More QR questions....

[kov82]

---

Members don't see this ad.

how do you do these? are the last two too difficult/different for the DAT?


A construction firm receives an important contract and
hires 15 temporary workers in addition to its full-time
staff. If the entire full-time staff of 25 could complete
the job in five months, and if temporary workers work
5/6 as fast as full-time workers, how much time will
be saved by hiring the additional workers?
A. 1 2/3 answer
months
B. 1 7/8
months
C. 2 1/6
months
D. 2 1/5
months
E. 3 1/3
months

A new eight-lane highway costs $7,500,000 per mile
(5280 feet). If each lane measures 11 feet across, how
much would it cost to pave a square mile of highway?
A. $85,227
B. $450,000,000 answer
C. $600,000,000
D. $3,600,000,000
E. $4,950,000,000


A square room measuring 15 feet on a side is 10 feet
high. If a gallon of paint covers 450 square feet,
approximately how many gallons will be required to
paint the walls of this room?
A. 2
B. 1.25
C. 1.33 answer
D. 0.75
E. 1.83


The spokes on an old bicycle wheel extend from the
hub to the outer rim at an average spacing of 7.5°. If
the diameter of the hub is 10 centimeters and the
diameter of the rim is 60 centimeters, what is the total
length of steel wire used for the spokes?
A. 24 meters
B. 1 meter 20 centimeters
C. 12 meters answer
D. 6 meters 75 centimeters
E. 2 meters 40 centimeters


The minute hand on a clock is twice as long as the
hour hand. In a given amount of time, how many
times greater is the distance traveled by the end of the
minute hand than traveled by the tip of the hour hand?
A. 35
B. 12
C. 47
D. 24 answer
E. 23

 

[PooyaH]

A square room measuring 15 feet on a side is 10 feet
high. If a gallon of paint covers 450 square feet,
approximately how many gallons will be required to
paint the walls of this room?
A. 2
B. 1.25
C. 1.33 answer
D. 0.75
E. 1.83
===============
This is an easy one:

15 x 10 = 150 (the area of each side)
you should know that there are 4 sides in a square room, so

150 x 4 = 600

and

600 / 450 = 1.33

 

[PooyaH]

A construction firm receives an important contract and
hires 15 temporary workers in addition to its full-time
staff. If the entire full-time staff of 25 could complete
the job in five months, and if temporary workers work
5/6 as fast as full-time workers, how much time will
be saved by hiring the additional workers?
A. 1 2/3 answer
months
B. 1 7/8
months
C. 2 1/6
months
D. 2 1/5
months
E. 3 1/3
months
==============
lets use week.workers as our unit again. (in this case month.workers)
5 months x 25 workers = 125 month-workers (the entire job)

the new workers work 5/6 as fast as the full-time workers, so

15 workers x 5/6 = 12.5 (this means that 12.5 full-time workers would get the job done as fast as 15 new workers would -in another words 12.5 full-time workers = 15 new workers)

So we can say 25 + 12.5 = 37.5 workers (we have 37.5 workers)

125 months-workers / 37.5 = 3.33

5 months - 3 1/3 months = 1 2/3 months (they would save)

 

[razblo]

A new eight-lane highway costs $7,500,000 per mile
(5280 feet). If each lane measures 11 feet across, how
much would it cost to pave a square mile of highway?
A. $85,227
B. $450,000,000 answer
C. $600,000,000
D. $3,600,000,000
E. $4,950,000,000

I had to use a little backwards math/logic to figure out the relationship for this one but I eventually got it.

8 lanes x 11 feet = 88 across feet for every $7,500,000

5280 feet/88 feet = 60

$7,500,000 x 60 = $450,000,000

 

[Streetwolf]

A square room measuring 15 feet on a side is 10 feet
high. If a gallon of paint covers 450 square feet,
approximately how many gallons will be required to
paint the walls of this room?
A. 2
B. 1.25
C. 1.33 answer
D. 0.75
E. 1.83

You just need to know how many sq ft are in the room and divide by 450...

Here you have a square room 15x15 which means the walls all have a width of 15 ft. The height is always 10 ft. So each wall is 15x10 = 150 ft^2. There are 4 walls so you have 600 ft^2. Take that and divide by 450 ft^2 and you get 1.33 gallons.

Remember not to include the floor in this problem!! Also remember that we are NOT working with volume!!

The spokes on an old bicycle wheel extend from the
hub to the outer rim at an average spacing of 7.5°. If
the diameter of the hub is 10 centimeters and the
diameter of the rim is 60 centimeters, what is the total
length of steel wire used for the spokes?
A. 24 meters
B. 1 meter 20 centimeters
C. 12 meters answer
D. 6 meters 75 centimeters
E. 2 meters 40 centimeters

First consider one spoke. If the diameter of the rim is 60 cm then the radius is 30 cm (each spoke starts at the center and goes out so you use radius). If the diameter of the hub is 10 cm then the radius is 5 cm. So the length of the spoke is 25 cm.

Now how many spokes are there? They are spaced 7.5 degrees apart, with 360 degrees total in the circle, which means there are 360/7.5 = 48 spokes. If each spoke is 25 cm then there are 1200 cm worth of spokes. Since there are 100 cm in a meter, we have 12 meters of spokes.

The minute hand on a clock is twice as long as the
hour hand. In a given amount of time, how many
times greater is the distance traveled by the end of the
minute hand than traveled by the tip of the hour hand?
A. 35
B. 12
C. 47
D. 24 answer
E. 23

Picture the path of each hand as a circle. The path of the minute hand is a larger circle than the path of the hour hand.

The distance traveled around a circle is just a portion of the circumference. If the minute hand is twice as long as the hour hand, then its radius is twice as long:

r(m) = 2*r(h)

Since circumference is just a linear measurement, the distance traveled in any given portion of the clock is twice as much for the minute hand as it is for the hour hand. In other words if the minute hand and hour hand both traveled from the 4 to the 5, the minute hand would travel twice the distance because the circular path its on stretches further out.

The other thing we need to consider is speed. The minute hand travels faster than the hour hand. But by how much? Just consider 1 hour. The minute hand travels a full circle and during this time the hour hand goes from one number to the next (5 minutes). So the minute hand travels 60 minutes for every 5 minutes that the hour hand travels. Thus the minute hand travels 12 times faster than the hour hand.

If it travels 12x faster and it covers 2x the distance, that means it actually covers 24x the distance compared to the hour hand. That's your answer.