GRE Quant
Mary buys a car from a mean salesman who charges her 12% over the original price of a $15,000 car. Luke buys the same car from a much nicer salesman who gives him an 8% discount off of the original price. How much more does Mary spend on the car than Luke does?
12% of 15,000 is 0.12 * 15,000 = 1800. 8% of 15,000 is 0.08 * 15,000 = 1200; therefore in total, Mary spent 1800 + 1200 = $3000 more.
Column A: 25% Column B: 0.40
2/5% = 0.40% = 0.004. Therefore, Column B is greater.
There are four aces in a standard deck of playing cards. What is the approximate probability of drawing two consecutive aces from a standard deck of 52 playing cards?
Answer: .005Explanation: The probability of two consecutive draws without replacement from a deck of cards is calculated as the number of possible successes over the number of possible outcomes, multiplied together for each case. Thus, for the first ace, there is a 4/52 probability and for the second there is a 3/51 probability. The probability of drawing both aces without replacement is thus 4/52*3/51, or approximately .005.
In a bag, there are 10 red, 15 green, and 12 blue marbles. If you draw two marbles (without replacing), what is the approximate probability of drawing two different colors?
Calculate the chance of drawing either 2 reds, two greens, or two blues. Then, subtract this from 1 (100%) to calculate the possibility of drawing a pair of different colors. The combined probability of RR, GG, and BB is: (10 * 9) / (37 * 36) + (15 * 14) / (37 * 36) + (12 * 11) / (37 * 36) This simplifies to: (90 + 210 + 132) / 1332 = 432 / 1332 Subtract from 1: 1 - 432 / 1332 = (1332 - 432) / 1332 = approx. 0.6757 or 67.57%
A grade school pays Mr. Day a salary of $24,585 per school year. Each school year contains 165 days. Suppose Mr. Day is sick for a week (5 work days) and the school doesn't have to pay him for those days. Instead, they must pay a substitute teacher to teach his classes. They pay the substitute $90 per day. Totally, how much does the school save for the week Mr. Day is sick?
Divide Mr. Day's salary by 165 to determine how much the school pays him per day: Mr. Day makes $149 per day. They only have to pay substitute $90 per day, saving them $59 per day. To figure out how my they save totally, multiply by 5 to get how much they save for the week Mr. Day is sick: $295
Box A has 10 green balls and 8 black balls. Box B has 9 green balls and 5 black balls. What is the probability if one ball is drawn from each box that both balls are green?
Note that drawing balls from each box are independent events. Thus their probabilities can be combined with multiplication. Probability of drawing green from A: 10/18 = 5/9 Probability of drawing green from B: 9/14 So: 5/9 * 9/14 = 5/14
In a sequence of numbers, the first two values are 1 and 2. Each successive integer is calculated by adding the previous two and mutliplying that result by 3. What is fifth value in this sequence?
Our sequence begins as 1, 2. Element 3: (Element 1 + Element 2) * 3 = (1 + 2) * 3 = 3 * 3 = 9 Element 4: (Element 2 + Element 3) * 3 = (2 + 9) * 3 = 11 * 3 = 33 Element 5: (Element 3 + Element 4) * 3 = (9 + 33) * 3 = 42 * 3 = 126
A singing group has 10 boys and 20 girls. Half the boys and half the girls have blue eyes. What is the probability that a student chosen at random from the group is a boy OR has blue eyes?
P(boy) = 10/30 = 1/3 P(blue eyes) = 1/2 P(boy and blue eyes) = 5/30 = 1/6, because we are told that half (or 5) of the 10 boys have blue eyes P(boy or blue eyes) = P(boy) + P(blue eyes) - P(boy and blue eyes) = 1/3 + 1/2 - 1/6 = 2/3
Harry borrowed $5000 from his parents at a rate of simple interest of 2% annually and paid it back in full in 30 months. What is the total amount of interest and principal his parents charged him?
Principal = $5000 (original amount) Interest = 30 months = 2 years and a half $5000⋅2%=$100⋅2 years=$200 half a year's interest is 1%=$50 Total interest = $250
A high school has 200 students. 120 are male, 50 are upper division students, and 40 are upper division male students. What is the probability of choosing a lower division female student, given the student is female?
There are 200 students in total, and 120 of them are male, so 80 must be female. We also know that there are 50 upper division students, and 40 of them are male, so 10 must be female. If 10 of 80 females are upper division, the other 70 females have to be lower division students, so the probability of choosing a lower division student, given the student is female, is 70/80 = 7/8.
What is the probability of drawing 2 hearts from a standard deck of cards without replacement?
There are 52 cards in a standard deck, 13 of which are hearts 13/52 X 12/51 = 1/4 X 12/51 = 12/ 204 = 3/51 = 1/17
What percentage of profit is made on a product sold for $20 if its overall production cost was $17.50?
To find the profit percentage, you must first determine the amount of profit made on this transaction. If the sale price was $20 and the production cost $17.50, then the profit made was: 20 -17.5 = $2.50. The profit percentage is determined by dividing the amount of profit made by the original price, or 2.5 / 17.5 = (approx.) 0.14286 or 14.29%.
a is 15 percent of 20 7 is b percent of 140
a is 15 percent of 20: a=(15/100)(20)=300/100=3 7 is b percent of 140: 7=(b/100)(140)=b(140/100) b=(100/140)(7)=(100/20)=5 Quantity B is greater.
Consider the following sequence of integers: 5, 11, 23, 47 What is the 6th element in this sequence?
consider the change in each element. Notice that in each case, a given element is twice the preceding one plus one: 11 = 2 * 5 + 1 23 = 11 * 2 + 1 47 = 23 * 2 + 1 To find the 6th element, continue following this: The 5th: 47 * 2 + 1 = 95 The 6th: 95 * 2 + 1 = 191
Three cars, A, B, and C, are in a race. A is twice as likely to win as B, and B is twice as likely to win as C. What is the probability that B or C wins?
find their individual probabilities of winning. Since B is twice as likely to win as C, P(B) = 2 * P(C). Since A is twice as likely to win as B, P(A) = 2 * P(B) = 2 * 2 * P(C) = 4 * P(C). We also know that the probabilities must sum to 1, so P(A) + P(B) + P(C) = 1, meaning P(C) + 2 * P(C) + 4 * P(C) = 1. Then P(C) = 1/7, so P(B) = 2 * P(C) = 2/7. Our answer is therefore P(B or C) = P(B) + P(C) = 2/7 + 1/7 = 3/7.
What is the interest rate on an account if an original balance of $12050 rises to $12670 after one year if it is only compounded yearly?
standard formula for simple interest (which is merely a derivative of standard applications of the formulas used for percentages in general). (1+r)⋅12050=12670 Divide both sides by 12050, but leave the fractions for the time being: 1+r=1267012050 Solve for r: r=(12670/12050)−1 This is: r=(12670−12050)/12050=0.05145228215768 Which is the same as: 5.145228215768%, or 5.15% when rounded.
What is the sum of the odd integers 1,3,5,...,97,99?
Begin by looking at the first and the last elements: 1 and 99. They add up to 100. Now, consider 3 and 97. Just as 1 + 99 = 100, 3 + 97 = 100. This holds true for the entire list. Therefore, it is crucial that we find the number of such pairings. 1, 3, 5, 7, and 9 are paired with 99, 97, 95, 93, and 91, respectively. Therefore, for each 10s digit, there are 5 pairings, or a total of 500. To get all the way through our numbers, you will have to repeat this process for the 10s, 20s, 30s, and 40s (all the way to 49 + 51 = 100). Therefore, there are 500 (per pairing) * 5 pairings = 2500.
Choose a number at random from 1 to 5. Column A The probability of choosing an even number Column B The probability of choosing an odd number
Column B is greater There are two even numbers and three odd numbers, so P (even) = 2/5 and P (odd) = 3/5.
Aperture Industries is made up of 370 employees who work a total of 11,000 hours per week. If the number of weekly hours per employee has a normal distribution and standard deviation of 6 hours, approximately how many employees work more than 36 hours per week?
First find the average number of hours worked by every employee: 11000/370 = 29.7 ~ 30 hrs/week. Next, recognize that a single standard deviation encompasses 34% of the population on 1 end of the curve, or 68% of the population both above and below the mean. Since a standard deviation of 6 hours means that 68% of the population works between 24 to 36 hours per week, finding the amount that works over 36 hours is 100-68 = 32; 32/2 = 16% of the entire workforce on 1 end of the curve. .16(370) = 59.2 or 59 employees work over 36 hrs/week.
A cake order cost $45.40 before tax. If the tax rate is 6.5%, what is the price of the cake after tax is applied?
For all percentage problems, you need to convert your percentage to a decimal before working on your equation. You can solve this problem one of two ways. The first way, which is less efficient, is to multiply the original amount by the tax rate and then add that to the original: 45.4⋅0.065=2.951 45.4+2.951=48.351 or: $48.35 The easier way to do this is to multiply your original amount by 1 plus the tax rate. (This does the addition for you in one step.) 45.4⋅1.065=48.351 or: $48.35 Notice that your problem is asking for the total new cost, not the amount of tax to be added!
Joe has a set of 10 books that he hasn't yet read. If he takes 3 of them on vacation, how many possible sets of books can he take?
He can choose from 10, then 9, then 8 books, but because order does not matter we need to divide by 3 factorial (10 * 9 * 8) ÷ (3 * 2 * 1) = 720/6 = 120
Two fair dice are thrown. What is the probability that the outcome will either total 7 or include a 3?
If rolled twice, there are 6 * 6 = 36 possible outcomes. Each number is equally probable in a fair die. So only need to count the number of outcomes that fulfill the requirement of adding to 7 or including a 3. These include: 1 6 2 5 3 4 4 3 5 2 6 1 3 1 3 2 3 3 3 5 3 6 1 3 2 3 5 3 6 3 This is 15 possibilities. Thus the probability is 15/36 = 5/12.
The probability that events A and/or B will occur is 0.88. Quantity A: The probability that event A will occur. Quantity B: 0.44.
Relationship cannot be determined from information given The only probabilites that we know from this is that P(only A) + P(only B) + P (A and B) = 0.88, and that P(neither) = 0.12. We cannot calculate the probability of P(A) unless we know two of the probabilites that add up to 0.88
a is chosen randomly from the following set:{3, 11, 18, 22}b is chosen randomly from the following set:{ 4, 8, 16, 32, 64, 128}What is the probability that a + b = 27?
Since any of the first set can be summed with any of the second set, the addition sign in the equation works like a conjunction. As such, there are 4 * 6 = 24 possible combinations of a and b. Only one of these combinations, 11 + 16 = 27, works. Thus the probability is 1/24, or about 0.04
At Jill's school fair, there is a game with 25 balloons hung on a dart board. 10 are blue, 8 are red, and 7 are green. Jill throws a dart and pops a blue balloon. What is the probability that the next balloon she hits will also be blue?
Since one blue balloon has already been popped, there are now 9 blue balloons left, and 24 balloons left overall. Therefore the probability that the next balloon Jill hits is also blue is 9/24 = 3/8.
In a bowl containing 10 marbles, 5 are blue and 5 are pink. If 2 marbles are picked randomly, what is the probability that the 2 marbles will not both be pink?
Solve for the probability of choosing 2 marbles that are pink and subtracting that from 1 to obtain the probability of selecting any variation of marbles that are not both pink. The probability of picking 2 marbles that are both pink would be the product of the probability of choosing the first pink marble multiplied by the probability of choosing a second pink marble from the remaining marbles in the mix. This would be 1/2 * 4/9 = 2/9. To obtain the probability that is asked, compute 1 - (2/9) = 7/9. The probability that the 2 randomly chosen marbles are not both pink is 7/9
What is the simple interest rate on an account that accrued $450 after a year if the original deposit was $7505? Round your answer to the nearest hundredth.
The easiest way to do this is to translate the question into "is / of language." The question is asking, "What percentage of 7505 is 450?" Remember, is means equals and of indicates multiplication. "What" means a variable like x. Therefore, we can rewrite our sentence as: x⋅7505=450 Solving for x, we get: x=450/7505=0.0599600266489 This is 5.99600266489%. Rounding to the nearest hundredth, you get 6.00 or 6.
The first term in a sequence of integers is 2 and the second term is 10. All subsequent terms are the arithmetic mean of all of the preceding terms. What is the 39th term?
The first term and second term average out to 6. So the third term is 6. Now add 6 to the preceding two terms and divide by 3 to get the average of the first three terms, which is the value of the 4th term. This, too, is 6 (18/3)—all terms after the 2nd are 6, including the 39th. Thus, the answer is 6.
Quantity A: The probability that all students have their birthdays in January. (There are 31 days in January). Quantity B: The probability that all students have their birthdays on a Saturday this year. (Assume there are 52 Saturdays in a year).
The probability of a single event happening is equal to the number of ways it can happen divided by the total number of outcomes. Because this problem asks about 31 students, we have to raise our probability to the 31st power because it's the probability of 31 different events happening. Now we can figure out the probability of one January birthday (31 days in January/365 days in a year) and the probability of all Saturday birthdays (52 Saturdays in a year/365 days in a year). So thus the probabilities that ALL of the students will have either type of birthday is: (31/365)^31 and (52/365)^31 Since the numbers are raised to the same power, we can simply look at the base to determine which is larger and which is smaller. Since the probability of having a birthday on Saturday (roughly 1/7) is greater than having a birthday in January (roughly 1/12), then Quantity B is greater.
The dealer gives you 4 cards from a regular 52-card deck, without replacement. What is the probability of receiving a spade, a heart, a diamond, and then a club, in that order?
The probability of choosing a spade is 13/52. Now we have 51 cards to choose from, so the probability of then choosing a heart is 13/51. Now we have 50 cards left, with 12 spades, 12 hearts, 13 diamonds, and 13 clubs, so the probability of choosing a diamond is 13/50. Lastly we choose a club out of the remaining 49 cards with probability 13/49. Therefore the answer is (13/52) * (13/51) * (13/50) * (13/49)
If a sweater has a total cost of $54 after tax, what is the cost of the sweater before tax, if the sales tax is 4.5%?
The total cost of the sweater is the original cost plus a 4.5% tax, which can be expressed in the equation: TC=C+T Where TC is the total cost, C is the original cost, and T is the tax. Now, we will plug in the information we know. Since the original cost of the sweater is unknown, we will use the variable x. 54=x+.045x .045 is the decimal expression of 4.5%. Now, solve for x. Consolidate the x variable. 54=1.045x Divide both sides by 1.045. 51.67=x $51.67 is the cost of the sweater before tax.
A classroom has 9 boys and 9 girls. One student is chosen at random as the class leader, and a second student is chosen at random as a back-up leader. Quantity A: The probability of choosing a boy to be the leader and choosing a girl to be the back-up Quantity B: The probability of choosing boys for both roles
There are 18 students in the class, and 2 must be selected from the 9 girls and 9 boys. Key to this question is noting that the 2 students must be unique: ie once a student is selected to lead the class, he or she cannot be chosen to be the back-up. Since these are independent events, the probability of each event is found, and the events are multiplied by each other to find the total. Quantity A: P(boy leader) = 9/18 = 1/2 as there are 9 boys out of a possible 18 students. Once the boy has been chosen, there are 8 boys and 17 students total from which to choose the second student. P(girl back-up) = 9/17 because there are 9 girls and 17 students left. P(Quantity A) = (1/2)(9/17) = 9/34 Quantity B: P(boy leader) = 9/18 = 1/2 as there are 9 boys out of a possible 18 students. Once the boy has been chosen, there are 8 boys and 17 students total from which to choose the second student. P(boy back-up) = 8/17 because there are 8 boys and 17 students left. P(Quantity B) = (1/2)(8/17) = 8 / 34 = 4/17
What is the minimum amount of handshakes that can occur among fifteen people in a meeting, if each person only shakes each other person's hand once?
This is a combination problem of the form "15 choose 2" because the sets of handshakes do not matter in order. (That is, "A shakes B's hand" is the same as "B shakes A's hand.") Using the standard formula we get: 15!/((15 - 2)! * 2!) = 15!/(13! * 2!) = (15 * 14)/2 = 15 * 7 = 105
There are 20 people eligible for town council, which has three elected members. Quantity A The number of possible combinations of council members, presuming no differentiation among office-holders. Quantity B The number of possible combinations of council members, given that the council has a president, vice president, and treasurer.
This is a matter of permutations and combinations. You could solve this using the appropriate formulas, but it is always the case that you can make more permutations than combinations for all groups of size greater than one because the order of selection matters; therefore, without doing the math, you know that B must be the answer
If a student borrows $200,000 at an interest rate of 6% compounded annually, when she graduates in 4 years how much money will she owe? Round to the nearest dollar.
This problem requires knowledge of the compound interest formula, A=P(1+r/n)^nt. Where A is the amount of money owed, P is the sum borrowed, r is the yearly interest rate, n is the amount of times the interest is compounded per year, and t is the number of years. We know that the student borrowed $200,000 compounded annually at a %6 interest rate, therefore by plugging in those numbers we find that after she graduates in 4 years she will owe $252,495
In how many different orders can 8 players sit on the basketball bench?
Using the Fundamental Counting Principle, there would be 8 choices for the first player, 7 choices for the second player, 6 for the third, 5 for the fourth, and so on. Thus, 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 or 8! = 40, 320
How many different license passwords can one make if said password must contain exactly 6 characters, two of which are distinct numbers, another of which must be an upper-case letter, and the remaining 3 can be any digit or letter (upper- or lower-case) such that there are no repetitions of any characters in the password?
consider the three "hard and fast conditions" - the digits and the one upper-case letter. For the first number, you will have 10 choices and for the second 9 (since you cannot repeat). For the captial letter, you have 26 choices. Thus far, your password has 10 * 9 * 26 possible combinations. Given remaining options, have 8 digits, 25 upper-case letters, and 26 lower-case letters (i.e. 59 possible choices). Since cannot repeat, will thus have for your remaining choices 59, 58, and 57 possibilities. Putting all of this together, you have: 10 * 9 * 26 *59 * 58 * 57 or 456426360 choices.
Max has 5 red marbles and 3 green marbles. He meets his friend Bob who has 4 white marbles and 4 green marbles. They combine them into a bag and pull individual marbles out one at a time with replacement. Quantity A: The probability of picking a green marble from only Max's collection of marbles Quantity B: The probability of picking a green marble from the combined bag of Max and Bob's marbles
evaluate Quantity A. Max has 5 red marbles and 3 green marbles, so the probability of picking a green marble is 3/8. Next let's evaluate Quantity B. The bag of combined marbles now has 5 red, 7 green, and 4 white, so the probability of picking a green marble is 7/16. To see which fraction is larger, we can make the two fractions have the same denominator. 3/8 is equivalent to 6/16, so now we can compare 6/16 to 7/16. Clearly Quantity B is bigger.
Mike has a bag of marbles. 5 are green, 8 are red, and 3 are blue. He pulls one marble out of the bag and it is green. He pulls out another one and it is red. He does not return these marbles to the bag. What is the probability that the next marble he pulls out of the bag will be green?
need to find out how many marbles are in the bag in total. 5 + 8 + 3 = 16. He removes a green marble so now there are only 15 in total. When he removes the red one there are then 14 marbles in the bag. 14 is your denominator. The odds of picking a green one are 5 - 1 or 4 because there are only 4 green marbles left in the bag; therefore, the odds of picking another green marble is 4/14
There are 6 photos in a bag, numbered 1 to 6. The proportions of photos, P(i) for number i, are as follows: P(1) = 1/4, P(2) = 1/8, P(3) = 1/8, P(4) = 1/8, P(5) = 1/8, P(6) = 1/4. If a photo is drawn at random from the bag, what is the chance that the number on the photo is 3 or greater?
simply add up the proportions of the photos with numbers greater than or equal to 3. P(3 or 4 or 5 or 6) = P(3) + P(4) + P(5) + P(6) = 1/8 + 1/8 + 1/8 + 1/4 = 5/8
