DAT QR QUESTIONS

There are seven bridges connected to an island. How many different ways can someone enter the island on one bridge and leave on a different bridge? A. 7 ways B. 14 ways C. 25 ways D. 42 ways E. 49 ways

- D. 42 ways - it' simply 6*7 which = 42 possibilities

See other side

- Remember when you sqrt, you have to sqrt the entire thing including the X!! then you can solve for X.

Check the definition side for problem

- it says with 4 dollars he can buy 16 apples exactly. So divide it so you know apples per dollar exactly: 16/4= 4 apples/ 1 dollar now you know that each apple cost .25 each. so with 4 apples costing .20 more, you know that its only .80 for 5 oranges. and we can divide to determine the cost per oranges: .80/5oranges= .16 cents per orange. -Now use the $4 to determine how much oranges you can buy with $4: 4/0.16= 25 oranges.

An organic apple costs $1.60 more than a regular apple. If the cost of a regular apple and an organic apple together is 280% of the cost of a regular apple, how much does an organic apple cost?

- set up system of equation: Using RA as regular apple and OA as organic apple RA + 1.60 = OA RA + OA = 2.8 RA Plugging in the OA from the first equation into the second, RA + (RA + 1.60) = 2.8 RA 2 RA + 1.60 = 2.8 RA 1.60 = 0.8 RA 2 = RA OA would be $2 + $1.60= $3.60

see the other side for problem*

- set x is just 10, 20,30,..60.... 90. set y is just 12, 24,36....60... 96. quant A. says the intersection of the two sets, which only meets at 60. quant b also says 60, so theyre both equal.

What are the interquartile range?

- the value inside of the box

According to a survey, the average number of keys kept on a given person's keychain is normally distributed with a mean of 4 and a standard deviation of 1. If a person is chosen at random, what is the probability that this person has less than 3 keys on their key chain? A. 5% B. 16% C. 34% D. 50% E. 68%

- this questions is asking what is the possibility that we pick someone with 3 keys on their key chain. ** we know that the fist standard deviation is only 68%** so with the that random person being at 3, they're outside that 68% 68-100= 32 ** remember that this 32 is on a graph and is split between the two** 32/2= 16% chance of choosing someone with 3 keys on their chain.

Three positive integers x, y, and z sum up to 65. The ratio of x:y:z is 5:4:4. What is the difference between x and z?

- we have to know its scaling factors, Let k be a scaling factor for the three positive integers. We have x = 5k, y = 4k, and z = 4k. Therefore: x + y + z = 65 5k + 4k + 4k = 65 13k = 65 k = 5 This means x = 5(5) = 25, and z = 4(5) = 20. The difference is 25 - 20 = 5.

A survey was conducted to determine the number of televisions in a household. The data was found to be normally distributed with a mean of 3 televisions and a standard deviation of 1 television. Approximately what percent of the population owns more than 5 televisions in their households? A. 1% B. 2.5% C. 5% D. 10% E. 33%

-B. 2.5% -Remember that with a normal distribution, 68% of values are within 1 standard deviation of the mean, 95% are within 2 standard deviations, and 99.7% are within 3 standard deviations. The normal distribution is symmetrical. - the mean is 3 so a standard deviation of 1 means it's +/- 1 so the 68% range= 2-4, second standard deviation range is 1-5 and thats 95%. the question asks about percent of pop owning more than 5 tvs. So if we take 95%-100%= 5%/2 we would get 2.5% because of the symmetry of normal distribution.

A regular hexagon has a perimeter of 12. What is the area of the hexagon? A. 6 B. 6√3 C. 8 D. 8√3 E. 12√3

-B. 6√3 -hexagons area formula: 3 x Sq. 3/2 x (S^2)

Grace is twice as old as her sister. How old is Grace? 1) Grace was three times as old as her sister two years ago. 2) The sum of Grace's age and her sister's age equals 12. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

-D. EACH statement ALONE is sufficient. - know that you can form eq. from each statement alone: st. 1 says G- 2 = 3 (S-2) St. 2 says G+S=12 ^^ get better at these!

look at definition:

-Remember with these, that its too vague and that the integers can still be a negative to give a negative value; I.E y=5 and x= -1 which would =-1 in quantity A!!

Johnny has 15 toys with a total value of $125. If some of Johnny's toys are worth $5 and the others are worth $10, how many toys does Johnny have that are worth $5? -5toys -7toys -8toys -10toys -13toys

-since johnny has a total of 15 toys, let x+y= 15 so we know that 10x + 5y = $125 now we set up systems of linear equations: x + y = 15 x = 15 - y Substitute this expression for x in the second equation, to solve for y: 10x + 5y = 125 10(15 - y) + 5y = 125 150 - 10y + 5y = 125 -5y = -25 y = 5

The standard deviation of {10, 15, 20, 25, 30} can be best approximated by which of the following? -3.3 -7.5 -12.2 -14.6 -15.7

-standard deviation is a measure of how far data is from the mean Since this data set is symmetrical, the middle number 20 is the mean. If we find each number's distance from the mean, we get the following list: {10, 5, 0, 5, 10}. The average of these values is (10 + 5 + 0 + 5 + 10) / 5 = 30 / 5 = 6. This is only an estimate, but we can expect the actual standard deviation to be close. Answer choice [B] is by far the closest to 6

If (x + y)3 = (x - y)2 = 64 and x > y, what is the value of x?

-start this by splitting each first: (x + y)3 = 64 AND (x - y)2 = 64 then take the sq rt of both sides: (x + y) = 4 AND (x - y) = 8 use the linear combination method to combine both equation together and simplify: x=6

If the z-score of Jamie's test score is -0.23, what is the best representation of this z-score? A.Jamie's test score is 0.23 points below the mean. B.Jamie's test score is 0.23 standard deviations below the mean. C.Jamie's test score is 0.23 standard deviations above the mean. D.23% of Jamie's classmates received a lower score than Jamie. E.23% of Jamie's classmates received a higher score than Jamie.

.Jamie's test score is 0.23 standard deviations below the mean. negative z score represents a SD below the means

The odd numbers on a regular die are painted red. On a second regular die, the numbers that are one less than a perfect square are painted red. If both dice are thrown, what is the chance that both come up red? A. 1/12 B. 1/6 C. 1/3 D. 3/12 E.7/12

A. 1/12 -we know that the first sentence is saying that the probability will be 1/2. -the second sentence is saying that the probability will be one less than a perfect square are painted red. A perfect square is a number that is the square of another whole number. Some examples are 1, 4, 9, 16, 25 (or 12, 22, 32, 42, 52). The only perfect squares that appear on a die are 1 and 4, so the only number one less than a perfect square on a die is 4 - 1 = 3. so, 1/6 now we can multi the two to give us our probability of both dice coming up red.

What expression describes the shaded region in the picture, between the lines y = -x and y = 2x + 5? A. y ≥ -x and y ≤ 2x + 5 B. y ≥ -x and y ≥ 2x + 5 C. y ≤ -x and y ≤ 2x + 5 D. y ≤ -x and y ≥ 2x + 5 E. y = x and y ≤ 2x + 5

A. y ≥ -x and y ≤ 2x + 5 ** when looking at this image, you'll see the two separate lines that are represented by blue an yellow** -the blue line is obviously a Negative slope so x would be negative. Y= - X and you'll see that the shaded region is above the line so it would mean that it is "greater than" Y> -X -The yellow line is given y = 2x + 5 . If we look at the graph, the yellow line has shaded region below the yellow line which would mean that Y< 2x+5

Three positive integers are in the ratio of 13:6:3 and they sum to 132. What is the difference between the largest and smallest numbers? A.60 B.70 C.78 D.88 E.110

A.60 -You need to find the scaling factors: Let k be a scaling factor for the three positive integers. Their values are 13k, 6k, and 3k, so we have: 13k + 6k + 3k = 132 22k = 132 k = 6 This means the largest number is 13(6) = 78 and the smallest is 3(6) = 18. Their difference is 60.

What is the probability of 5 consecutive heads or 5 consecutive tails in five tosses of a fair coin? A. 1/32 B. 1/16 C. 1/8 D. 1/4 E. 1/2

B. 1/16 ** we have to calculate the probability of the possibility of it landing on heads AND tails consecutivly** we know a coin flipped 5 times is 1/32, but we have to divide that by two because of the possibility of it landing on one side all those times in a row.

A bag is filled with 20 pieces of Candy A and 10 pieces of Candy B. If you choose 2 pieces of candy at random without replacement, what is the probability of picking one piece of Candy A first and one piece of Candy B second? A. 2/9 B. 20/87 C. 1/3 D. 40/87 E. 2/3

B. 20/87 Watch if it says with replacement or without replacement!

A drawer contains 6 black socks and 8 gray socks. If you pick a sock at random, then pick another sock at random without replacing the first one, what is the chance that both socks are gray? A. 15/91 B. 4/13 C. 1/2 D. 8/14 E. 64/91

B. 4/13 - theres a total of 14 socks in the drawer, and we know that the probability of choosing the first grey sock so it 8/14. -now it says "without replacement" so we subtract 1 from both 7/13 now just multiply: **note that you can reduce the 7 and 14 before pluggin it into the calc**: 8/2 x 1/13 = 8/26 reducing down to 4/13!

A population of rabbits grows by 10% every month. If the population begins with 1,000 rabbits, how many rabbits will there be in 6 months? A. 1,234 rabbits B. 1,451 rabbits C. 1,772 rabbits D. 2,003 rabbits E. 2,304 rabbits

C. 1,772 rabbits - the best way to approach this question is by using the compound interest formula: A=P(1+r/n)^nt A=final pop. size P= initial size r= intrest rate n= the rate its growing at (1 month) t= number of time periods (6 months)

Approximately what is the measure of each interior angle in a regular 13-gon? A. 144 degrees B. 148 degrees C. 152 degrees D. 160 degrees E. 172 degrees

C. 152 degrees -remember this formula: 180(n-2)=sum of internal angles. where N = the sides of the polygon so if n= 13: 180(13-2)= 1980 1980/13 because it asks for each! each angle= 152 degrees.

Bill can mow a lawn in one hour and twenty minutes. If Bill and Dave can mow the lawn together in a half-hour, how long does it take for Dave to mow the lawn alone? A. 30 minutes B. 36 minutes C. 48 minutes D. 50 minutes E. 90 minutes

C. 48 minutes -Recognize that this is a combine rate problem: 1/ Ta + 1/Tb = 1/ Tc plug it in and solve!

Half of the population of Cool Town owns a bicycle, and 25% of the population owns a car. If 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from Cool Town owns either a car or a bicycle or both? A. 10% B. 50% C. 65% D. 75% E. 100%

C. 65% -In order to make this problem easier, let's assume Cool Town has a population of 100 people. Therefore, 50 people own a bike, 25 people own a car, and 10 people own both. We can also say that 50 - 10 = 40 people only own a bike and 25 - 10 = 15 people only own a car. The total amount of people that would own only a car, only a bicycle, OR both would be 40 + 15 + 10 = 65. Since the population of Cool Town is 100, the total probability would be 65/100, or 65%.

How many different ways (orders) can you arrange 6 different playing cards? A. 6 ways B. 36 ways C. 720 ways D. 1,296 ways E. 46,656 ways

C. 720 ways -The number of permutations of n distinct objects is n! = n × (n - 1) × (n - 2) × ... 1. so just 6x5x4x3x2x1

A horse runs two 7 furlong races in a week. What is the distance in miles the horse will run in 13 weeks? A furlong is 1/8th of a mile. A.3 1/4 B.11 3/8 C.22 6/8 D.43 7/8

C.22 6/8

Julia took 4 courses at her college this past semester. She earned an A in Chemistry (3 credits), a B in Chemistry Lab (1 credit), an A in Spanish (4 credits), and a C in Fruit Science (1 credit). If grades are weighted such that an A is four grade points, a B is three grade points, and a C is two grade points, what is Julia's grade point average from this past semester? A. 2.89 B. 3.00 C. 3.50 D. 3.67 E. 4.00

D. 3.67 -You have to know the formula for GPA: GPA= Total Grade Pt./ total credits. - Summing up the grade points from each class gives us the total number of grade points: total grade points = 4(3) + 3(1) + 4(4) + 2(1) = 33 -Summing up the credits from each class gives us the total number of credits: total credits = 3 + 1 + 4 + 1 = 9 now we can just plug it in to find the GPA: 33/9 = 3.67

Train A leaves a city traveling at 100 miles per hour. Train B leaves from the same city in the same direction of Train A traveling at 150 miles per hour. If Train A leaves 3 hours before Train B, how long will it take for Train B to catch up to Train A? A. 3 hours B. 4 hours C. 5 hours D. 6 hours E. 8 hours

D. 6 hours -Train A: 100t +300 Train B: 150t -100(3) + 100t = 150t 300 + 100t = 150t 300 = 50t t = 6 hours

If an angle is two more than three times its complement, what is the measure of this angle? A. 20 degrees B. 34 degrees C. 52 degrees D. 68 degrees E. 74 degrees

D. 68 degrees - the questions states that the angle is 2 more than 3 times its complement. 2+ 3(90-x)= x since we know that x + x=90 then we solve: x = 3(90 - x) + 2 x = 270 - 3x + 2 4x = 272 x = 68º

How many ways can the letters in APPALOOSA be arranged? A. 2,405 ways B. 2,505 ways C. 9,050 ways D. 13,530 ways E. 15,120 ways

E. 15,120 ways -There are 9 different elements or 9! but you also have to taken into account the number of repeats for letters: since there's 3A's, 2P's, and 2O's we put those all in the denominator.

How many lines can be drawn between a set of 7 distinct points? A. 10 lines B. 12 lines C. 15 lines D. 19 lines E. 21 lines

E. 21 lines -A line forms a connection between 2 points, so we can see the question as asking for how many ways there are to choose 2 points to connect from a set of 7 points. - we need to know the combination formula (when order doesn't matter):

Samantha's pie stand has 17 average visitors per day for the past 6 days. How many people must visit her stand on the seventh day to maintain her quota of 20 visitors per day? A. 17 people B. 18 people C. 20 people D. 23 people E. 38 people

E. 38 people -If you follow the eq. you can solve these problems pretty easily: average= Total visitors/ # of days 17 visitors= total visitors over the last 6 days/ 6 days-- * now you multiply 6 by both sides to determine the number of visitors over the last 6 days. and you do the same for the seven days. Once you have both totals of total visitors, you subtract it form each other to determine the amount needed for the average to be 20 visitors per day.

A farmer has a piece of land with an area of 4 square yards. If a cow can graze grass at a rate of 2 square feet per hour, how long will it take 3 cows to graze the entire piece of land? A. 1 hour B. 2 hours C. 3 hours D. 4 hours E. 6 hours

E. 6 hours -we have to convert our yrds to feet first, so we take the 4yrds^2 and mult by the 3ft but we have to sq the 3. thus, we get 36ft^2 given that we have 3 cows that graze at 2ft^2 per hour, we can use diminutional analyses to give us 36ft/ 6ft/hour= 6hrs

A square has an area equal to 49. What is the length of the largest bisecting line going between opposite points of the square? A. 4 B. 4√2 C. 6 D. 7 E. 7√2

E. 7√2 -we know that all sides of the square = 7 because 49=S^2 and we just squre root both sides to give us the size of each square. ** the question states that we have a bisecting line, which means it's a line going between two corners** This will give us a two 45-45-90 triangles. BUT we have to know that with these triangles, you also get S, S, S√ 2. we know that S= 7 so you get 7√2

For which of the following could set {-100, -50, -25, 25, 50, 100} satisfy G ∪ F? A. F = {x ≥ 100}, G = {x ≤ -100} B. F = {|100|}, G = {-50, -25} C. F = {x < 100}, G = {x < -100} D. F = {x < 25}, G = {x < -25} E. F = {x ≥ 14}, G = {x ≤ -14}

E. F = {x ≥ 14}, G = {x ≤ -14} -The union G ∪ F means every number in the set must be inside G, F, or both. We can eliminate choices by checking if each number in the set is in either G or F. - so looking at the choice, E. is the only one that makes sense and incorporates every answer option.

For Z scores, if it is negative that means it is....

Negative Z score means you have a standard deviation below the mean.

What is the log2x = 2

Take the base of the log and raise it to whatever it's equal to, to get rid of the log sign.

What is a complement angle?

When two angels sum up to 90 degrees.