46957.If n ≠ 0, which of the following must be greater than n?
I.2n
II. n²
III.2 - n
I.2n
II. n²
III.2 - n
I only
II only
I and II only
II and III only
None
46958.Running at the same constant rate, 6 identical machines can produce a total of 33 widgets per hour. At this rate, how many widgets could 14 such machines produce in 3 hours?
66
231
462
693
909
Explanation:
Rates are best expressed in fractions with units. The rate of the 6 equal machines is
6R=33 widgets/1 hour ,
where R is the rate of one machine working, since all machines work at an equal rate. To find the rate for 14 machines, not 6, we can multiply both sides of the equation by 14/6:
(14/6) 6R = 33 widgets/1 hour (14/6)
14R = 33 widgets/1 hour (14/6)
We now have 14 machines on the left as we want. The right side is going to give us 6 hours on the right if we multiply it out, but we want 3 hours, so we can multiply the right side by 1 ...
14R = 33 widgets/1 hour (14/6) ((1/2)/(1/2))
14R = 33 X 7 widgets/3 hours
14R = (210 + 21 widgets)/3 hours
= 231 widgets/3hours
For 14 machines, we have 231 widgets in 3 hours.
We can make an estimate to check that this is in the ballpark. The original 6 machines made 33 widgets in 1 hour. And 14 is more than double the number of machines, so they are doing something over 66 widgets an hour. And they are working for 3 hours, so the result will be something like 66 or 70 times 3, so around 210 widgets per hour. Indeed, we could have used that method to start and gotten the answer very quickly, because there is only one answer choice even close to the estimate.
The correct answer is (B).
Rates are best expressed in fractions with units. The rate of the 6 equal machines is
6R=33 widgets/1 hour ,
where R is the rate of one machine working, since all machines work at an equal rate. To find the rate for 14 machines, not 6, we can multiply both sides of the equation by 14/6:
(14/6) 6R = 33 widgets/1 hour (14/6)
14R = 33 widgets/1 hour (14/6)
We now have 14 machines on the left as we want. The right side is going to give us 6 hours on the right if we multiply it out, but we want 3 hours, so we can multiply the right side by 1 ...
14R = 33 widgets/1 hour (14/6) ((1/2)/(1/2))
14R = 33 X 7 widgets/3 hours
14R = (210 + 21 widgets)/3 hours
= 231 widgets/3hours
For 14 machines, we have 231 widgets in 3 hours.
We can make an estimate to check that this is in the ballpark. The original 6 machines made 33 widgets in 1 hour. And 14 is more than double the number of machines, so they are doing something over 66 widgets an hour. And they are working for 3 hours, so the result will be something like 66 or 70 times 3, so around 210 widgets per hour. Indeed, we could have used that method to start and gotten the answer very quickly, because there is only one answer choice even close to the estimate.
The correct answer is (B).
46959.
ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?
ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?
2.25
3
4
4.5
6
46960.There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?
78
80
87
91
94
Explanation:
The average of the first 16 students is 77. This means, the sum of these 16 scores is
sum = (average)*(number of scores) = 77*16 = 1232
Once Taqeesha takes her test, the average of all 17 scores is 78. This means, the sum of these 17 scores is:
sum = (average)*(number of scores) =78*17 = 1326
Once we had the sum of the 16 scores, all we had to do was add Taqeesha’s score to that total to get the sum of all 17. Therefore, the difference in these two sums is Taqeesha’s score. 1326 – 1232 = 94.
The average of the first 16 students is 77. This means, the sum of these 16 scores is
sum = (average)*(number of scores) = 77*16 = 1232
Once Taqeesha takes her test, the average of all 17 scores is 78. This means, the sum of these 17 scores is:
sum = (average)*(number of scores) =78*17 = 1326
Once we had the sum of the 16 scores, all we had to do was add Taqeesha’s score to that total to get the sum of all 17. Therefore, the difference in these two sums is Taqeesha’s score. 1326 – 1232 = 94.
46962.A car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, what is the average speed of the entire trip?
36 mph
40 mph
44 mph
52 mph
58 mph
Explanation:
In phase #1 of the trip, the car traveled 40 mi at 20 mph. That time of this phase was:
time = distance/rate = (40 mi)/(20 mph) = 2 hr
In phase #2 of the trip, the car traveled 180 mi at 60 mph. That time of this phase was:
time = distance/rate = (180 mi)/(60 mph) = 3 hr
The total distance of the trip = 40 mi + 180 mi = 220 mi
The total time of the trip = 2 hr + 3 hr = 5 hr
The average speed of trip is given by
speed = distance/time = (220 mi)/(5 hr) = 44 mph
In phase #1 of the trip, the car traveled 40 mi at 20 mph. That time of this phase was:
time = distance/rate = (40 mi)/(20 mph) = 2 hr
In phase #2 of the trip, the car traveled 180 mi at 60 mph. That time of this phase was:
time = distance/rate = (180 mi)/(60 mph) = 3 hr
The total distance of the trip = 40 mi + 180 mi = 220 mi
The total time of the trip = 2 hr + 3 hr = 5 hr
The average speed of trip is given by
speed = distance/time = (220 mi)/(5 hr) = 44 mph
46963.litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
(1 litre = 1000cm³)
6
8
10
20
40
46964.If an object travels at five feet per second, how many feet does it travel in one hour?
30
300
720
1800
18000
46965.What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
90
95
100
105
110
46966.A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
48
32
24
18
12
46967.In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
6
15
24
33
54
46968.For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
48
49
50
51
52
46969.
In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
18
13.5
9
4.5
3
46970.A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?
12
11
10
9
8
46971.A student s average (arithmetic mean) test score on 4 tests is 68. What must be the student s score on a 5th test for the student s average score on the 5 tests to be 70?
70
72
74
76
78
Explanation:
This question is about averages. Typically, average questions are made easier by working with the sums, using the twist on the average equation:
Sum of the items = (average of items) (number of items).
From the first 4 tests, we have
Sum of the items = (68) (4)=240+32 = 272.
Using this equation again separately, if the fifth test gives an overall average of 70, then
Sum of 5 items = (70) (5) = 350
The difference of the sums is 350-272=78, so that would have to be the fifth test score to meet the condition stated by the question. The correct answer is (E).
This question is about averages. Typically, average questions are made easier by working with the sums, using the twist on the average equation:
Sum of the items = (average of items) (number of items).
From the first 4 tests, we have
Sum of the items = (68) (4)=240+32 = 272.
Using this equation again separately, if the fifth test gives an overall average of 70, then
Sum of 5 items = (70) (5) = 350
The difference of the sums is 350-272=78, so that would have to be the fifth test score to meet the condition stated by the question. The correct answer is (E).
46972.
Which of the following could be a value of x, in the diagram above?
Which of the following could be a value of x, in the diagram above?
10
20
40
50
any of the above
46973.Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
11/P + 6
P/11 +6
17 - P/6
17/P
11.5P
46974.Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
10
15
20
25
30
46975.A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
$35,000
$45,000
$55,000
$65,000
$75,000
Explanation:
The 15 managers have an average salary of $120,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $120,000*15 = $1,800,000
The 75 associates have an average salary of $30,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $30,000*75 = $2,250,000
When we add those two sums, we get the total payroll of all 90 employees.
$1,800,000 + $2,250,000 = $4,050,000
So, we have 90 employees, and together they earn $4,050,000, so the average is
average = $4,050,000 ÷90 = $45,000
The 15 managers have an average salary of $120,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $120,000*15 = $1,800,000
The 75 associates have an average salary of $30,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $30,000*75 = $2,250,000
When we add those two sums, we get the total payroll of all 90 employees.
$1,800,000 + $2,250,000 = $4,050,000
So, we have 90 employees, and together they earn $4,050,000, so the average is
average = $4,050,000 ÷90 = $45,000
46976.Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
4
7
8
12
it cannot be determined from the information given.