ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 3
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#1. The area of a circle is 64 π. What is the circumference of the circle?
Use the formula of areas of circles.
Area = πr² ⇒ 64 π = πr² ⇒ 64 = r² ⇒ r = 8
Radius of the circle is 8. Now, use the circumference formula:
Circumference = 2πr = 2π (8) = 16 π
#2. A $40 shirt now selling for $28 is discounted by what percent?
Use the formula for Percent of Change
28−40/40 ×100 % = –30 % (negative sign here means that the new price is less than old price).
#3. In 1999, the average worker’s income increased $2,000 per year starting from $24,000 annual salary. Which equation represents income greater than average? (𝐼 = income, 𝑥 = number of years after 1999)
Let 𝑥 be the number of years. Therefore, $2,000 per year equals 2000𝑥.
starting from $24,000 annual salary means you should add that amount to 2000𝑥.
Income more than that is: I > 2000𝑥 24000
#4. From last year, the price of gasoline has increased from $1.25 per gallon to $1.75 per gallon. The new price is what percent of the original price?
The question is this: 1.75 is what percent of 1.25?
Use percent formula:
part =percent/100×whole
1.75 = percent/100 × 1.25 ⇒ 1.75 = percent × 1.25/100 ⇒ 175 = percent × 1.25 ⇒ percent = 175/1.25 = 140
#5. A boat sails 40 miles south and then 30 miles east. How far is the boat from its start point?
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: a² b2 = c2
40² 30² = c² ⇒ 1600 900 = c² ⇒ 2500 = c² ⇒ c = 50
#6. Which of the following could be the product of two consecutive prime numbers?
Some of 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 (bingo!)
5 × 7 = 35 (not in the options)
#7. Sophia purchased a sofa for $530.40. The sofa is regularly priced at $624. What was the percent discount Sophia received on the sofa?
The question is this: 530.40 is what percent of 624?
Use percent formula:
part =percent/100×whole
530.40 = percent/100×624 ⇒ 530.40 = percent ×624/100 ⇒ 53040 = percent × 624 ⇒
percent =53040/624 = 85
530.40 is 85 % of 624. Therefore, the discount is: 100% – 85% = 15%
#8. The score of Emma was half as that of Ava and the score of Mia was twice that of Ava. If the score of Mia was 60, what is the score of Emma?
If the score of Mia was 60, therefore the score of Ava is 30. Since, the score of Emma was
half as that of Ava, therefore, the score of Emma is 15.
#9. A bag contains 18 balls: two green, five black, eight blue, a brown, a red and one white. If 17 balls are removed from the bag at random, what is the probability that a brown ball has been removed?
If 17 balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a brown ball is 1 out of 18. Therefore, the probability of not
choosing a brown ball is 17 out of 18 and the probability of having not a brown ball after
removing 17 balls is the same.
#10. The average of five consecutive numbers is 38. What is the smallest number?
Let 𝑥 be the smallest number. Then, these are the numbers:
𝑥, 𝑥 1, 𝑥 2, 𝑥 3, 𝑥 4
average =sum of terms/number of terms ⇒ 38 = 𝑥 (𝑥 1) (𝑥 2) (𝑥 3) (𝑥 4)/5 ⇒38 =5𝑥 10/5 ⇒ 190 = 5𝑥 10 ⇒ 180 = 5𝑥 ⇒ 𝑥 = 36
#11. How many tiles of 8 cm2 is needed to cover a floor of dimension 6 cm by 24 cm?
The area of the floor is: 6 cm × 24 cm = 144 cm²
The number of tiles needed = 144 ÷ 8 = 18
#12. A rope weighs 600 grams per meter of length. What is the weight in kilograms of 12.2 meters of this rope? (1 kilograms = 1000 grams)
The weight of 12.2 meters of this rope is: 12.2 × 600 g = 7320 g
1 kg = 1000 g, therefore, 7320 g ÷ 1000 = 7.32 kg
#13. A chemical solution contains 4% alcohol. If there is 24 ml of alcohol, what is the volume of the solution?
4% of the volume of the solution is alcohol. Let 𝑥 be the volume of the solution.
Then: 4% of 𝑥 = 24 ml ⇒ 0.04 𝑥 = 24 ⇒ 𝑥 = 24 ÷ 0.04 = 600
#14. The average weight of 18 girls in a class is 60 kg and the average weight of 32 boys in the same class is 62 kg. What is the average weight of all the 50 students in that class?
average =sum of terms/number of terms
The sum of the weight of all girls is: 18 × 60 = 1080 kg
The sum of the weight of all boys is: 32 × 62 = 1984 kg
The sum of the weight of all students is: 1080 1984 = 3064 kg
average =3064/50 = 61.28
#15. The price of a laptop is decreased by 10% to $360. What is its original price?
Let 𝑥 be the original price.
If the price of a laptop is decreased by 10% to $360, then:
90 % 𝑜𝑓 𝑥 = 360⇒ 0.90𝑥 = 360 ⇒ 𝑥 = 360 ÷ 0.90 = 400