QR questions from ADEA DAT

[ddsshin]

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I finished the QR section on the DAT from the ADEA website, and it does not have any explanation. Some of the questions, I don't understand.. can you guys help??
10. a person travels to work at an average speed of 40mph, and returns home at 60 mphs, which of following is average spped for entire trip?
answer is C.... but isnt it 50?????? why C??

29. a painting which is 4 ft wide and 5 ft long is surrounded by a rectangular frame 6 inchese wide. what percent of the area of the picture and the frame is occupied by frame?
answer is 33 1/3. I really don't understand the question.... why is that answer????

32. if y= x+2 / x-3... which represent x?

answer is 3y+2/ y-1
I don't know how to get this.... I know if I plug in numbers, that answer is correct but how do you come up with that answer?????

36. each of the circle I ,II, III is tangent to the other two circles... the areas of circules are 4pi, 9pi and 16pi. which represents the length of perimeter of the triangle formed by joining the center of 3 circles??

I don't understand when it says,,,, each of the circle 1,2,3 is tangent to the other two circle??? waht is that mean???? the answer is 18.....
There is a diagram, but i can't put in here.... any explanation why 18???

37. the number 1,2,3,6 have avg of 3 and variance of 3.5
what is avg and variance of the set of numbers 3,6,9,18?
I know average is 9, but the variance is 31.5 in the answer.
isnt it 42????????????????????/ don't get it.....

ok, I think that's it.... help appreciated!!!!!

 

[PooyaH]

10. you need to know the distance formula: Distance = Speed x Time
When the distance isn't given, just pick a number! here 120 miles would be a good one. So if the distance travelled each way is 120 miles, then the time for the first route would be Time = Distance / Speed, so

Time = 120 miles / 40mph = 3 hrs

The time for the second route would be:

Time = 120 miles / 60mph = 2 hrs

The total time = 5hrs and the total distance = 240 miles, thus

The avg speed = 240 mph / 5 hrs = 48 mph

 

[PooyaH]

32.
y = x+2 / x-3 (cross multiply)
yx -3y = x+2 (now just solve for x)
yx -x = 3y+2
x(y-1) = 3y+2
x = 3y+2 / y-1

 

[PooyaH]

29. The area of the painting is 20 ft^2. The area of the painting + frame = 5ft x 6ft = 30 ft^2 (you add half a foot to each side since the frame is 6 inches wide)
The area which the frame occupies would be 30 - 20 ft = 10 ft^2
Now the percentage of the frame covering the area of painting + frame would be 10 / 30 = 33 1/3%

 

[sugarhype10]

36. When it says that the circles are tangent, it means that they are all touching each other, just like the picture shows. Notice that there are two lines of the triangle in each of the circles; those lines are the same lengths are the circles' radii! So, the area of circle I is 4pi, and because area = pi*r^2, you know that r must equal 2. Therefore, the two lines inside circle 1 each equal 2. Do the same for the other circles and you find that the radius for circle II equals 3, which means the two lines inside cirlce II both equal 3. The two lines for circle III both equal 4. Adding all of those little lines up, you get 2+2+3+3+4+4=18.

37. In order to find the variance, do:
(1/4)[(3-9)^2+(6-9)^2+(9-9)^2+(18-9)^2]
You do (1/4) because there are 4 variables (3,6,9,18), and you are subtracting 9 from each of those variables because 9 is your mean.
So, doing the math, you get:

(1/4)[36+9+81], which equals 31.5

 

[Streetwolf]

Even easier for mean/variance:

All #s are multipled by 3. Since mean is linear it gets multiplied by 3 and the new mean is 9.

Since variance is a squared parameter you multiply it by 3^2 (which is 9) and get 3.5*9 = 31.5.