Hi Guys, I really hope some angel would help me with them. I know the answer to many of them but I dont know the correct reasoning and explanation behind them so if someone can help me with it, it would be great !
1-A street vendor sells two newspapers, one for 25 cents and the other for 40 cents. If she sold 100 newspapers for $28.00, how many newspapers did she sell at 25 cents?
a)80
b)60
c)50
d)40
e)20
2- The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n?
a)w- 2n
b)w-n + 1
c)w- 2(n- 1)
d)n- 6 + w
c)w-n/w
3- Phil is making a 40-kilometer canoe trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes longer will it take him than if he makes the entire trip at 20 kilometers per hour?
A)15
b)20
c)35
d)45
e)50
4-
A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
a)1/4
b)1/3
c)2/5
d)4/9
e)1/2
5-
The cost to rent a boat for a fishing trip is x dollars, which is to be shared equally among the people taking the trip. If 12 people go on the trip rather than 20, how many more dollars, in terms of x, will it cost per person?
a)x/8
b)x/12
c)x/16
d)x/20
e)x/30
6-
The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following includes the entire range of values for z?
a)0 < z < 4
b)0 < z < 8
c)0 < z < 10
d)8 < z < 10
c)8 < z < 50
7-
A vending machine dispenses gumballs in a regularly repeating cycle of 10 different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent in order for 3 gumballs of the same color to be dispensed?
a)$1.00
b)$1.75
c)$2.00
d)$2.25
e)$2.50
8-
The average (arithmetic mean) of 5 positive numbers is 8. If the average of 4 of these numbers is 5.5, what is the value of the other number?
a)2.5
b)18
c)20
d)22
e)30
9-
Twenty percent of the trees in an orchard are apple trees, and 1/3 of the trees that are not apple trees are cherry trees. If 3/4 of the trees in the orchard are fruit trees, and the only types of fruit trees in the orchard are apple trees, cherry trees, and plum trees, what fraction of the trees in the orchard are plum trees?
a)1/30
b)3/40
c)1/12
d)17/60
e)13/45
10-
What is the smallest positive integer that is evenly divisible by both 21 and 9?
a)21
b)42
c)63
d)126
e)189
11-
A picket fence is composed of x pickets, each of which is 1/2 inch wide. If there are six inches of space between each pair of pickets, which of the following represents the length of the fence in feet?
a)13/12 x
b)13/12 x-6
c)13/14 x
d)13x+1/24
e)13x-1/24
12-
If a rocket can travel x/5 miles every y seconds, how many miles can it travel in z minutes?
a)xy/5z
b)xz/5y
c)xyz/6
d)12xy/z
e)12xz/y
1-A street vendor sells two newspapers, one for 25 cents and the other for 40 cents. If she sold 100 newspapers for $28.00, how many newspapers did she sell at 25 cents?
a)80
b)60
c)50
d)40
e)20
2- The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n?
a)w- 2n
b)w-n + 1
c)w- 2(n- 1)
d)n- 6 + w
c)w-n/w
3- Phil is making a 40-kilometer canoe trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes longer will it take him than if he makes the entire trip at 20 kilometers per hour?
A)15
b)20
c)35
d)45
e)50
4-
A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
a)1/4
b)1/3
c)2/5
d)4/9
e)1/2
5-
The cost to rent a boat for a fishing trip is x dollars, which is to be shared equally among the people taking the trip. If 12 people go on the trip rather than 20, how many more dollars, in terms of x, will it cost per person?
a)x/8
b)x/12
c)x/16
d)x/20
e)x/30
6-
The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following includes the entire range of values for z?
a)0 < z < 4
b)0 < z < 8
c)0 < z < 10
d)8 < z < 10
c)8 < z < 50
7-
A vending machine dispenses gumballs in a regularly repeating cycle of 10 different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent in order for 3 gumballs of the same color to be dispensed?
a)$1.00
b)$1.75
c)$2.00
d)$2.25
e)$2.50
8-
The average (arithmetic mean) of 5 positive numbers is 8. If the average of 4 of these numbers is 5.5, what is the value of the other number?
a)2.5
b)18
c)20
d)22
e)30
9-
Twenty percent of the trees in an orchard are apple trees, and 1/3 of the trees that are not apple trees are cherry trees. If 3/4 of the trees in the orchard are fruit trees, and the only types of fruit trees in the orchard are apple trees, cherry trees, and plum trees, what fraction of the trees in the orchard are plum trees?
a)1/30
b)3/40
c)1/12
d)17/60
e)13/45
10-
What is the smallest positive integer that is evenly divisible by both 21 and 9?
a)21
b)42
c)63
d)126
e)189
11-
A picket fence is composed of x pickets, each of which is 1/2 inch wide. If there are six inches of space between each pair of pickets, which of the following represents the length of the fence in feet?
a)13/12 x
b)13/12 x-6
c)13/14 x
d)13x+1/24
e)13x-1/24
12-
If a rocket can travel x/5 miles every y seconds, how many miles can it travel in z minutes?
a)xy/5z
b)xz/5y
c)xyz/6
d)12xy/z
e)12xz/y
