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Math Errors
| Question | Answer |
|---|---|
| The Grizzly Bear Express is heading north at 65 mph. The Penguin Express is heading the opposite direction at 45 mph. If they are 250 miles apart, how long will it take for them to meet (in minutes)? | 2.27 hours. Add up the speed of the trains, do distance/speed to get time. Then convert the hours to minutes. |
| The average price of a fish dinner across 8 different restaurants is $16. If the price of fish nation-wide went up $2, what is the new average of fish plates? | $18.00 |
| A yacht usually travels 150 miles on a river in 10 hours. However, with the river's current, it takes only 8 hours. What is the speed in miles per hour of the river? | Determine the speed of the yacht alone and the yacht with the current. The yacht's speed with the current is the sum of the yacht's usual speed and the river's speed. |
| If you flip a fair coin 7 times, what is the probability getting heads exactly twice? | 2^7 = 128 is all possible combinations of head and tails for the 7 coin flips. Use 7! / (7-2)!2! for the favorable possibilities. 21/128 |
| Chris can paint a wall in 2 hours, but Pat can paint the same wall in 1.5 hours. How fast could they paint a wall together (in minutes)? | rate = wall/time. Find both rates and then add them together. Once you have that, set up a cross multiplication to find how long it takes to paint one wall. Convert hours to minutes. |
| A rabbit is 54 meters away from a fox (and closer to a bush). The rabbit runs to the bush at 8 meters per second, and it takes the rabbit 12 seconds to reach the bush. How fast is the fox running if it reaches the bush 3 seconds after the rabbit? | Do v * t.= distance to find out how far the rabbit runs. Do 12 s + 3 s = 15 s for how long the fox took to run to the bush. Add both distances together 96 + 54 and put that over the time. |
| How much pure alcohol must be added to a 72 mL solution that is 5% alcohol to make it 10% alcohol? | Pure alcohol = 72 mL × 0.05 = 3.6 mL. Total volume of the new solution = 72 mL + x. (3.6 + x)/(72 + x) = 0.10 |
| For 6 hours, Jose kayaks upstream against a river at 9 mph. He decides to turn around and rows downstream for 2 hours at a constant speed, until he reaches the dock he started at. What is the water’s speed? | First, we calculate the distance Jose covers as he kayaks upstream. 9 miles/hour * 6 hours = 54 miles. Then speed downstream = 54 miles/2 hours = 27 mph. Set up x - 7 = 9 mph upstream and x + y = 27 downstream. Add equations, x = 18, solve for y -> 9. |
| If the operating costs are three times the average salary, and the doctor works five days a week for 50 weeks a year, how much must the doctor charge per patient to break even, assuming they see 10 patients per day? | Determine the operating cost of the practice by multiplying the Chicago average salary by 3. Determine how many patients a doctor sees in a year. 50 weeks * 5 = 250 days. 250 * 10 patients = 2,500 patients. 900,000/2,500 = 360 per patient. |
| In the smaller quadrilateral, the three shortest sides are 8 cm, 10 cm, and 14 cm. In the larger quadrilateral, the two longest sides measure 42 cm and 48 cm. What is the length of the longest side in the smaller quadrilateral? | Smaller: 8, 10, 14, x Larger: ?, ?, 42, 48 We see that we have the second longest side for both quadrilaterals. They are similar quadrilaterals, so let’s setup a proportion. 42/14 = 3. By dividing the longest x by this, we get 18. |
| What is the area in the third quadrant for 4x + 3y = -24 | first find the x and y intercepts and then solve for the area of a triangle. x = -6, y = -8. Do base equation -> (6*8)/2 = 24 |
| If a boat takes 3 hours to travel upstream (against current) to a certain point, and 2 hours to return downstream (with the current) to its original point, what is the speed of the current? Assume the total distance for the round trip is 24 miles. | Find mph for both upstream and downstream, then make two equations b - c = 4 and b + c = 6. Subtract second equation by the first, solve for c = 1 mph. |
| Mr. and Mrs. Jankins plan to have 3 children and want 2 boys and 1 girl. What is the probability of this happening, assuming they do not care about the order of births? | 1/2 * 1/2 * 1/2. Because these children can be born in any order, there are 3 possibilities (BBG, BGB, GBB). Multiply the probability above by 3. |
| Evaluate the type of the algebraic equation: 1/x Linear, quadratic, or cubic? | None of the above, cause linear has a ^1 and this would have ^-1 |
| A sack has 4 red marbles and 6 yellow marbles. What is the probability of picking 4 red marbles and 1 yellow marble without replacement? | Use the combination formula to find the amount of possibilities. Then find the amount of ways to choose 4 red marbles and the amount of ways to choose one yellow (1 * 6 = 6). Do 6/252 for your answer. |
| A plane takes 5 hours to reach its destination while flying against the wind and 4 hours to return to the starting point with the wind. If destination is 400 miles from the starting point, what is the speed of the wind current? | 10, make two equations then factor one into the other |
| x^2 shape | concave up |
| x^2/3 shape | less steep concave down than x^1/3 |
| x^1/3 shape | steep concave down |
| x^3 shape | The upwards L |
| x^-1 shape | Two slopes at the corners, don't hit the actual x or y axises |
| x^-2 shape | Two slopes on either side of the y axis reaching up towards positive infinity |
| You have two dice and each has two sides of 1s, two 2s, and two 3's painted on it. You roll them, what's the chances of getting a sum of 4? | 1/3, total outcomes are 36, there would be double of each outcome |
| Patty walks at a pace of 3 mph along a river. It takes her 4 hours to get from the beginning to the end. She then sits on a log and sails back down to where she began and it takes 2.5 hours. What is the current speed (miles per hour) of the river? | 4.8 mph. Find total distance. Next, because we know that the distance upstream and downstream is exactly the same, we can find the speed of the water if it took 2.5 hours to sail down the entire river. |
| If A<B and C<D, which of the following must be true? | (A – B)(C – D) > 0 |
| What does a z score of 2+ mean? | it means the score is 2 standard deviations above the mean |
| 68-95-99.7 rule | 68% falls within u - o to u + o 95% falls within u - 2o + u + 2o 99.7% falls within u - 3o to u + 3o |
| If two dice are rolled, what is the probability of not getting a 6 on either of them? | 25/36 |
| What is the arithmetic average of m and n? (1) The average of m and 2n is 10 (2) The average of 2m and 6n is 30 | Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. You can write two equations and subtract them but you CANNOT do this with just one. |
| A patch of black oil in a circular pond doubles in size every hour. If it takes 12 hours for the patch to cover the entire pond, how long would it take for the patch to cover half the pond? | Remember the patch of black oil doubles in size every hour. This implies that one hour ago, the patch was half the size that it was. Therefore: 11 hours |
| The average of three numbers is 35. The range of the numbers is 26. The largest number is three more than twice the smallest number. What is the second highest number? | (x+y+z)/3 = 35 -> (x+y+z) = 105 Make two equations z - x = 26 and z = 3 + 2x, solve for x, and then substitute so you can solve for z. Finally, solve for y. Answer is 33 |
| If the following formula describes how the selling price S of a commodity is related to its cost C, which of the following statements is true? S = 4C + 9 | An increase of the cost by $1 results in an increase of the selling price by $4. |
| Kansas and North Dakota are the biggest producers of wheat in the United States. If last year, Kansas produced 2/5 of all wheat, North Dakota produced 1/3 of all wheat, and all other states produced 16 million tons combined, how much did Kansas produce? | 2/5 + 1/3 = 11/15 16 * 15/4 = 60 million tons total 2/5 * 60 = 24 tons from Kansas |
| In a classroom, 3/5 of the students are boys and the rest are girls. If 3/4 of the boys and 4/5 of the girls handed their homework on time, what fraction of the total students did not hand in their homework on time? | 23/100 |
| The number 3 * 2^-4 is how many times the number 6 * 4^-4? | 8. Do 3/6, then rewrite 4^-4 as 2^-8, then do the rest of the math. |
| Simplify logb(b)+ logb(b). | logb(b) + logb(b) = logb(b^2) logb(b^2) = 2logb(b) -> 2 * 1 = 2 This works because logx(x) = 1, so the final answer is 2. |
| Product Rule | logb(mn) = logb(m) + logb(n) |
| Quotient Rule | logb(m/n) = log(m) - log(n) |
| Power Rule | logb(m^n) = nlogb(m) |
| How to solve a log question | logb(x) = y -> b^y = x |
| In a roll of two fair dice, what is the probability of getting a sum equal to ten? | List all the outcomes that will yield a sum of 10: 5 & 5 - 4 & 6 - 6 & 4 So 3 outcomes 3/36 = 1/12 |
| If a - b = 13/15 and a + b = 15/26, what is the value of a^2 - b^2? | (a-b)(a+b) -> a^2 - b^2, so you just multiply (13/15)(15/26) = 1/2 |
| Simplify the following expression: 1 / (x + (1/x)) | Make x and 1/x have the same denominator by turning x into x^2 / x. Then solve for the rest to get (x / (x^2 + 1)) |
| If a^2 - 2ab + b^2 = 2 then (a - b)^6 = ? | a^2 - 2ab + b^2 can be simplified to (a-b)^2. Meanwhile, a^2 + 2ab + b^2 = (a + b)^2. So, if that equals 2 then put that to the third power to get 6. 2^3 = 8. |
| Which of the following is true for the graph of y = b? | It has a range of b. It would be a horizontal line, range is defined as all possible values of y. From the graph, the only possible value of y is b. |
| A manufacturing company places a six-symbol code on their product. The first 3 symbols are the letters X, Y, and Z, and the last 3 symbols are digits. How many such codes are possible if repeats are allowed? | Since repeats are allowed, the first 3 symbols can be any of the 3 letters, hence: 3 × 3 × 3 The last 3 symbols can be any of the 10 digits 0-9, hence: 10 × 10 × 10 # of possible codes is: 3 × 3 × 3 × 10 × 10 × 10 = 27 × 1,000 = 27,000 |
| In how many ways can 6 people be arranged in 6 chairs? | We have 6 people and 6 chairs. The first person can sit in any of the 6 chairs. The next person can sit in any of the remaining 5 chairs, so on. 6 × 5 × 4 × 3 × 2 × 1 = 720 |
| In a basket of 10 eggs, 3 are rotten. If Dave selects 2 eggs at random without replacement, what is the probability that both eggs are good? | 7/10 * 6/9 = 7/15 |
| What is the standard deviation of the set {5, 6, 9, 12}? | 2.74, don't forget that taking the square root of all of the sums is part of the equation! |
| x ≠ 0, (-x)^2 vs. -x^2 | Quantity A is greater |
| Kevin drives three times farther in 36 minutes than what Lucy drives in 30 minutes. If Kevin drives at a speed of 40 mph, then at what speed in miles per hour is Lucy driving? | 16 mph. First, calculate the distance that Kevin drives, keeping in mind that Kevin drives at 40 mph for 36 minutes. Divide that by 3 for Lucy's distance. Then do distance = speed * t for her speed. |
| x ≠ 0, x^3 vs. -x^3 | The relationship cannot be determined from the information given. Remember to try both negative and positive values for these types of equations! |
| If 2x + 3y = 7x - 4y, what is x/y? | 7/5 |
| If 5x + 3y = 15 and 3x + y = 4, what is the value of 2x + 2y? | 11 |
| If b^2 - 4ac < 0, | the quadratic equation has no real roots. |
| If b^2 - 4ac = 0, | the quadratic equation has two equal real roots (one root). |
| If b^2 - 4ac > 0, | the quadratic equation has two distinct real roots. |
| How many liters of a 10% acid solution must be mixed with 10 liters of a 30% acid solution to produce a solution that is 15% acid solution? | 30 liters. (0.10x+0.30(10)=0.15(x+10)) |
| James drives from City A to City B at 70 mph. Three hours later, Grant also starts driving from City A to City B, but at a speed of 100 mph. If they continue driving at their respective speeds, how many miles away from City A will they meet? | 700. 70(t*3) = 100 * t -> 7 hr * 100 = 700 miles |
| z-score formula | z = (x - u)/o |
| If a coin is flipped 3 times, what is the probability of obtaining at least one tail? | 7/8. P(event happening) = 1 - P(event not happening) P(all heads) = 1/2 * 1/2 * 1/2 = 1/8 1 - 1/8 = 7/8 |
| Is x < 0 ? 1) xy < 0 2) x|y| < 0 | Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. |
| A bag contains 4 red marbles, 6 green marbles, and 2 white marbles. What's the probability of picking a red marble and a white marble with replacement? | Because the order of the marbles is not specified, we multiply the probability we calculate below by 2. 4/12 * 2/12 * 2 = 1/9 |
| In how many ways can 3 different algebra books and 3 different physics books be arranged on a shelf? | Since there are 6 total books, n = 6. 6! = 720 ways. |
| Dana’s test scores on the first four exams are 80, 78, 70, and 60. If Dana wants to increase her test average by 8 points, what is the minimum average she needs on her last 2 exams to accomplish her goal? | 96.0 |
| Non Mutually Exclusive | P(A or B) = P(A) + P(B) - P(A and B) P(A or B) = P(A) + P(B) |
| Mutually Exclusive | P(A or B) = P(A) + P(B) |
| P(A|B) = | P(A ∩ B) / P(B) |
| In the figure below, lines l and m are parallel. What is the measure of angle x? | If the line is transverse, you can subtract x from 180. |
| What is 0.5% of 12% of 150? | 0.09. There is a percent symbol on the calculator! |
| If a 4L solution is 80% concentrated lime juice and 20% water, how much 30% concentrated lime juice must be added so that the concentration of the resulting solution is 50% concentrated lime juice? | You would set up the equation like lime juice/total volume. Do (3.2+0.3x) / (4 + x) = 0.5. |
| Evaluate 5log2(32). | 25 |
| 480 miles apart. A train starts at a certain time from Station X headed towards Station Y at 60 mph. Two hours later, a train departs from Station Y headed towards Station X and 48 mph. How far from Station X do the two trains meet? | 320 miles 60(t) + 48(t-2) = 480, then multiply by 60 for the mile amount. |
| Weighed 50 lab mice and found the mean to be 100 g and the standard deviation to be 7 g. To adjust for inaccuracies, the researcher multiplied each weight by 2. What is the new mean and standard deviation of the new set of data? | μ = 200 g, σ = 14 g |
| A and B are two independent events. P(A) vs. P(A|B). | The two quantities are equal. If two events, A and B, are independent, then P(A) = P(A|B). |
| If 27^x = 64 what is 3^x equal to? | You would rewrite 64 as x^3 and set it equal to 27. 3^3 = 4^3 Then (3^x)^3 = 4^3 The answer is 4 if you interchange the numbers. |
| 70% of students in a summer camp are boys, and of these 20% are left-handed. What percent of the students in the summer camp are boys and right-handed? | 56%. |
| Two fair dice are rolled. What is the probability of rolling a sum that is odd? | 1/2. Half of the numbers are odd. |
| A committee of 4 people is to be selected from a group of 9. If the selection is made randomly, how many different groups can be made? | 126 |
| union of the sets | contains elements in both sets without repetition - all of the elements together, but no doubles |
| intersection of the two sets | only the elements that are found in both |
Created by:
smurtab