Correct answer: 11
Choice (E) is correct. The highway portion of the trip will be 4/5 x 300 = 240 miles. Since the car uses 30 miles per gallon on the highway, it will use 240/30=8 gallons of gas on the highway portion of the trip. The remainder of the trip, 300 – 240 =60 miles, will be in the city, so the car will use 60/20 = 3 gallons in the city. Therefore, the car will use 8 + 3 =11 gallons of gas altogether.
Correct answer: -10
The largest possible value of one of the other five integers is -10.
Correct answer: 40
Since 16 chairs are empty, and this represents 2/5 of the total enrollment, then the full class must consist of
Class = 5/2 × 16 = 40 students
Use proportions
2/5 = 16/x Cross multiply.
2x = 80 Divide each side by 2 to solve for x.
x = 40 students
Correct answer: 8.08
503.384 ÷ 62.3 = 8.08
Correct answer: 40
|4x+3y|−|4x−3y|
To solve, we replace each variable with the given value.
|4(5) + 3(7)| - |4(5) - 3(7)| .
|20 + 21] - |20 — 21|
Simplify. Remember that terms inside of the absolute value are always positive.
|41| - |-1| = 41 - 1 = 40
Correct answer: 75 mph
Distance = rate x time
Plug in the the values for distance and time, and solve for rate.
450 = r x 6
and
r = 75
Correct answer: 1.97
2.01 ÷ 1.02 = 1.97
Correct answer: $2.60
Begin by determining the total cost of the onions and carrots, since these prices are given. This will equal (2 x $3.69) + (3 x $4.29) = $20.25. Next, this sum is subtracted from the total cost of the vegetables to determine the cost of the mushrooms: $24.15 - $20.25 = $3.90. Finally, the cost of the mushrooms is divided by the quantity (lbs) to determine the cost per pound:
Cost per lb = $3.90/1.5 = $2.60
Correct answer: 2
There are 2 marbles pink bag has less than the marbles that each child will receive.
Correct answer: 16
a+3 = 14 => a = 11
2a-6 = 2(11) – 6 = 22-6 = 16
Correct answer: x−y=−3
We can use the point slope form of a line, substituting
m = 1, x₁ = 4,y₁ = 7.
y - y₁ = m(x - x₁)
y - 7 = 1(x - 4)
y - 7 = x - 4
y - 7 - y + 4 = x - 4 - y + 4
-3 = x - y
or
x - y = -3
Correct answer: 3
Begin working with the innermost parentheses and work your way out.
-3 - [(2 - 1) - (3+4)]
= -3 - [(1) - (7)]
= -3 - [1 - 7]
=-3 - [-6]
=-3 + 6
=3
Correct answer: 3:11
Since the figure represents the number line, the distance from point A to point B will be the difference, B-A, which is 5 – (-6) = 11. The distance from point B to point C will also be the difference, C-B, otherwise 8 – 5 = 3. So the ratio BC:AB will be 3:11.
Correct answer: $1,060
1,060 - 50% = 530
Correct answer: y = -(1/3)x+6
The slopes of two perpendicular lines are negative reciprocals of each other. This also means that the product of the two slopes equals -1. A perpendicular line has the negative reciprocal slope of another line. Since the slope of the given line is 3 , the slope of a perpendicular line is -1/3 . The basic equation is then y = (-1/3)x+b. We need to use the point (0,6) to find b. Let’s do that: 6 = -1/3(0)+b . Therefore, b=6 , and the complete perpendicular line equation is y = -(1/3)x+6.
Correct answer: 108
The sequence is generated by alternately adding 2, then multiplying by 2:
3 + 2 = 5
5 X 2 = 10
10 + 2 = 12.
12 x 2 = 24
24 + 2- = 26
26 x 2 = 52
52 + 2- = 54
54 x 2 = 108
Correct answer: 2304
3003 - 699 = 2304
Correct answer: 51.8%
Candidate A’s vote percentage is the number of votes that he obtained divided by the total number of votes cast. Then, multiply that decimal by 100 to convert the decimal into a percentage. Therefore, Candidate A’s Vote is: Percentage 36800/(36800 + 32100 + 2100) × 100 = 51.8%
Correct answer: 11
The value of X is 11.
Correct answer: 60
The correct answer is A. 60 students. To solve this problem, first find the total number of students in the combined biology and chemistry courses [213 + 155 = 368] Subtract from this total the number of students taking both courses, as they should only be counted once [368 - 78 = 290] . This leaves you with the number of students enrolled in biology and/or chemistry. The difference between this total of students and the number of students in the high school will be the number of students not studying either subject [350 - 290 = 60] .60 students are not enrolled in Biology and/or Chemistry. A is the correct answer.
A. Correct.
B. 70 would be an answer resulting from faulty arithmetic or other human errors.
C. 50 would be an answer resulting from faulty arithmetic or other human errors.
D. 78 is the number of students studying both subjects.
E. 18 is the difference between the actual number of students in the high school class and the total number of enrolled students in the combined science courses. This is a trap answer that faulty logic may lead one to choose.
Correct answer: 28−2t
The perimeter of a polygon is the sum of the lengths of its sides.
Let:
X = Length of one of those other two sides
Now we can set up an equation and solve it for x in terms of t:
2x + 4(t + 1) = 60
=> 2x + 4t + 4 = 60
=> 2x = 60 - 4 - 4t
=> 2x = 56 - 4t
=> x = 28 - 2t
Correct answer: 98
This is a good problem to do in your head. Note that 10% of 70 is 7. 140%, then, is 14 × 7, or 98.
Correct answer: 50%
The rate of increase equals the change in the account balance divided by the original amount, $80. Multiply that decimal by 100 to yield the percentage of increase. To determine the change in the balance subtract the original amount from the new balance: Change = $120 - $80 = $40. Now, determine the percentage of increase as described above: Percent = $40/$80 × 100 = 50%.
Correct answer: 31
3,4,6,9,13,18,24,31,39
Correct answer: 4:1
Choice (E) is correct. Jamal ran 360 feet, which is equal to 120 yards. Thus, the ratio of Jamal's distance to Lonnie's distance is 120 yards to 30 yards, which is the same as 4:1
