet, while the other alphabets are ignored. Repeats are permitted. However, there is only one five-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist? 97,656,240 97,656,249 97,656,250 97,656,290 97,656,299

R) 4,400

A developer has land that has x feet of lake frontage. The land is to be subdivided into lots , each of which is to have 80 or 100 ft of lake frontage. If 1/9 of the lots are to have 80 ft of frontage and the remaining 40 lots are to have 100 ft of frontage, what is the value of x? 400 3200 3700 4400 4760

A Probability that the man will hit the target even if he hits it once or twice or all five times in the five shots that he takes. So, the only case where the man will not hit the target is when he fails to hit the target even in one of the five shots that he takes. Now, probability of hitting the target in one shot = 1/5 Probability of missing the target in one shot = 1 - 1/5 = 4/5 so , the probability of missing in all four shots = (4/5)^5 = 1024/3125 Therefore, probability of hitting at least one = 1 - 1024/3125 = 2101/3125 = 0.67 Hence, quantity A is greater.

A man can hit a target once in 5 shots. Column A Probability that he will hit his target at least once if he fires 5 shots in succession Column B 0.5

R) A. r2-r

A rectangular game board is composed of identical squares arranged in a rectangular array of r rows and r+1 columns. The r rows are numbered from 1 to r and the r+1 columns are numbered from 1 through r+1. If r>10, which of the following represents the number of squares on the board that are NEITHER in the 4th row nor the 7th column? r2-r r2-1 r2 r2+1 r2+r

R= 20 Había que buscar la forma de que las ecuaciones "se parecieran": Por lo general dejar un número sólo si es lo único que se ve,... hacerlo. Text Explanation This one appears hard, but can be vastly simplified with a clever trick. From the Pythagorean Theorem in the triangle, we can get: Then we are given: We re-wrote those two equations because we plan to use the Difference of Two Squares formula:

A right triangle has legs of 6 and x, and a hypotenuse of r. If 5r = 5x + 9, what is the value of r + x?

R= 105 n 1 hour, Atu will travel a distance of 56 miles and Brek will travel a distance of 49 miles. Hence, the total distance traveled by the two people in one hour will be 105 miles. That means you can subtract a distance of 105 miles from the total distance of 420 miles. That is, they have come 105 miles closer together, and there is still a distance of 315 miles between them. After the second hour, you subtract another 105 miles from 315 miles, so they then have 210 miles left to travel. After the third hour, you subtract another 105 miles from 210 miles and they have 105 miles left to travel—that number looks familiar, doesn't it? If they have 105 miles between them, and they collectively move 105 mph, then it will be exactly one hour before they meet. And there's our answer: 105 miles

A-town and B-ville are connected by a straight, 420-mile road. At noon, Atu left A-town for B-ville, and Brek left B-ville for A-town. If Atu travels at 56 miles per hour and Brek travels at 49 miles per hour, how many miles apart will Atu and Brek be 1 hour before they meet?

R) C

A> The number of integers between 100 and 500 that are multiples of 11 B> 36

11pi*r/18 If angle ABC is equal to 90o, then AC would have been the diameter of the circle and arc ABC would have been a semi-circle. But angle ABC is 100o, which is greater that 90o and therefore the length of the minor arc AB must be less than half the circumference(πr) . So, all answers greater than πr can be eliminated. This includes options B and D. Option A can also be ruled out. If the length of the minor arc AB is 8πr9 , then the length of arc AC is: arc AC=arc AB+arc BC=8πr9+5πr18=16πr18+5πr18=21πr18>πr a contradiction. Arc AC must be less than πr , the semi circle, because chord AC is less than the diameter (note that this does not pass through the center of the circle). We are left with choices C and E. A full circle is 2πr . Arc BC is given as 5πr8. We are also given that ∠ABC=100∘. Note that ∠ABC is an inscribed angle, that is, its vertex lies on the circle. It is important to remember that the measure of an inscribed angle is half of the measure of the central angle intercepting the same arc. This implies that the central angle intercepting arc AC is 200∘, which is 200360=1018 of the circle (note that a circle has 360∘). Thus, arc AC must be 1018 of the whole circle or arc AC=(1018)×2πr=20πr18 . Now, we can compute for arc AB: arc AB+arc BC+arc AC=2πr arc AB=2πr−arc BC−arc AC=36πr18−5πr18−20πr18=11πr18 The correct answer is C.

ABCD is an inscribed quadrilateral in the given circle with center O and radius r. If ∠ABC=100o and length of minor arc BC=5πr18, then what is the length of the minor arc AB? 8pi*r/9 18pi*r/11 11pi*r/18 9pi*r/8 4pi*r/9

Ali tiene 90 años Let A be Ali's age in years. If S is his son's age in years, then his son is 52S weeks old. If G is his grandson's age in years, then his grandson is 365G days old. Since Ali's grandson is about as many days as his son in weeks, 365g=52s Also, as Ali's grandson is as many months as he is in years, 12G=A Now, as Ali, his grandson, and his son together are 150 years, we can write g+s+m=150 A12+365A52×12+A=150 52A+365A+624A=624×150 A=624×1501041=89.91≈90 So, Ali is 90 years old.

Ali's grandson is about as many days as his son in weeks, and his grandson is as many months as he is in years. Ali's grandson, his son and he together are 150 years. How old is Ali right now, rounded off to the nearest integer?

13 Ojo! sólo es el valor de en medio con un número non de personas.

Annual profits (in $) Number of investors 0-9,999 12 10,000-19,999 p 20,000-29,999 8 30,000-39,999 7 40,000-49,999 9 The table above shows the distribution of annual profits earned by a group of investors, in $. What is the minimum number of investors, p, earning profits in the interval $10,000 − $19,999 such that the median profit earned by all these investors is in this interval $10,000 − $19,999? 8 9 12 13 18

B

Ashley's score was 20% higher than Bert's score. Bert's score was 20% lower than Charles' score. Column A Column B Ashley's score Charles' score

D OJO! algunos rectángulos son cuadrados. As the perimeter of the rectangle is 64, several combinations of lengths and widths are possible such as: Case #1: Length and width are 31 and 1. The area of this rectangle is 31 x 1 = 31 < 255. Case #2: Length and width are 30 and 2. The area of this rectangle is 30 x 2 = 60 < 255. Case #3: Length and width are 20 and 12. The area of this rectangle is 20 x 12 = 240 < 255. In each of these cases, the area of the rectangle is less than 255. However, there is one exception. If the length and width of the rectangle is equal i.e. if the rectangle is a square, then the sides of the rectangle are all equal to 16 and the area of this rectangle is 16 x 16 = 256 > 255. Therefore, the correct answer is D.

Column A The area of a rectangle with a perimeter of 64 Column B The area of a trapezoid whose lengths of the two parallel sides are 7 and 8 and has a height of 34

R=30

For the first 5 hours of a trip, a plane averaged 120 kilometers per hour. For the remainder of the trip, the plane travelled an average speed of 180 kilometers per hour. If the average speed for the entire trip was 170 kilometers per hour, how many hours long was the entire trip? 15 20 25 30 35

R= 3, 5 Una buena forma de aprender nCr es la forma corta= (primeros r valores de n)/ r!

From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k ? Indicate all such values. 1 2 3 4 5 6 7

R= 8 Sacar la factorización prima, y de ahí contar... cualquier divisor es la mezcla de estos números.

How many odd, positive divisors does 540 have? 6 8 12 15 24

9 tiene que ser 2+un múltiplo de ambos (de 12 y 8)

How many positive integers up to 200 yield a remainder of 2 when divided by 12 and also yield a remainder of 2 when divided by 8?

R= 4320 Ojo, el número no puede empezar con 0!

How many six-digit numbers can be formed using the digits 4, 5, 6, 7, 8, 9, 0 if no digits can be repeated? 640 1440 2880 4320 5760

Correct answer: 0.75

If (IMAGEN) , what is the greatest possible value of x?

R= 108 Había que empezar por la segunda expresión.... eventualmente todo quedaba como 2^k, que es el dato que me dan.

If 2^k = 3, then 2^(3k+2) = 29 54 81 83 108

0 Ojo, es la misma ecuación, pero con una de las respuestas sustituyo en la otra

If 4(2−x)/ (3+x) =x, what is the value of x2+7x−8?

R = 5/ 4

If 5x+y = 125 and 3x-3y = 1/9, then y = -5/2 1/4 1/2 5/2 5/4

100q

If 6000% of p equals 6000q, then p =

b/15, b2/18, b2/45 como 750a debe ser un cuadrado perfecto, a debe ser 30 haciendo que b sea 150. a es 30 por la factorización prima de 750 (para que sea 2 perfecto le hace falta un 2, un 3 y un 5) If 750a=b2 , then 750a must be a perfect square. Putting it in other words, when we prime factorize 750a, we should get primes in pairs for it to be a perfect square. The prime factorization of 750=2×3×(5×5)×5 . So, we have a 2, a 3 and a 5 missing in 750 for it to be a perfect square. Then there primes must be factors of a, only then will 750a=b2 be true. So, the minimum value of a must be 2×3×5=30 . Which means, b = 150. Now, let's solve each answer choice one at a time. b11 = 150/11 is not an integer. b15 = 150/15 = 10 is an integer. b60 = 150/60 is not an integer. b218 = 150218=150×15018=1250 is an integer. b245 = 150245 = 150×15045 = 500 is an integeris an integer. The correct answers are B, D and E.

If 750a=b2 where a and b are positive integers, then which of the following must be an integer? Indicate all such values. b/11 b/15 b/60 b2/18 b2/45

a-b=1, ab=12

If a and b are integers, a>b, a2b2=144 and (a−b)2=1 , which of the following MUST be true? Indicate all such statements. a+b=7 a-b=1 a-b=-1 ab=12 ab=-12

R= 346 Since we are dealing with squares of a, b and c, their sign won't affect the result in anyway. First, let's list out the first few squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 etc. Since we need to find the differences between consecutive perfect squares, let's list the differences too: 4-1=3 9-4=5 16-9=7 And so on. The list is 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 etc. If you notice, all the above numbers are odd. In fact, the difference of any two consecutive perfect squares results is an odd number. So, (a2−b2) is an odd number, and so is (b2−c2) and the product of these two i.e. two odd numbers will also be odd. So, the result should be an odd number. Since the question asks for the number that cannot be 'odd', our answer must be an even number. The only even number among the answer choices is 346. Hence, the correct answer choice is D.

If a, b, and c are consecutive integers such that a > b > c then which of the following cannot be the value of (a2−b2)*(b2−c2)? 47 83 165 346 489

B= 5/4

If square ABCD has area 25, and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square? Note: Figure not drawn to scale 3/4 5/4 6/5 4/3 5/3

R= -60, -30 1) puedo sumar desigualdades SI LOS SIGNOS APUNTAN EN LA MISMA DIRECCIÖN

If y - 3x > 12 and x - y > 38, which of the following are possible values of x? Indicate all such values. -60 -30 -6 4 20 40 80

-2/7 Begin by solving the inequality. Remember that an absolute value is the distance from zero and therefore is always positive i.e. |b|≥0 If |b|≥0 , then 0≤|b|≤−6a which also means 0≤−6a . Putting in words, this inequality says that -6a is positive or zero and for this to be true a must be either negative or zero (since negative (-6)times negative (a) = positive (-6a) and any number multiplied by zero is zero) So, from the inequality, we were able to deduce that x is either a negative number or zero i.e. x≤0 . Now, let's solve the equation with absolute value: 3a+7=|4a−5| The most reliable way to solve this is by creating two separate equations that consider the two possible scenarios given by the absolute value sign (positive/zero and negative). The positive case: 3a+7=4a−5 4a−3a=7+5 a=12 The negative case: 3a+7=−4a+5 7a=5−7 7a=−2 a=−27 Therefore, a=12 or a=−27 But we already deduced that a must be either zero or negative. Thus a=12 is not possible and the correct answer is C.

If |b|≤−6a and 3a+7=|4a−5|, what is the value of a? -4 -1/5 -2/7 3/4 12

3<=b-a<=10 The smallest value of the range of possible values is given by the largest possible value minus the smallest possible value. The greatest value of b−a will occur when b is as large as possible and a is as small as possible. That is, b−a≤7−(−3)=10 The smallest value of b−a will occur when b is as small as possible and a is as large as possible. That is, b−a≥5−2=3 So, 3≤b−a≤10 The correct answer is E

If −3≤a≤2 and 5≤b≤7 which of the following represents the range of all possible values of b−a?

22 Si s es negativo... st debe serlo. Solo un resultado positivo no.

If −3≤s≤0 and t>22, which of the following CANNOT be the value of st? -77 -66 -22 0 22

Correct answer: 30 Cuando no sea explícito, sólo iniciar con a! a1= a a2= ar a3= ar*r= ar2 a4= ar2*r= ar3 a5= ar^4.....

In a certain sequence of all positive terms, {a1, a2, a3, ...} each term equals the previous term times a constant factor. If (a1)(a5) = 900, what is the value of a3?

solo 50 Since the average age of the 10 students in 5, the sum of their ages is 50. As the standard deviation of this data set is not specified, the data in the set can be as close to the mean as possible or can go as far as it can. So, let's find the extreme values so we can eliminate the impossibilities. Since the ages can only take whole numbers, the lowest possible age of a student is 1 (because the age cannot be 0). To find the other extreme, we will need to equate all the ages of the students in the class to 1 except one for student. So, the ages could be 1, 1, 1, 1, 1, 1, 1, 1, 1, x. Since the mean of this set is 5, we can write 1+1+1+1+1+1+1+1+1+x10 which implies 9 + x = 50 and that x = 41. Therefore, the extreme values are 1 and 41. Any whole number between these values can be the age of the students in the class. 50 is outside this range and therefore cannot be the age of the students. The correct answer is F.

In a class, the average (arithmetic mean) age, rounded to the nearest whole number, of 10 students is 5. Which of the following CANNOT be the age of the students in this class? Indicate all such values. 1 5 10 30 40 50

A First, you will need to find the concentration of each can: Can A: 1212+18=1230=25=40% Can B: 99+3=912=34=75% Since both these mixtures are combined to create a new solution that is exactly 7 liters acid and 7 liters water, the concentration of the new solution must be 714×100=50% . So, x liters of solution from can A is mixed with y liters of solution from can B to form (x+y) liters of 50% concentrated acid solution. We can write this algebraically as: 0.4x+0.75y=(x+y)×0.5 0.4x+0.75y=0.5x+0.5y 0.25y=0.1x y=0.4x But we know that (x+y)=14 . So, plugging this value into x×0.4+y×0.75=(x+y)×0.5 gives us x×0.4+y×0.75=14×0.5 0.4x+0.75y=7 By replacing the value of y with y=0.4x in the above equation, we get: y+0.75y=7 1.75y=7 y=4 But we know that y=0.4x , so 4=0.4×x 40.4=x x=10 Hence, the answer is A.

In a laboratory, can A contains a mixture of 12 liters of hydrochloric acid and 18 liters of water and can B contains a mixture of 9 liters of hydrochloric acid and 3 liters of water. The solutions from each can must be combined to form a new solution that is exactly 7 liters acid and 7 liters water? Column A The amount of solution taken from can A. Column B The amount of solution taken from can B.

231 Ojo- los problemas que digan "at least" quizás es mejor usar 1-eso. 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?

D The vowels in the word ANALYSIS are A, A, and I respectively. Since the vowels must appear together, treat the three vowels as one block. So there are six such blocks, five of them consonants and one of them is the three vowels together in one block. These 6 blocks can be arranged in 6P6 or 6! ways. As there are 2 S's among the consonants, the 6! needs to be divided by 2! to account for all the different number of ways of arranging the blocks. That is 6!2! ways exist for arranging the 6 blocks. Within the block containing the 3 vowels, there are two A's. Hence, there are 3!2! ways of arranging the members of the block containing the vowels. In total, there are (6!2!)(3!2!) ways of arranging the letters according to the requirements of the question. The correct answer is D.

In how many ways can the letters of the word ANALYSIS be rearranged such that the vowels always appear together? (A, E, I, O, and U are the vowels in the English alphabet). 8!/3! 8!2!/(3!5!) 3!5!/2!2! (6!/2!)(3!/2!) 6!2!/3!3!

R= 1/2, 3/5, 4/7 First, figure out the slope from (1, 3) exactly through (4, 5). Rise = 2, and Run = 3, so slope = 2/3. This is the slope of the line that, starting at (1, 3), would go directly through (4, 5). If we want to go under (4, 5), we need a slope less than 2/3. In many cases, finding a common denominator makes the comparison quick & easy.

In the standard x,y-plane, Line L passes through the point (1, 3). If Line L passes below the point (4, 5), then which of the following could be the slope of Line L? Indicate all possible slopes. 1 1/2 2/3 3/5 4/5 4/7 5/4 5/6

C= w/xy PITA! FAQ: Is there an algebraic approach? Yes, although we don't need to use it. In fact, it's most important to realize that we can solve this by plugging in real numbers for those variables, because that's an absolutely crucial strategy for the test. But here's an algebraic approach anyway: Let's start with the sentence "It takes 1 pound of flour to make y cakes." From this we will set up an equation. Let's call if equation A. 1 (pounds of flour) = y (cake) Here, I am just treating "pounds of flour" and "cakes" like units of measurement (such as feet, miles, kilograms, seconds, etc). Now, the next sentence says "The price of flour is w dollars for x pounds." Let's set up another equation for that. We'll call it equation B w (dollars) = x (pounds of flour) We want an equation that relates dollars to cakes. Notice that if we multiply both sides of equation A by x, then we will have "x (pounds of flour)" in both equations and will be able to set them equal. x (pounds of flour) = xy (cake) w (dollars) = x (pounds of flour) Since the right side of the top equation and left side of the bottom equation are the same, they must be equal to each other. (w) (dollars) = (xy) (cake) We want to solve for 1 (cake), so divide both sides by xy. (w/(xy)) (dollars) = 1 (cake) Answer choice (C).

It takes 1 pound of flour to make y cakes. The price of flour is w dollars for x pounds. In terms of w, x and y, what is the dollar cost of the flour required to make 1 cake? xy/w y/wx w/xy wx/y wxy

R= 75 Siempre con problemas de velocidad (distancia, tiempo) que involucran 2 tramos tengo al menos uno de los totales. En este caso me dicen que el total de tiempo es 6. (OJO: podía también tener la distancia total de 120 y plantear así las ecuaciones (t1 y t2=6-t1) sólo necesitaba un paso adicional- usar la fórmula de v1)

It took Ellen 6 hours to ride her bike a total distance of 120 miles. For the first part of the trip, her speed was constantly 25 miles per hour. For the second part of her trip, her speed was constantly 15 miles per hour. For how many miles did Ellen travel at 25 miles per hour? 60 62.5 66 2/3 75 90

R= E. hacer pruebas! no asumir numeros.

Kevin is more than 15 years old. Column A Six years more than twice Kevin's age Column B Thrice of Kevin's age five years ago

(9,12) y (5,12) Distancia entre dos puntos!

On the xy-coordinate plane, points X, Y, and Z form a right triangle with the right angle at point Z such that the length of XY is an integer. Point X lies on the y-axis and point Y lies on the x-axis. If XZ is parallel to the x-axis, and YZ is parallel to the y-axis, which of the following could be the coordinates of point Z? Indicate all such possibilities (3,5) (9,12) (5,12) (8,10) (8,12)

22.5 Let the number of hours to complete the fast pipe be P. So, the number of hours to complete the slow pipe will be 1.25P Also, both the pipes together fill the poll in ten hours. Therefore, work done per hour by the fast pipe is 1P and the slow pipe is 11.25P. Both together is 110 Thus, 1p+11.25p=110 10+101.25=p P = 18 Then 1.25p=22.5 , so the slower pipe takes 22.5 hours.

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?

The standard deviation is a measure of the spacing between the data points, what is called the "spread" of the data distribution. If we take one set, e.g. {1, 2, 4, 8}, and create a new set by adding the same amount to each and every number, e.g. {21, 22, 24, 28}, the new set has exactly the same spacings as the old set. If we think of the first set as a pattern of dots on the number line, then second set is exactly the same pattern, just shifted up on the number line. Therefore, the two sets have exactly the same standard deviation. That's exactly what's happening here. If we take Set Y and add 5 to each of the three entries, then we get Set X. We could say (Set Y) + 5 = (Set X). When all we do is add the same number to every element, that doesn't change the spacing, so the two sets have exactly the same standard deviation. Answer = C It would be a BIG mistake to try to calculate the standard deviation for both these sets. Most GRE standard deviation question will not expect calculations ---- rather, they will expect you to notice patterns such as this.

Set X:{5,6,9} Set Y:{0,1,4} Column A Standard deviation of set X Column B Standard deviation of set Y

R= 450 tip 1/4= (60+.2x)/(150+x)

Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume? 37.5 75 150 240 450

R= 600

Sue planted 4 times as many apple seeds as she planted orange seeds. 15 percent of the apple seeds grew into trees, and 10 percent of the orange seeds grew into trees. If a total of 420 apple trees and orange trees grew from the seeds, how many orange seeds did Sue plant? 540 600 660 720 760

R= C La clave es que las dimensiones son iguales. FAQ: Since diagrams are not drawn to scale, how do we know the dimensions will always be 4/3? Good question - that's the trap in this question. Diagrams are not necessarily drawn to scale; however, the question states that all four small rectangles have the same dimensions. Since the three stacked rectangles on the left equal the length of the rectangle on the right, we know the ratio must be 4/3 as indicated in the explanation.

The four small rectangles have the same dimensions Column A DC/BC Column B 4/3

A. La columna A es 1.08X10e9, ya que se debe convertir a horas, pero luego calcular distancia como d=v*t

The speed of light is approximately 3 x 105 kilometers per second. Column A Approximate number of kilometers that light can travel in 1 hour. Column B 1.08 x 10e8

(10m)n can actually be written as 10mn and since the answer choices are possible values of mn, it should be readily apparent to you that we are dealing with some ridiculously HUGE numbers and hence cannot solve this the usual algebraic way. But exponents are pattern-driven. So, we will need to identify the pattern here. We do this by considering smaller numbers for mn, say 2. If mn = 2 then 10mn−64=102−64=100−64=36 . If mn = 3 then 10mn−64=103−64=1000−64=936 . If mn = 4 then 10mn−64=104−64=10000−64=9936 . As you can see, we do have a pattern here. 10mn−64 always ends in 36, and the number of 9s in the result seems to be (mn-2) Let's transform this into an algebraic equation: The sum of the digits of 10mn−64=(mn−2)×9+3+6=(mn−2)×9+9=(mn−1)×9 But according the statement in the question, this must be equal to 369. Therefore, (mn−1)×9=369 mn−1=3699=41 mn=42 Hence, the correct answer is E.

The sum of the digits of (10^mn)−64 is 369. What is the value of mn? 38 39 40 41 42

R= 1/4 Dibujar un cìrculo 30-60-90

The triangle in a diagram is equilateral. The smaller circle is tangent to all three sides of the triangle. The larger circle passes through all three vertices of the triangle. What is the ratio of the area of the smaller circle to the area of the larger circle?

R) 10 como siempre, la clave es dejar ambos lados con la misma base.

What is the least integer n such that (1/2^n)<0.001 10 11 500 501 There is no such integer

R= 11,100 Cuando tenga un número NON de elementos, usar (lo sé porque hago y-x+1 ) usar {(y-x+1)*(suma de extremos)/2}

What is the sum of all integers from 45 to 155 inclusive? 10,000 10,100 11,000 11,100 13,200

R= 2e11, 75 En estas preguntas, llevar todo a su factorización prima. Si es divisor, debe tener los términos ahí escondidos

Which of the following are divisors of 1.2x10^10? 2^11 75 5^10 18 3^9 36

B, C, D Notar que los tres son negativos. Por ello la respuesta tienen que ser tres. Organizarlos por orden y los tres menores son!

Which three of the following, when multiplied by each other, yields the lowest product? Indicate all such answers -17/19 24/-23 -19/21 16/-15 15/-17

R= A, 72.

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool? 72 75 84 96 108

R) D Relationshipt cant be dtermined

a<0<b A> a^-10 B= b^-5

R= 23

f 2^2n + 2^2n + 2^2n + 2^2n = 4^24, then n = 3 6 12 23 24

E

f(s)=s2 where s is an integer such that 3.2<|s|+2<6.5 . Column A f(s) for the greatest value of s Column B f(s) for the least value of s

D

p, q, r and s are positive numbers Column A (p+q)% of (r+s) Column B (r+s) % of (p+q)

A. This is pretty straightforward question. To solve this question, we need to rewrite the inequalities in the question. #1 x - z < 0 Adding z on both sides gives x < z #2 x + 3y > 0 Subtracting 3y on both sides gives x > -3y Combining both these inequalities, we get z > x > -3y. Therefore, z > -3y which means Quantity A is greater than Quantity B. The correct answer choice is A.

x - z < 0 and x + 3y > 0 Column A z Column B -3y

E. Ojo! no puedo asumir nada respecto a la naturaleza de los números (no necesariamente son enteros positivos).

x is 50 percent of y and z is 200 percent of y. Column A x Column B z