GED Mathematical Reasoning Preparation Course: Number sense, operations, ratios and percents

1. Frage 1 von 18

   What is |−9| + |4|?

   • A5
   • B13
   • C−5
   • D−13
   Antwort anzeigen

   Antwort: B. 13

   Absolute value is the distance from 0, so |−9| = 9 and |4| = 4. Then 9 + 4 = 13.

2. Frage 2 von 18

   What is the distance between −7 and 5 on a number line?

   • A2
   • B−2
   • C12
   • D35
   Antwort anzeigen

   Antwort: C. 12

   Distance = |5 − (−7)| = |12| = 12. Count 7 steps to 0, then 5 more.

3. Frage 3 von 18

   Which list shows 0.45, 2/5, 0.5 and 3/8 from smallest to largest?

   • A3/8, 2/5, 0.45, 0.5
   • B0.45, 0.5, 2/5, 3/8
   • C3/8, 0.45, 2/5, 0.5
   • D2/5, 3/8, 0.45, 0.5
   Antwort anzeigen

   Antwort: A. 3/8, 2/5, 0.45, 0.5

   As decimals: 3/8 = 0.375, 2/5 = 0.4, 0.45 and 0.5. So the order is 3/8, 2/5, 0.45, 0.5.

4. Frage 4 von 18

   What is the greatest common factor of 24 and 36?

   • A12
   • B6
   • C72
   • D4
   Antwort anzeigen

   Antwort: A. 12

   The factors of 24 and 36 that they share are 1, 2, 3, 4, 6 and 12. The greatest is 12.

5. Frage 5 von 18

   Without a calculator: 2 1/2 × 1 3/5 = ?

   • A4
   • B4 1/10
   • C1 9/16
   • D2 3/10
   Antwort anzeigen

   Antwort: A. 4

   Change to improper fractions: 5/2 × 8/5 = 40/10 = 4. Do not multiply the whole numbers and fractions separately.

6. Frage 6 von 18

   Without a calculator: 3/4 ÷ 3/8 = ?

   • A9/32
   • B1/2
   • C2
   • D6
   Antwort anzeigen

   Antwort: C. 2

   To divide, multiply by the reciprocal: 3/4 × 8/3 = 24/12 = 2.

7. Frage 7 von 18

   Which expression is undefined?

   • A0 ÷ 8
   • B8 ÷ 0
   • C8 − 8
   • D0 × 8
   Antwort anzeigen

   Antwort: B. 8 ÷ 0

   You cannot divide by zero, so 8 ÷ 0 is undefined. The other three all equal 0.

8. Frage 8 von 18

   What is 18 − 3 × (2 + 4)² ÷ 9?

   • A−18
   • B12
   • C6
   • D60
   Antwort anzeigen

   Antwort: C. 6

   Parentheses: 2 + 4 = 6. Exponent: 6² = 36. Then 3 × 36 = 108, 108 ÷ 9 = 12, and 18 − 12 = 6.

9. Frage 9 von 18

   What is √81 + ∛64?

   • A17
   • B13
   • Cabout 12.04
   • D145
   Antwort anzeigen

   Antwort: B. 13

   √81 = 9 because 9 × 9 = 81. ∛64 = 4 because 4 × 4 × 4 = 64. So 9 + 4 = 13.

10. Frage 10 von 18

    What is the value of 16^(1/2)?

    • A32
    • B8
    • C4
    • D256
    Antwort anzeigen

    Antwort: C. 4

    An exponent of 1/2 means the square root. √16 = 4.

11. Frage 11 von 18

    Which number equals 4.2 × 10⁵?

    • A0.000042
    • B42,000
    • C4,200,000
    • D420,000
    Antwort anzeigen

    Antwort: D. 420,000

    Multiplying by 10⁵ moves the decimal point 5 places to the right: 4.2 → 420,000.

12. Frage 12 von 18

    A 12-ounce box of cereal costs $3.48 and a 20-ounce box costs $5.40. Which is the better buy?

    • ANeither; they cost the same per ounce
    • BThe 12-ounce box, because it costs less
    • CThe 12-ounce box, at $0.29 per ounce
    • DThe 20-ounce box, at $0.27 per ounce
    Antwort anzeigen

    Antwort: D. The 20-ounce box, at $0.27 per ounce

    Unit price = price ÷ ounces: $3.48 ÷ 12 = $0.29 and $5.40 ÷ 20 = $0.27. The lower unit price is the better buy.

13. Frage 13 von 18

    A recipe uses 3 cups of flour for 24 cookies. How many cups do you need for 40 cookies?

    • A4
    • B19
    • C5
    • D6
    Antwort anzeigen

    Antwort: C. 5

    Set up a proportion: 3/24 = x/40. Then x = 3 × 40 ÷ 24 = 5 cups.

14. Frage 14 von 18

    On a map, 1 inch stands for 15 miles. Two towns are 3.5 inches apart on the map. How far apart are they?

    • A52.5 miles
    • B45 miles
    • Cabout 4.3 miles
    • D18.5 miles
    Antwort anzeigen

    Antwort: A. 52.5 miles

    Multiply by the scale: 3.5 × 15 = 52.5 miles.

15. Frage 15 von 18

    A jacket costs $80. It is 25% off, and then 6% sales tax is added to the sale price. What is the final cost?

    • A$56.40
    • B$21.20
    • C$64.80
    • D$63.60
    Antwort anzeigen

    Antwort: D. $63.60

    Sale price: $80 × 0.75 = $60. Tax: $60 × 0.06 = $3.60. Total: $60 + $3.60 = $63.60.

16. Frage 16 von 18

    Rent goes up from $1,200 to $1,290 a month. What is the percent increase?

    • A90%
    • B9%
    • C7.5%
    • Dabout 7.0%
    Antwort anzeigen

    Antwort: C. 7.5%

    Percent change = change ÷ original = $90 ÷ $1,200 = 0.075 = 7.5%. Divide by the original amount, not the new one.

17. Frage 17 von 18

    You borrow $2,500 at 4% simple interest per year for 3 years. How much interest do you pay?

    • A$100
    • B$3,000
    • C$2,800
    • D$300
    Antwort anzeigen

    Antwort: D. $300

    Simple interest I = Prt = $2,500 × 0.04 × 3 = $300. The total you repay would be $2,800.

18. Frage 18 von 18

    Lena earns $18 an hour and 1.5 times that rate for hours over 40 in a week. She works 46 hours. What is her gross pay?

    • A$1,242
    • B$774
    • C$882
    • D$828
    Antwort anzeigen

    Antwort: C. $882

    Regular pay: 40 × $18 = $720. Overtime rate: $18 × 1.5 = $27, and 6 × $27 = $162. Total: $720 + $162 = $882.

Tastatur: 1–4 zum Antworten, Eingabetaste für die nächste Frage.

Die echte Prüfung: 145 on each GED subject