DAT QR Missed Questions

A fair coin is flipped 5 times, what is the probability of getting a tail in the fifth flip? (Strategy)

A coin flipping five times are all independent events. There is ALWAYS a 50% chance of getting tails, so thats the answer.

What is the conversion between miles and meters?

1600m/1mile

Currently, Tommy is five times as old as Bianca. In eight years, Tommy will only be three times as old as Bianca. How old is Tommy right now? (Problem approach+solution) A. 8 B. 16 C. 24 D. 32 E. 40

40; Write equation relating first relationship given (Tommy=5*Bianca). Then, write second relationship given (Tommy+8=3(Bianca+8)). Plug in what you know T is to solve for B, then plug that into your original equation to solve for Tommy's age. If there is a year gap don't forget to account for that from both parties.

In how many ways can 3 different algebra books and 3 different physics books be arranged on a shelf? (Strategy)

Amount of book factorial (mult by eachother)

How do you find the IQR on a box plot?

Area in the box Topbox number-Bottom box number

How many four-digit numbers can be made from the following digits {1, 3, 5, 7} if no digits are repeated?

No digits are repeated and there are 4 digits possible. So we just multiply 4*3*2*1 to get our answer of 24.

Can we identify the percentage of each box in the interquartile range if it is not normal distribution?

No

Which of the following lines is perpendicular to the x-axis?

Perpendicular to the x axis would be a vertical line. Vertical lines have equations of x=constant. So this is the answer.

Dana is 20 years younger than her mother. In 4 years, the mother will be twice as old as Dana. How old is the mother now? (Strategy)

Write equations. We can see that D=M-20. We can also see that M+4=2(D+4). So just find a common variable and plug it in to solve for M. Note that since Diana's mother is twice as old as her, M=2D.

If x and y are odd integers, which of the following must be even? x,y>1 (Just problem approach)

"Plug and check" solution. Pick two odd numbers and check them for each choice. You will be looking to see which is an integer (we don't want that because it doesn't fit the problem criteria) and which is going to ALWAYS produce an even number. Remember that an odd number +/-1 has to be even, and 2 even numbers multiplied together will always give an even number.

How many yards are in a meter?

1.1

If 2x2 - ax + 6 = 0 has two distinct real roots, which of the following must be true? A. a2 < 48 B. a2 = 48 C. a2 > 48 D. a2 = 12 E. a2 = 24

A; Must remember real roots formula: b^2-4ac>0 for 2 real roots.

Five fair coins are tossed. What is the probability of the toss yielding at least four heads? A. 3/16 B. 1/4 C. 9/32 D. 5/16 E. 11/32

A; calculate the total combinations possible (2 outcomes^5 occurrences= 32 total combinations). Find out how many combos are possible for each scenario (all five are heads=1, four are heads and 1 is tails= 5!/(5-1)! = 5 permutations). Take the total number of permutations over the total number of combos possible and that is your answer.

Which of the following equations forms a perpendicular line to the line 16 = 3y + 5x? A. 10y = 6x + 15 B. 4 = 3y + 5x C. y = -3x⁄5 + 8 D. 2x = 16 - 10y E. 5y = -x - 4

A; convert the given equation to y=mx+b form to find the slope. Take the reciprocal of the slope for a perpendicular line. Remember that the reciprocal of the slope flips as well as SWITCHES SIGN. Rearrange equations given to find the right answer.

Quantity A: The numerical value for the internal angle of a regular 14-gon Quantity B: The numerical value for the area of a circle with circumference 16π A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

B; The total sum of internal angles is equal to 180deg(sides of shape-2). Divide that by the number of angles in the polygon and we can find that the internal angle of a 14 gon is 154. Circle circumference is pi*d. That means 16 is d, and r is 8. Circle area=pir^2, so we can find that it is 201. Thus, we know definitively that quantity B is greater.

Hose A takes 45 minutes to fill the swimming pool. Hose B takes 1.5 hours to fill the same pool. How many minutes does it take to fill the swimming pool if both hoses are operating at the same time? A. 15 minutes B. 30 minutes C. 45 minutes D. 75 minutes E. 150 minutes

B; Work problem. Write an equation. 1 pool/45min*xmin+1 pool/90min*xmin= 1 pool. Solve for x, and you get 30.

If 5a - 10b = 61 and 12a - 3b = 131, then what is the value of a + b? A. 8 B. 10 C. 16 D. 20 E. 24

B; use subtraction method. Subtract smaller equation from larger equation. Manipulate to get a and b. In this case, we are able to manipulate to get a+b by itself when doing the subtraction method. This saves us a lot of time.

Find a solution set for x: |5 - 2x| < 19 A. x > 7 B. -7 < x < 12 C. x < -7 or x > 12 D. x > -7 E. x > 7 or x < -12

B; write equation as -a<x<a (where a is the equation by the law of inequalities and absolute values). Solve to get X alone. Remember to flip the sign of the equation when you mult/divide by a negative number. Then, you will arrive at your answer.

A bowl contains 8 white marbles, 6 red marbles and 2 black marbles. Two marbles are drawn, without replacement. Quantity A: The probability of both marbles drawn being white. Quantity B: The probability of one marble being black from the two drawn. A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

C; First, calculate the probability of drawing both white (Quantity A). 8white/16total*7white/15total=56/240 chance. Second, calculate the two scenarios of drawing one black and add them together (Quantity B). One black first: 2black/16total*14other/15total=28/240 chance. One black second: 14other/16total*2black/15total=28/240 chance. 28/240+28/240=56/240 chance which is equal to quantity A.

The volume and the surface area of a cube are equal. What is the edge length of the said cube? A. 1 B. 4 C. 6 D. 9 E. 16

C; First, remember the SA and volume formulas for a cube. SA=6s^2, while volume=s^3. Set the SA and volume equal to eachother then solve for what s would equal, which is 6.

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? A. 3L B. 4L C. 6L D. 8L E. 10L

C; first, calculate the starting amt of lime juice from the total volume multiplied by conc of lime juice. Next, set up a ratio of amt lime juice/total volume so that we can get that equal to 1/2 (50%). Then, write the starting amt of lime juice+0.3(30% conc)*added volume as the numerator and starting amt total+added volume as the denominator. Cross multiply with the equation set equal to 1/2 and solve for X (added amount).

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? (Strategy)

Concentration problem. Use ALLIGATOR METHOD. Write x liters/liters known. Then, write percent conc over percent conc. Finally, draw a line and write the final conc. Subtract final conc from denominator (numerator of new fraction) and then final conc from numerator (denominator of new fraction). Take this value and set it equal to your first fraction and solve for x.

How many distinct lines can be drawn connecting eight points on a plane? A. 8 B. 15 C. 21 D. 28 E. 56

D; Either draw a diagram with 8 points and just see how many unique lines you can draw, or use 8 choose 2 and solve 8!/2!(8-2)!

If the price of a concert ticket increases by 20%, then increases by another 20%, and then increases again by 10%, what is approximately the overall percent increase of the ticket? A. 40% B. 48.5% C. 50% D. 58% E. 60%

D; Pick a starting value like one. Then, increase up to the percentage listed in the problem. At the end, your percent increase is just the amount of the decimal after the 1.

Station X and Station Y are 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? A. 108 miles B. 180 miles C. 240 miles D. 320 miles E. 400 miles

D; Set up equation relating the times equal to the total distance in miles and account for the fact that train 2 departed two hours later. 60t+48(t-2)=480. Solve this equation for t, then use the time multiplied by the speed for station X to find miles travelled before the trains met. 5.33hr*60mph=320 miles.

At the end of 2014, John deposited $1000 into his bank account. If he didn't deposit any more money into the account, and the account earns 4.2% interest per annum, how much money is in the account by the end of 2019? (to the nearest cent)? A. $1042.00 B. $1131.37 C. $1210.00 D. $1228.40 E. $1279.99

D; Use the repeated percent increase formula: Final amount=Principal(original)*(1+r)^n. Where principal is the starting sum, r is the rate in decimal form, and n is the number of increases. Plug in the values and solve.

An equilateral triangle has sides of length 12. What is its area? A. 24√2 B. 24√3 C. 36 D. 36√3 E. 72

D; With the equilateral triangle formula we know that the area will be s(sqrt(3))/4. So we can just plug 12 in for s. If we don't remember the formula, we can use the 30-60-90 rule that says the ratio of a 30-60-90 triangle will be 1-root3-2 respectively. From there, we can split the equilateral triangle into two similar 30-60-90 triangles and use the ratios to calculate the height. Once we have the height, we can do 1/2bh (b as original base, h as height calculated) to get the answer.

x<0<y Quantity A: -3(x+y) Quantity B: -xy A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

D; first we must determine the relationship from the inequality given. We can see x is negative while y is positive. Now we will look at how that fits into our equations. Testing values or just imagining the values we could plug in, we know that we cannot determine this relationship without definitive quantities because the answer would change.

For a college student at a particular university, the mean number of classes taken per semester is 4, with a standard deviation of 1. Assuming that the data taken at this university is normally distributed, what is the percentage of students that are taking 6 or less classes per semester? A. 2.5% B. 5% C. 95% D. 97.5% E. 99.7%

E; Draw/picture the bell curve. Remember the 68-95-99.7 rule. Note that the value in question is 2 standard deviations away from the mean. We can see from the bell curve that 2.5% is the total that will take more than 6 classes, so we can subtract that from 100% and find that there are 97.5% of people that take 6 or less classes.

The probability that Joe wins his first boxing match is 0.47. The probability that Joe wins his second boxing match is 0.85. What is the probability that Joe wins at least one of these two matches? A. 0.50 B. 0.61 C. 0.75 D. 0.85 E. 0.92

E; First, calculate the probability he loses both matches. Multiply 1-winning chance1*1-winning chance2 to get this. Then, subtract that from one. That is his probability of losing both matches. Subtract that from 1 to get the probability of anything that is not losing both (ie, winning at least one).

If two fair dice are rolled, what is the probability of getting a sum of 8? (strategy)

Find the chances of rolling a sum of 8 by writing out all the ways you could get that. Then, calculate the total number of possible outcomes (6*6=36). The probability will be ways you can get a sum of 8/number of possible outcomes.

If you flip a coin 4 times, what is the probability of obtaining at least one tail? (Strategy)

Find the probability of flipping all heads which will be the only scenario where we can't get at least one tail. 1/2*1/2*1/2*1/2=1/16. 1-1/16=answer.

Dennis has $4.00 in nickels dimes and quarters. If he has four more quarters than nickels, and 3 times as many dimes as nickels, how many dimes does he have? (Strategy)

First, write an equation using the values of nickels, dimes, and quarters added up to 400 cents. Then, write individual relationships given in the problem to get a common variable that we can sub. Lastly, plug in your variables to solve, then plug in your answer to the relationship to get the number of dimes.

What is the percent increase formula?

Larger number/Small number. Decimal is the percent increase.

Lily and Nada share silver coins in the ratio 7:3. If Lily gives 3 silver coins to Nada, the ratio becomes 5:3. How many silver coins did Lily have initially? (Strategy)

Set up an equation. The initial ratio was 7/3, so 7x-3/3x+3 after Lily gives the coin is the new ratio. Set that equal to 5/3, then solve for x. Once you have x, multiply that by 7 as that is what Lily had initially.

C and D are positive integers. Is C odd? 1) C + D is even 2) C2 × D is odd A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

Testing statement 1, we can see that there is not enough info because an even or odd number could give an even product. Testing statement 2, we know that to get an odd product both factors must be odd. We also know that an odd number squared will be odd. Thus, we know that C has to be odd.

Evaluate 5log2(32) A. 10 B. 25 C. 64/5 D. 64 E. 160

The power log rule says that LogB(X^n)=nLogB(x). So saying that Log2(32)=X, we know that 2^x=2^5 and thus that X=5 for this log normally. We can then plug that into our original equation to perform (5 (Log2(32)*5) and get an answer of 25. Steps: Solve for original log then multiply by the number in the equation we were given.

How do you find the ranges on a box plot graph?

Top-Bottom

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?

Use "9 choose 4". So 9!/4!(9-4)! is what we are solving. We can work that equation out to get 126.

James leaves Jimsville travelling toward Granitville 650 miles away at 70 mph. Two hours later, Grant leaves Granitville travelling towards Jimsville at 100 mph. What is the ratio of the distance travelled by James to the distance travelled by Grant when they meet?

We know the sum of the total distances so we can set G+J equal to 650. We know that James travelled 70t while Grant travelled 100(t-2) because he left 2 hrs later. Now, we just set this equal to 650 and solve for x. Once we get x, we use that to find the total number of miles travelled for both Grant and James. Then, we can put it into a fraction James/Grant and simplify it.

The scores on a math exam worth 100 points are normally distributed with a mean of 70 and a standard deviation of 8. If Allen's z-score on the exam is -1.5, what grade did he receive on the exam? (Formula)

standard z score= observed value-mean of sample/standard deviation of sample.