Full-Length GED Math Practice Test-Answers and Explanations

25- Choice B is correct
The equation of a line is in the form of \(y=mx+b\), where m is the slope of the line and b is the y-intercept of the line.
Two points \((1,0)\) and \((0,1)\) are on line A. Therefore, the slope of the line A is:
slope of line A\(=\frac{y_2- y_1}{x_2 – x_1} = \frac{1-0}{0-1}=\frac{1}{-1}=-1 \)
The slope of line A is \(-1\). Thus, the formula of the line A is: \(y=mx+b=-x+b\), choose a point and plug in the values of \(x\) and \(y\) in the equation to solve for b. Let’s choose point \((0, 1)\). Then:
\(y=x+b→1=0+b→b=1\)
The equation of line A is: \(y=-x+1\)
Now, let’s review the choices provided:
A.\((1,2) ⇒2=-1+1\). This is not true
B. \((-1,2)⇒2=1+1=2\). This is true
C. \((2,1)⇒1=-2+1=-1\). This is not true
D. \((3,1)⇒1=-3+1=-2\). This is not true

26- Choice A is correct
Use distance formula: Distance \(=\) Rate \(×\) time \(⇒ 540 = 75 ×\) T, divide both sides by \(\frac{75. 540 }{75} =\) T ⇒ T \(= 7.2\) hours.
Change hours to minutes for the decimal part. 0.2 hours \(= 0.2 × 60 = 12\) minutes

27- Choice D is correct
Let \(x\) be the number. Write the equation and solve for \(x\).
\(\frac{3}{5} ×22= \frac{3}{7}. x ⇒ \frac{3×22}{5}= \frac{3x}{7} \), use cross multiplication to solve for \(x\).
\(7×22=5x ⇒154=5x ⇒ x=30.8\)

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28- Choice B is correct
To find the discount, multiply the number by (\(100\% –\) rate of discount).
Therefore, for the first discount we get: \((D) (100\% – 15\%) = (D) (0.85) = 0.85 D\)
For increase of \(10 \%: (0.85 D) (100\% + 10\%) = (0.85 D) (1.10) = 0.935 D = 93.5\%\) of \(D\)

29- Choice C is correct
Use the formula for Percent of Change: \(\frac{New Value-Old Value}{Old Value} × 100 \% \)
\(\frac{34-45}{45} × 100 \% = –24.44 \%\) (negative sign here means that the new price is less than old price).

30- Choices D and E are correct
(If you selected 3 choices and 2 of them are correct, then you get one point. If you answered 2 or 3 choices and one of them is correct, you receive one point. If you selected more than 3 choices, you won’t get any point for this question.) Some of the prime numbers are: \(2, 3, 5, 7, 11, 13\)
Find the product of two consecutive prime numbers:
\(2 × 3 = 6\) (not in the options)
\(3 × 5 = 15\) (Choice D)
\(5 × 7 = 35\) (Choice E)
\(7 × 11 = 77\) (not in the options)
Choices D and E are correct.

31- Answer is 249
The ratio of boys to girls is \(3:5\). Therefore, there are 3 boys out of 8 students. To find the answer, first, divide the total number of students by 8, then multiply the result by
\(3. 664 ÷ 8 = 83 ⇒ 83 × 3 = 249\)

32- Choice A is correct
The question is this: 440 is what percent of 550?
Use percent formula: part \(= \frac{percent}{100} ×\) whole
\(440 = \frac{percent}{100} × 550 ⇒ 440= \frac{percent ×550}{100} ⇒44000 =\) percent \(×550\) percent \(= \frac{44000}{550} = 80. 440\) is \(80 \%\) of 550. Therefore, the discount is: \(100\% – 80\% = 20\%\)

33- Choice B is correct
If the score of Mia was 48, therefore the score of Ava is 16. Since the score of Emma was half as that of Ava, therefore, the score of Emma is 8.

34- Choice A is correct
The sample space S of the experiment described is as follows:
\(S={(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)} \)
Let E be the event “the die shows an odd number and the coin shows ahead”. Event E may be described as follows.
\(E={(1, H),(3,H),(5,H)}\)
The probability P(E) is given by P(E) \(= \frac{n(E)}{n(S)} = \frac{3 }{12} = \frac{1}{4}\)

35- Choice A is correct
Let \(x\) be the smallest number. Then, these are the numbers:
\(x, x+1, x+2, x+3, x+4\)
average \(= \frac{sum of terms}{number of terms} ⇒ = \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5}⇒30=\frac{5x+10}{5} ⇒ 150=5x+10 ⇒ 140=5x ⇒ x=28\)

36- Choice D is correct
The area of the floor is: \(8\) cm \(× 20\) cm \(= 160\) cm\(^2\) The number of tiles needed \(= 160 ÷ 10 = 16\)

37- Choice B is correct
The weight of 9.6 meters of this rope is: \(9.6 × 500\)g \(= 4800\) g \(1\) kg \(= 1,000\) g, therefore, \(4800\) g \(÷ 1000 = 4.8\)kg

38- Choice B is correct
\(2.5\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution. Then:
\(2.5\%\) of \(x = 30\) ml \(⇒ 0.025 x = 30 ⇒ x = 30 ÷ 0.025 = 1200\) ml

39- Choice C is correct
average \(= \frac{sum of terms}{number of terms}\)
The sum of the weight of all girls is: \(15 × 62 = 930\) kg
The sum of the weight of all boys is: \(28 × 70 = 1960\) kg
The sum of the weight of all students is: \(930 + 1960 = 2890\) kg
average \(= \frac{2890}{43} = 67.21\)

40- Choice C is correct
Let \(x\) be the original price. If the price of a laptop is decreased by \(12\%\) to \($385\), then:
\(88 \%\) of \(x=385⇒ 0.88x=385 ⇒ x=385÷0.88=$437.5\)

41- Choice A is correct
Write the numbers in order: \(14,14,15,16,18,22,62\) Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 16.

42- Choice A is correct
Surface area of cone formula is: A\(=πr(r+\sqrt{h^2+r^2})\). For r\(=17\) and h\(=20\) A\(=π(17)(17+\sqrt{20^2+17^2} )≈2309.79\)

43- Choice D is correct
Let \(x\) be the number of years. Therefore, \($2,100\) per year equals \(2100x\).
starting from \($22,000\) annual salary means you should add that amount to \(2100x\).
Income more than that is: \(I > 2100x + 22000\)

44- Choice B is correct
The question is this: 1.65 is what percent of 1.05?
Use percent formula: part \(= \frac{percent}{100} ×\) whole
\(1.65 = \frac{percent}{100} × 1.05 ⇒ 1.65=\frac{percent ×1.05}{100} ⇒165=\)percent \(×1.05 ⇒\) percent\(=\frac{165}{1.05}=157\%\)

45- Choice D is correct
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(20^2 + 15^2 = c^2 ⇒ 400 + 225 = c^2 ⇒ 625 = c^2 ⇒ c = 25\)

46- Choice A is correct
For each option, choose a point in the solution part and check it on both inequalities.
\(y>2x,y≥-x+2\)
A. Point \((0, 5)\) is in the solution section. Let’s check the point in both inequalities.
\(5>0\), It works
\(5≥0+2\), it works (this point works in both)
B. Let’s choose this point \((5, 0)\)
\(0>10\) That’s not true!
\(0≥-5+2\), it works
C. Let’s choose this point
\((–5, 0) 0>-10\), it works
\(0≥10+2\) That’s not true!
D. Let’s choose this point
\((0, 5) 5>0\), That’s not true!
\(5≥0+2\) it works

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