46997.Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?
1 litre paint
1 litre water
½ litre water and one litre paint
½ litre paint and one litre water
½ litre paint
46998.Cyclist A averages 19.9 miles per hour and Cyclist B averages 15.1 miles per hour. If each cycle is ridden 1,500 miles, approximately how many more hours will Cyclist B ride than Cyclist A?
18
20
25
30
36
Explanation:
This computation looks beastly, but the question says "approximately," so we can take the speed of A to be 20 miles per hour and that of B to be 15 miles per hour. (When we get to the stage of evaluating the answers, we ll recall that we approximated and question whether we have answered precisely enough.)Cyclist A rides at a constant rate of 20 miles/1 hour . Without changing the rate, we want to get it to express the time for 1500 miles. To do this, we can multiply the fraction by 1:
$\\dfrac{20 miles}{1 hour} \\times \\dfrac{\\dfrac{1500}{20}}{\\dfrac{1500}{20}} = \\dfrac{1500 miles}{\\dfrac{1500}{20} hour}$
So, A will take 1500/20 hours. B will take 1500/15 hours, which is more, because the denominator is smaller.
It s easy enough to compute directly, but I would prefer to use the common denominator of 60:
(1500/15) - (1500/20)
$\\dfrac{4(1500)}{60}$ = 150/60=25
Our estimate is 25.
The correct answer is (C).
This computation looks beastly, but the question says "approximately," so we can take the speed of A to be 20 miles per hour and that of B to be 15 miles per hour. (When we get to the stage of evaluating the answers, we ll recall that we approximated and question whether we have answered precisely enough.)Cyclist A rides at a constant rate of 20 miles/1 hour . Without changing the rate, we want to get it to express the time for 1500 miles. To do this, we can multiply the fraction by 1:
$\\dfrac{20 miles}{1 hour} \\times \\dfrac{\\dfrac{1500}{20}}{\\dfrac{1500}{20}} = \\dfrac{1500 miles}{\\dfrac{1500}{20} hour}$
So, A will take 1500/20 hours. B will take 1500/15 hours, which is more, because the denominator is smaller.
It s easy enough to compute directly, but I would prefer to use the common denominator of 60:
(1500/15) - (1500/20)
$\\dfrac{4(1500)}{60}$ = 150/60=25
Our estimate is 25.
The correct answer is (C).
46999.A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
2.5π
3π
5π
4π
10π
47002.
All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?
All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?
2
2√2
3
√10
√20
47003.
If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?
If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?
9
10
11
12
13
47004.Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?
11
10
9
8
7
47005.ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?
12
9√3
9
8
3√3
47006.
In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a²π, what is the area of the square?
In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a²π, what is the area of the square?
2a²
4a
4a²
16a²
64a²
47007.If the product of 6 integers is negative, at most how many of the integers can be negative?
2
3
4
5
6
47008.The slope of the line passing through the point (5,5) is 5/6. All of the following points could be on the line except
(2.5, 2)
(11, 10)
(8, 7.5)
(-1, 0)
(-7, -5)
47009.When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 hours to paint a house of the same size. How long would it take for Lisa to paint a house of the same size by herself?
5 hr
6 hr
7 hr
12 hr
20 hr
Explanation:
Here, the rate equation becomes:
(# of houses) = (painting rate) x (time)
When Mary paints a house, it takes her 4 hours. Thus
(1 house) = (Mary’s rate) x (4 hr)
so her rate is 1/4.
When Mary & Lisa paint together, it takes 3 hrs. Thus
(1 house) = (combined rate) x (3 hr)
and the combined rate = 1/3.
To find a combined rate, we add individual rates.
(combined rate) = (Mary’s rate) + (Lisa’s rate)
1/3 = 1/4 + (Lisa’s rate)
(Lisa’s rate) = {1/3}-{1/4}={1/3}*{4/4}-{1/4}*{3/3}={4/12}-{3/12}={1/12}
Lisa’s rate is 1/12 of a house every hour, or in other words, 1 house in 12 hrs. Thus, it would take her 12 hours to paint a house of the same size.
Here, the rate equation becomes:
(# of houses) = (painting rate) x (time)
When Mary paints a house, it takes her 4 hours. Thus
(1 house) = (Mary’s rate) x (4 hr)
so her rate is 1/4.
When Mary & Lisa paint together, it takes 3 hrs. Thus
(1 house) = (combined rate) x (3 hr)
and the combined rate = 1/3.
To find a combined rate, we add individual rates.
(combined rate) = (Mary’s rate) + (Lisa’s rate)
1/3 = 1/4 + (Lisa’s rate)
(Lisa’s rate) = {1/3}-{1/4}={1/3}*{4/4}-{1/4}*{3/3}={4/12}-{3/12}={1/12}
Lisa’s rate is 1/12 of a house every hour, or in other words, 1 house in 12 hrs. Thus, it would take her 12 hours to paint a house of the same size.
47010.A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
2
4
6
8
10
47011.A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
30
24
12
8
6
47012.A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
17
28
35
39
50
47013.During a certain season, a team won 80 percent of its first 80 games and 56 percent of its remaining games. If the team won of its games in the entire season, what was the total number of games that the team played?
180
170
156
120
105
Explanation:
This question is a good candidate for plugging in answer choices, but we can set up the equation first. Let s calculate the number of wins overall:
(0.80)80 + (0.56)R = (2/3) (80+R)
Where R is the number of games remaining after the first 80. We are actually looking for 80+R. We can use the balance concept of averages here. The R games really pulled down the winning average, from 0.80 to approximately 0.67. Since that distance is about 0.13, and since the distance from 0.67 to 0.56 is 0.11, R must be greater than 80, probably about 13/11 the size of 80. That rules out (C) through (E) and makes (A) appear probable. Let s try it. If 80+R=180, then
(0.80)80 + (0.56)100 = (2/3) (80+100)
64 + 56 = 120
This statement is true. The correct answer is (A).
This question is a good candidate for plugging in answer choices, but we can set up the equation first. Let s calculate the number of wins overall:
(0.80)80 + (0.56)R = (2/3) (80+R)
Where R is the number of games remaining after the first 80. We are actually looking for 80+R. We can use the balance concept of averages here. The R games really pulled down the winning average, from 0.80 to approximately 0.67. Since that distance is about 0.13, and since the distance from 0.67 to 0.56 is 0.11, R must be greater than 80, probably about 13/11 the size of 80. That rules out (C) through (E) and makes (A) appear probable. Let s try it. If 80+R=180, then
(0.80)80 + (0.56)100 = (2/3) (80+100)
64 + 56 = 120
This statement is true. The correct answer is (A).
47014.A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
0.75D
0.76D
0.765D
0.775D
0.805D