DAT Bootcamp Practice 8 Trouble

A commuter drives 30 miles each way between home and work every day. When traveling home from work, traffic causes his commute to take triple the amount of time it takes compared to the trip driving to work. If traveling to and from work takes a total of 2 hours, what is the commuter's average speed traveling to work?

Based on the information for the problem, we can write the following equation, with x representing the amount of time it takes the commuter to travel to work: X+3X = 2 hrs , x =0.5 hrs to travel to work 30 miles to work/ 0.5 hr =60mph (speed)

x+8 = |3x-2|

Must solve for both possible equations for abs value : +(x+8) = 3x-2 and -(x+8) =3x-2 , +(x+8) = 3x-2 -> x=5, -(x+8) =3x-2 -> -3/2.

a=b² QA: 1/a QB: 1/b

RELATIONSHIP CANNOT BE DETERMINED. a and b are positive and greater than 1 (using a = 4 and b = 2 as an example): The denominator b will be smaller, making the overall fraction in Quantity B larger. a and b are positive and less than 1 (using a = 0.04 and b = 0.2 as an example): The denominator a will be smaller, making the overall fraction in Quantity B smaller.

Based on the information for the problem, we can write the following equation, with x representing the amount of time it takes the commuter to travel to work:

1/120 + 1/180 mins =1/x 3/360 + 2/360 mins = 1/x , 5/360 = 1/x , 5x =360 x =72 mins

How many distinct ways can you select 2 people from a group of 10, if the order in which they are picked matters?

Since order is important, permutations can be used. The sample size, or n, is 10 and the number of items select¸or r, is 2. n!/ n-r! 10!/8! 10x 9 x 8 / 8! = 10 x 9 =90

Matt can paint 4 fences in 2 hours. Woody can paint 3 fences in one hour. How many fences can Matt and Woody paint together in 3 hours?

The most straightforward way to solve this problem is to first figure out how many fences Matt and Woody can paint in 3 hours while working individually, and then use those rates to determine how many fences they could paint together in 3 hours. Matt can paint 4 fences in 2 hours, so he can paint the following fences in 3 hours: 4/2 = X/3, X = 6 fences. Woody can paint 3 fences in 1 hour, so he can paint 9 fences in 3 hours. 6 fences +9 fences = 15 fences

How many different combinations of 3 apples can be picked from a set of 7 identical apples?

we can use combinations because we are not told that order matters n!/r! (n-r)! 7 x 6 x 5 / 3 x2 x1 = 210/6 = 35

A liquid hydrogen peroxide mixture is made up of hydrogen peroxide and water. How much pure hydrogen peroxide must be added to bring a 2 liter mixture of 50% hydrogen peroxide up to a mixture of 65% hydrogen peroxide?

with percentages converted into decimals and x being the liters of pure (100% = 1.0) hydrogen peroxide added: 2 *0.5 +x *1.0 = (2+x) *0.65 , solve for x : 1+x = 1.3 +0.65x 0.35x = 0.3 x = 0.86 liters

y ≠3 QA: y²-9 / y-3 QB: Y-3

y²-9 / y-3 = (y+3) (y-3) / y-3 = y+3 vs y-3 QA is greater

√8a²b⁶ / 2a⁵b Simplify

√8(a²)½(b⁶)½ / 2a⁵b = √8ab³/ 2a⁵b =2√2ab³/ 2a⁵b = √2b²/ a⁴

The mean and standard deviation of a set of numbers is given by x and y. If all of the numbers are divided by 2, how does x and y change?

both decrease

If , 3∧x+4 = 9∧2X+7 then which of the following is equal to x?

3∧x+4 = 3²(2X+7 ) , 3∧x+4 = 3∧4X+14 , x+4 = 4X+14 , -10 = 3x , x =-10/3

An apple weighs 4 ounces, while an orange weighs 6 ounces. If the weight of N apples is the same as the weight of (N-8) oranges, what is N?

4*N = 6*(N-8) , 4N =6N-48 , 2N =48 N=24

Ray's house in South Florida is 300 miles away from Gainesville. Ray's friend Ron lives in Ocala. If Ray's house is 10 times further away from Gainesville than Ray's house is from Ron's house, how long will it take for Ray to travel to Ron's house if he travels at 60 miles per hour.

To solve this problem, we need to first find the distance between Ray's house and Ron's house. Based on the information in the problem, the distance between Ray's house and Gainesville (300 miles) is 10 times the distance between Ray and Ron's houses. Therefore, the distance between Ray and Ron's houses is 30 miles. Now, we can use this distance and the given speed to calculate the amount of travel time necessary: 30 mi/ 60mph = 0.5 hrs

A new Apple computer costs $1000 more than a new Dell computer. If the Dell computer is 2/3 the cost of the Apple computer, what is the cost of the Dell computer?

We can solve this problem through a system of equations. I will use A = Apple computer and D = Dell computer: D+1000 = A D= 2/3*A D= (2/3)*(D+1000) D=2000