Quantitative Reasoning Missed Questions

QID 58207

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QID 56887

A box contains tiles numbered with integers ranging from g to -g, inclusive, where |g| > 4. If 5 tiles are chosen at random, each returned to the box after it is selected, and the corresponding integers are multiplied, which of the following is NOT a possible product of the 5 integers?

QID 57047

AD/BCE

QID 57055

AD/BCE

QID 58320

AD/BCE

QID 58492

AD/BCE - IMPORTANT ABSOLUTE VALUE/INEQUALITY RULE: once you isolate the absolute value to one side, you can then say greater than or less than whats on the other sides and use algebra normally

A portable recharging device can recharge 3 batteries at once, and it can charge the batteries while itself being charged from an outlet. The device can recharge a single dead battery in 3 hours, and it can be completely recharged from an outlet in 2 hours when it contains no batteries. A fully discharged device holding 3 dead batteries is plugged into an outlet. If the capacity of a battery is one-third the capacity of the device, and the device and batteries charge at constant rates, how much time will pass before the device is completely recharged? Question 4 Answer Choices 5 hours 6 hours 8 hours 9 hours 11 hours

Weird wording problem. Have to take the charge rate of the device and subtract the energy being taken from the device by charging the batteries.

See last two of required homework that I got wrong (class 6)

Hard Probability Questions

Machines A, B, and C take w, w+ 1, and w+ 9 hours, respectively, to individually complete a work assignment. If Machine A alone can complete the work in the same length of time as Machines B and C working together, how long does B alone take to complete the assignment? Question 7 Answer Choices 3 4 9 12 15

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QID 58208

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QID 58242

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QID 58243

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QID 58244 - The exponent needs to be divisible by 12 because the exponent must be a whole number after multiplying by the root!

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Stupid. Need to multiply by y^2/3 because when added to the 1/3 exponent in denominator thats what allows it to cancel and equal y

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QID 56917 (Answer is D)

A certain delicatessen sells two types of sandwiches: roast beef sandwiches for $6 each and vegetarian sandwiches for $5 each. There is no sales tax, but the delicatessen does charge a 15% delivery fee. If an office manager spends exactly $161 on an order that will be delivered, and the order is made up of more than 25 sandwiches, what is the least number of vegetarian sandwiches that can be included in the order? Question 3 Answer Choices 6 10 12 16 22

This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Determine "What is known" from the question stem and "What is needed" from the statements to answer the question. Begin by determining "What is known." The cost of the service is x dollars for the first mile and y dollars per additional mile. Translate this information into a mathematical equation, so that cost = x + y(miles − 1). Now, determine "What is needed." The question stem provides a single equation containing four variables. To determine the cost per additional mile, y, the statements must provide sufficient information to determine the values of the other three variables, x, cost, and miles. Evaluate the statements one at a time. Evaluate Statement (1). If the cost of a 5-mile ride is $5.35, then a client pays x dollars for the first mile and y dollars per mile for the remaining 4 miles, so that x + 4y = $5.35. Statement (1) provides the cost of the ride, as well as the length of the ride in miles, but it does not provide the cost of the first mile, x. Therefore, Statement (1) is insufficient. So, write down BCE. Now, evaluate Statement (2). The cost of a 7-mile ride is $1.30 more than the cost of a 5-mile ride. Use this information to create two equations. First, consider a 5-mile ride, for which cost = x + 4y. Next, consider a 7-mile ride, for which cost + $1.30 = x + 6y. Subtract the first equation from the second equation to find that $1.30 = 2y, or y = $0.65. Since Statement (2) provides one specific answer to the question, which is y = $0.65, the statement is sufficient. Eliminate choices C and E. The correct answer is choice B.

A rideshare service charges x dollars for the first mile and y dollars for each additional mile. What is the value of y ? 1.)A ride of 5 miles costs $5.35. 2.)A ride of 7 miles costs $1.30 more than a ride of 5 miles. AD/BCE

QID 57014

All of the 121 baseball players participating in a celebrity golf outing were born in either Asia, Australia, North America, or South America. If there are 25 percent fewer players that were born in Australia than were born in Asia, how many of the participating players were born in North America? 1.) The number of players who were born in South America is 40 percent greater than the number of players who were born in Asia. 2.) The ratio of the number of players who were born in North America to the number of players who were born in South America is 29:14. Question 6 Answer Choices AD/BCE

QID 56916 (answer is B)

Based on his estimate of the time required to complete a job, a contractor decides to charge $288 to complete a project. The project takes one hour longer to complete than the contractor had anticipated and as a result the contractor's hourly rate is $4 per hour less than he had estimated. How many hours did it take the contractor to complete the job? Question 6 Answer Choices 8 9 10 32 36

There are variables in the question stem and answer choices, so this is a Plugging In problem. Begin by choosing a simple value for p, such as p = 2, which means that because the same bracelets cost $1 more each at a neighboring retail chain store, at the neighboring retail chain the bracelets cost $3. Now, determine how many dollars will buy 10 more bracelets at the discount store than at the retail chain store, which provides the value of x. Since the ratio of the costs at the two stores is , multiply this fraction by 10 to determine the number of bracelets that would be sold by each store when exactly 10 more had been sold by the discount store. This results in a number of 20 bracelets being sold by the retail store and 30 being sold at the discount store. Now, Plug In $3 for the cost of the bracelets at the retail chain store to find that $60 divided by 3 would buy 20 bracelets at the retail store, while the same $60 divided by $2, or p, would buy 30 bracelets at the discount store. This means that if p = 2, then x = 60. Plug In p = 2 into all of the answer choices, looking for one that equals 60. Choice A is 10 × 3 = 30, so eliminate choice A. Choice B is 10 × 1 = 10, so eliminate choice B. Choice C is 10 × 6 = 60, so keep choice C. Plug In for the remaining answer choices just to make sure. Choice D is 10 × 2 = 20, so eliminate choice D. Choice E is 10 × 7 = 70, so eliminate choice E. The correct answer is choice C.

Bracelets cost p dollars each at a discount store. At a neighboring retail chain store, the same bracelets cost $1 more each, which means that x dollars will buy 10 more bracelets at the discount store than at the retail chain store. What is the value of x in terms of p ?

The question asks for the number of minutes that elapse before Car J catches up to Car K, and it provides information about the speed of the cars and the relative time at which each car departs from City A. The relationship between distance, rate, and time is defined by the equation D = RT. Thus, DJ = RJTJ, and DK = RKTK. While the two cars travel at different speeds and for different lengths of time, at the moment Car J catches up to Car K, both cars have traveled the same distance. Therefore, DJ = DK, and RJTJ = RKTK. Car K travels at a constant speed of 80% the constant speed of Car J, so 0.8(RJ) = RK, and RJTJ = 0.8RJTK. Car K travels 15 minutes longer than Car J does, so TJ + 15 = TK, and RJTJ = 0.8RJ(TJ + 15). Divide both sides of the equation by RJ, so that TJ = 0.8(TJ + 15). Distribute the 0.8 on the right side of the equation, so that TJ = 0.8TJ + 12. Subtract 0.8TJ from both sides of the equation, so that 0.2TJ = 12. Multiply both sides of the equation by 5, so that TJ = 60, and 60 minutes will elapse before Car J catches up to Car K. The correct answer is choice C.

Cars J and K are making the trip from City A to City B. Car J departs from City A 15 minutes after Car K does, and both cars travel along the same route. If Car K travels at a constant speed that is 80% the constant speed of Car J, then how many minutes will elapse before Car J catches up to Car K ? Question 8 Answer Choices 20 45 60 75 120

QID 57053

Cotto Toy Store sells Product X and Product Y at two different regular prices. During a sale, both products are discounted. Is the sale price of Product X greater than the sale price of Product Y ? 1.) Product X is discounted by $3 and Product Y is discounted by $8. 2.) Product X is discounted by 20% and Product Y is discounted by 40%. AD/BCE

When two things are moving toward each other, they grow closer at a rate equal to the sum of their individual rates. Statement (1) tells you that Sierra and Dylan are growing closer at a rate of (3x+4x) = 7x miles per hour. Since Sierra's rate is 3x miles an hour, she travels (3x/7x) = (3/7) of the total 90 miles, and you should write down AD. For Statement (2), if Sierra travels at 15 miles per hour and Dylan travels at 20 miles per hour, then you get one answer, but if Sierra travels at 5 miles an hour and Dylan travels at 10 miles an hour then you get another answer, so you can eliminate D. The correct answer is A

Exactly one straight road connects Albertville and Bowton, which are 90 miles apart. If Sierra leaves Albertville headed for Bowton at the same time that Dylan leaves Bowton headed for Albertville, and each travels along the road at a constant rate, how far will Sierra have traveled when they meet? Sierra travels at 3x miles per hour and Dylan travels at 4x miles per hour. Sierra travels at 5 miles per hour slower than Dylan does. Question 6 Answer Choices Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are not sufficient.

There are variables in the question stem and answer choices, so this is a Plugging In problem. Begin by choosing a smart value for m, such as m = 100, that will be divisible by all of the values in the question and the answer choices. If the track has a length of 100 meters and it is divided into fourths and fifths, then there are markers at 0, 20, 25, 40, 50, 60, 75, 80, and 100 meters. Subtract the markers from each previous marker to find the possible distances between two consecutive markers: 20 - 0 = 20, 25 - 20 = 5, 40 - 25 = 15, 50 - 40 = 10, 60 - 50 = 10, 75 - 60 = 15, 80 - 75 = 5, 100 - 80 = 20. These values indicate that the unique lengths the runner can travel between two consecutive markers are 5, 10, 15, and 20 meters. Plug In m = 100 into the answer choices, looking for values that match these unique lengths. Choices A and B each indicate two choices only, so eliminate them because there is a total of four possible values. Also, eliminate choice E because it indicates five possible values rather than four. Plug In m = 100 into choice C to get 100 ÷ 4 = 25, which is not one of the four values. Eliminate choice C. Plug In m = 100 into choice D to get 100 ÷ 20 = 5, 100 ÷ 10 = 10, 300 ÷ 20 = 15, 100 ÷ 5 = 20, which are the four values that match the unique lengths. The correct answer is choice D.

For the convenience of walkers and runners, a linear exercise track m meters in length has a distance marker placed at the beginning and end of the track, as well as at every fourth of its length and at every fifth of its length. If a runner were to travel the total length of a section of the track between consecutive markers, which of the following expresses the distance the runner could travel, in meters?

This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Start by determining "What is known" from the question and "What is needed" from the statements to answer the question. Determine "What is known" from the question stem. The question stem provides a relationship between two workers' rates and asks for their combined rate, so use the work equation Work = Rate × Time. If Chris' rate is r widgets per hour, then Jane's rate is r + 4 widgets per hour. Now, determine "What is needed." To find Chris and Jane's combined rate, the statements need to provide either Chris' or Jane's rate, or provide the time required for either Chris or Jane to produce a number of widgets. Evaluate the statements one at a time. Evaluate Statement (1). Statement (1) provides the number of widgets that Chris and Jane produced working together. However, no information is provided about the time required to produce these widgets, so no rates can be determined. Therefore, Statement (1) is insufficient. Write down BCE. Now, evaluate Statement (2). If t is the time it takes Jane to produce the widgets, then use the work equation to find that Jane produces (r + 4) × t widgets and Chris produces r × 2t widgets. Since they produced the same number of widgets, set these two expressions equal to each other to find (r + 4) × t = r × 2t. Cancel out the t from each side of the equation to yield r + 4 = 2r. Subtract r from each side of the equation to yield 4 = r. Therefore, Chris' rate is 4 widgets per hour and Jane's rate is 4 + 4 = 8 widgets per hour, and together their rate is 4 + 8 = 12 widgets per hour. The original question has one specific answer, so Statement (2) is sufficient. Eliminate choices C and E. The correct answer is choice B.

Jane and Chris work at a factory producing widgets. If Jane produces 4 more widgets per hour than does Chris, what is their combined rate? 1.) Last week, Chris and Jane together produced a total of 96 widgets. 2.) Last week, Chris worked twice as long as Jane and produced the same number of widgets as she did. AD/BCE

The answer choices in this question represent the information directly asked for by the question, and the question could be solved by writing and solving an equation, so Plug in the Answers. This question asks about factors, so consider factoring the answer choices. If the distinct prime factors of x are 2, 3, 5, and 19, then the product of these factors represents the smallest possible value of x. As the question lists only distinct prime factors, it is possible x contains more than one of each of these factors. Therefore, any product containing one or more of each of the prime factors 2, 3, 5, and 19 could also be a possible value of x. Factor the answer choices to see which prime factors they contain. Start with choice A, 30. The prime factorization of 30 is 2 × 3 × 5. The product of these three prime factors and 19 could produce a value of x, as such a product contains at least one of each prime factor of x, so eliminate choice A. Factor choice B, 228. The prime factorization of 228 is 2 × 2 × 3 × 19. The product of these factors and 5 could produce a value of x, as such a product contains at least one of each prime factor of x. Eliminate choice B. Factor choice C, 675. The prime factorization of 675 is 3 × 3 × 3 × 5 × 5. Only two of the four necessary factors of x are present in the prime factorization of 675. The product of these two distinct factors and any one of the prime factors of x cannot produce a possible value of x, as either 2 or 19 will be missing. Keep choice C and stop, because only one value can be an answer. However, were choice D and choice E factored, the prime factorization of 855 is 3 × 3 × 5 × 19 and the prime factorization of 950 is 2 × 3 × 3 × 5 × 5, respectively. The product of these sets of factors and either 2 or 19 could produce a value of x, as such a product contains at least one of each prime factor of x. Eliminate choices D and E. The correct answer is choice C.

The distinct prime factors of x are 2, 3, 5, and 19. Which of the following numbers, when multiplied by any one of the prime factors of x, could not be a possible value of x ? Question 5 Answer Choices 30 228 675 855 950

If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one odd number? 1/8 1/4 1/2 3/4 7/8

The question asks for probability and includes the phrase at least one. When a question says at least one subtract the probability of the undesired outcome from 1. The desired outcome is at least one even and at least one odd. Therefore, the two possible undesired outcomes are all even or all odd. On a six-sided die, there are 3 evens, so the probability of an even is 3/6 = 1/2 To find the probability that all rolls are even, multiply the probability that each of the three rolls will be even to get (1/2)^3 = 1/8. Find the probability of all odds. Similarly, on a six-sided die, there are 3 odds, so the probability of an odd is 1/2, and the probability that all three rolls will be odd is (1/2)^3 = 1/8. Since or in probability means addition, the probability of all even or all odd is 1/8 + 1/8 = 1/4. Subtract from 1 to get that the probability of at least one even and at least one odd is 1 - 1/4 = 3/4. The correct answer is choice D.

What is the volume of a certain cylinder? (1) The area of the base of the cylinder is 16π. (2) The area of the curved surface is 40π. Question 9 Answer Choices Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Your Answer Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Correct Answer EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

This is a Value Data Sufficiency question, so use Pieces of the Puzzle approach to assess the question. Determine "What is known" from the question stem and "What is needed" from the statements to answer the question. Begin by determining "What is known". The question stem does not give any information other than the question itself, so figure out "What is needed." To answer this question, the statement(s) must provide sufficient information to solve for the volume of a certain cylinder. The formula for the volume of a cylinder is V = πr^2h. So, in order to find the volume of the cylinder the radius and the height are needed. Evaluate the statements one at a time. Evaluate Statement (1). Since the base of a cylinder is a circle, write down the formula for the area of a circle and set it equal to 16π, so 16π = πr2. Solve for r by dividing by π, so 16 = r2. Take the square root of both sides to find 4 = r. This statement provides the value of the radius of the cylinder. However, there is no way to determine the value of h, so the volume of the cylinder with radius 4 will vary based on the height. When different numbers that satisfy a statement yield different answers to the question, the statement is insufficient. So, write down BCE. Now, evaluate Statement (2). Since the curved surface of a cylinder is essentially a rectangle, the formula for the curved surface is area = lw. The length is the distance around, or circumference, of the circular base, which is equivalent to 2πr. The width of the curved surface is simply the height of the cylinder or h. Write down the formula for the curved surface of a cylinder as area = 2πrh. Set the equation equal to the value of the curved surface 40π = 2πrh. Then cancel the π on both sides of the equation, so 40 = 2rh. Divide both sides by 2 to get 20 = rh. This gives the total value when the radius and height are multiplied. However, the volume of the cylinder is found by taking r2, and there is no way to determine the exact value of r. Because there is no way to solve for the individual variables, which would be necessary to find the volume, there is more than one potential answer. When different numbers that satisfy a statement yield different answers to the question, the statement is insufficient. Therefore, Statement (2) is insufficient. Eliminate B. Now, evaluate both statements together. Statement (2) indicates that 20 = rh. Statement (1) indicates r = 4. So, substitute r = 4 in the equation 20 = rh. Therefore, 20 = 4h. Divide both sides of the equation by 4 to find 5 = h. Since both the height and radius can be determined, it is possible to produce one consistent answer to the question. When there is only one consistent answer to the question based on the information provided, the information is sufficient. The correct answer is choice C.

Hard Ratio Question: A bowl of nuts contains almonds, cashews, and pecans. If there are 7 times as many almonds as there are cashews, what is the ratio of almonds to pecans? 1.) If 6 pecans were removed from the bowl, the ratio of cashews to pecans would be 2 to 3. 2.) There are 120 total nuts in the bowl. Question 11 Answer Choices Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are not sufficient.

Tough Ratio Question

QID 56892 (answer is D)

Two solutions are made by adding Chemical Z to water. Solution A is 40% Chemical Z and Solution B is 80% Chemical Z. A chemist combines Solution A and Solution B to make a mixture. If x percent of the Chemical Z in the combined mixture comes from Solution A, and if y percent of the total volume of the mixture comes from Solution A, which of the following expresses x in terms of y ?