ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 2
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#1. The price of a car was $20,000 in 2014, $16,000 in 2015 and $12,800 in 2016. What is the rate of depreciation of the price of car per year?
16000−20000 /20000 ×100 % = 20 % and 12800−16000 /16000 ×100 % = 20 %
#2. The width of a box is one third of its length. The height of the box is one third of its width. If the length of the box is 27 cm, what is the volume of the box?
If the length of the box is 27, then the width of the box is one third of it, 9, and the height of the box is 3 (one third of the width). The volume of the box is: V = lwh = (27) (9) (3) = 729
#3. If 60 % of A is 20 % of B, then B is what percent of A?
Write the equation and solve for B: 0.60 A = 0.20 B, divide both sides by 0.20, then:
0.60/0.20 A = B, therefore: B = 3 A, and B is 3 times of A or it’s 300% of A.
#4. A ladder leans against a wall forming a 60ᵒ angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?
The relationship among all sides of special right triangle
30° − 60° − 90° is provided in this triangle:
GED MATHEMATICAL REASONING
In this triangle, the opposite side of 30° angle is half of the hypotenuse.
Draw the shape for this question: The latter is the hypotenuse. Therefore, the latter is 60 ft.
GED MATHEMATICAL REASONING
#5. When a number is subtracted from 24 and the difference is divided by that number, the result is 3. What is the value of the number?
Let 𝑥 be the number. Write the equation and solve for 𝑥. (24 – 𝑥) ÷ 𝑥 = 3
Multiply both sides by x. (24 – 𝑥) = 3𝑥, then add x both sides. 24 = 4𝑥, now divide both sides by 4.
𝑥 = 6
#6. An angle is equal to one fifth of its supplement. What is the measure of that angle?
The sum of supplement angles is 180. Let 𝑥 be that angle. Therefore,
𝑥 5𝑥 = 180
6𝑥 = 180, divide both sides by 6: 𝑥 = 30
#7. John traveled 150 km in 6 hours and Alice traveled 180 km in 4 hours. What is the ratio of the average speed of John to average speed of Alice?
The average speed of john is: 150 ÷ 6 = 25 km
The average speed of Alice is: 180 ÷ 4 = 45 km
Write the ratio and simplify.
25 : 45 ⇒ 5 : 9
#8. If 40 % of a class are girls, and 25 % of girls play tennis, what percent of the class play tennis?
The percent of girls playing tennis is: 40 % × 25 % = 0.40 × 0.25 = 0.10 = 10 %
#9. In five successive hours, a car travels 40 km, 45 km, 50 km, 35 km and 55 km. In the next five hours, it travels with an average speed of 50 km per hour. Find the total distance the car traveled in 10 hours.
Add the first 5 numbers. 40 45 50 35 55 = 225
To find the distance traveled in the next 5 hours, multiply the average by number of hours.
Distance = Average × Rate = 50 × 5 = 250
Add both numbers.
250 225 = 475
#10. How long does a 420–miles trip take moving at 50 miles per hour (mph)?
Use distance formula:
Distance = Rate × time ⇒ 420 = 50 × T, divide both sides by 50. 420 / 50 = T ⇒ T = 8.4 hours.
Change hours to minutes for the decimal part. 0.4 hours = 0.4 × 60 = 24 minutes.
#11. What is the difference of smallest 4–digit number and biggest 4–digit number?
Smallest 4–digit number is 1000, and biggest 4–digit number is 9999. The difference is: 8999
#12. Right triangle ABC has two legs of lengths 6 cm (AB) and 8 cm (AC). What is the length of the third side (BC)?
Use Pythagorean Theorem: a² b² = c²
6² 8² = c² ⇒ 100 = c² ⇒ c = 10
#13. 25 is What percent of 20?
Use percent formula:
part = percent /100 ×whole
25 = percent/100 × 20 ⇒ 25 = percent ×20/100 ⇒ 25 = percent ×2/10, multiply both sides by 10.
250 = percent × 2, divide both sides by 2.
125 = percent
#14. Two third of 18 is equal to 2/5 of what number?
Let 𝑥 be the number. Write the equation and solve for 𝑥.
2/3 × 18 = 2/5. 𝑥 ⇒ 2×18/3 = 2𝑥/5, use cross multiplication to solve for 𝑥.
5 × 36 = 2𝑥 × 3 ⇒180 = 6𝑥 ⇒ 𝑥 = 30
#15. The marked price of a computer is D dollar. Its price decreased by 20% in January and later increased by 10 % in February. What is the final price of the computer in D dollar?
To find the discount, multiply the number by (100% – rate of discount).
Therefore, for the first discount we get: (D) (100% – 20%) = (D) (0.80) = 0.80 D
For increase of 10 %: (0.85 D) (100% 10%) = (0.85 D) (1.10) = 0.88 D = 88% of D