GED EXAM PRACTICE - MATHEMATICS, SCIENCE, SOCIAL
STUDIES, AND LANGUAGE ARTS COMPLETE QUESTIONS WITH
100% CORRECT ANSWERS
Question 1
Find a positive number which when increased by 11 is equal to 60 times the
reciprocal of the number.
A. 15
B. 4
C. 11
D. 7
Correct Answer: B – 4
Explanation: Let the number be x. The equation is x + 11 = 60(1/x). Multiply both
sides by x: x² + 11x = 60 → x² + 11x - 60 = 0 → (x + 15)(x - 4) = 0 → x = -15 or x = 4.
The positive number is 4. Check: 4 + 11 = 15, and 60 × 1/4 = 15. Correct. Option A
(15) gives 15+11=26, 60/15=4, not equal. Option C (11) gives 22 vs 60/11≈5.45.
Option D (7) gives 18 vs 60/7≈8.57.
Question 2
If x and y are two whole numbers such that x^y = 121, then the value of
(x−1)^(y−1) would be?
A. 1
B. 10
C. 121
D. 1000
,Correct Answer: B – 10
Explanation: 121 = 11². So x = 11 and y = 2 (both whole numbers). Then
(x−1)^(y−1) = (11−1)^(2−1) = 10¹ = 10. Option A (1) would require exponent 0.
Option C (121) would be 11² again. Option D (1000) would be 10³, not applicable.
Question 3
A ladder of a certain fixed length leans against a wall forming a 60° angle between
the ground and the ladder. If the bottom of the ladder is 10 feet away from the
wall, how long is the ladder?
A. 20 feet
B. 10 feet
C. 5 feet
D. 1.54 feet
Correct Answer: A – 20 feet
Explanation: The ladder forms a right triangle with the wall and ground. The angle
at the ground is 60°. The distance from the wall to the ladder bottom (10 ft) is the
adjacent side to the 60° angle. Cosine = adjacent/hypotenuse. cos60° = 0.5 = 10 /
ladder length → ladder length = .5 = 20 feet. Option B (10) would be
cos60°=1, impossible. Option C (5) would give cos=2. Option D (1.54) is cos≈6.5,
incorrect.
Question 4
An angle is equal to one fourth of its supplement. What would be the measure of
that angle?
A. 18
B. 36
C. 45
D. 72
,Correct Answer: B – 36
Explanation: Let the angle be x. Its supplement is 180° - x. The equation is x =
¼(180 - x) → multiply by 4: 4x = 180 - x → 5x = 180 → x = 36°. Check: supplement
= 144°, 144/4 = 36°. Correct. Option A (18) would give supplement 162,
162/4=40.5, not 18. Option C (45): supplement 135, 135/4=33.75. Option D (72):
supplement 108, 108/4=27.
Question 5
The complement of an angle exceeds the angle by 60°. Then the angle would be?
A. 30
B. 15
C. 35
D. 90
Correct Answer: B – 15
Explanation: Let the angle be x. Its complement is 90° - x. The equation: (90 - x) =
x + 60 → 90 - x = x + 60 → 90 - 60 = 2x → 30 = 2x → x = 15°. Check: complement =
75°, which exceeds 15° by 60°. Correct. Option A (30): complement 60, exceeds by
30. Option C (35): complement 55, exceeds by 20. Option D (90): complement 0,
exceeds by -90.
Question 6
If the difference between the two acute angles of a right triangle is 10°, what will
be the measure of the smaller one?
A. 50
B. 40
C. 80
D. 70
Correct Answer: B – 40
, Explanation: In a right triangle, the two acute angles sum to 90°. Let smaller = x,
larger = x + 10. Then x + (x + 10) = 90 → 2x + 10 = 90 → 2x = 80 → x = 40°. Smaller
angle = 40°, larger = 50°. Option A (50) is the larger. Option C (80) is too large.
Option D (70) is too large.
Question 7
A circle is inscribed in a square of area 4. What will be the area of the circle?
A. 2π
B. π
C. 16π
D. π/2
Correct Answer: B – π
Explanation: Square area = 4, so side length = √4 = 2. A circle inscribed in a square
has diameter equal to the side of the square, so radius = 2/2 = 1. Area of circle =
πr² = π(1)² = π. Option A (2π) would be radius √2 ≈1.414. Option C (16π) would be
radius 4. Option D (π/2) would be radius √0.5 ≈0.707.
Question 8
The circumference of a circle is xπ units and the area of the circle is yπ units. If x =
y, what would be the radius of the circle?
A. 1
B. 3
C. π
D. 2
Correct Answer: D – 2
Explanation: Circumference = 2πr = xπ → x = 2r. Area = πr² = yπ → y = r². Given x =
y, so 2r = r² → r² - 2r = 0 → r(r - 2) = 0 → r = 0 or r = 2. Radius = 2. Check:
circumference = 4π, area = 4π, x=y=4. Option A (1): circumference=2π, area=π, not
STUDIES, AND LANGUAGE ARTS COMPLETE QUESTIONS WITH
100% CORRECT ANSWERS
Question 1
Find a positive number which when increased by 11 is equal to 60 times the
reciprocal of the number.
A. 15
B. 4
C. 11
D. 7
Correct Answer: B – 4
Explanation: Let the number be x. The equation is x + 11 = 60(1/x). Multiply both
sides by x: x² + 11x = 60 → x² + 11x - 60 = 0 → (x + 15)(x - 4) = 0 → x = -15 or x = 4.
The positive number is 4. Check: 4 + 11 = 15, and 60 × 1/4 = 15. Correct. Option A
(15) gives 15+11=26, 60/15=4, not equal. Option C (11) gives 22 vs 60/11≈5.45.
Option D (7) gives 18 vs 60/7≈8.57.
Question 2
If x and y are two whole numbers such that x^y = 121, then the value of
(x−1)^(y−1) would be?
A. 1
B. 10
C. 121
D. 1000
,Correct Answer: B – 10
Explanation: 121 = 11². So x = 11 and y = 2 (both whole numbers). Then
(x−1)^(y−1) = (11−1)^(2−1) = 10¹ = 10. Option A (1) would require exponent 0.
Option C (121) would be 11² again. Option D (1000) would be 10³, not applicable.
Question 3
A ladder of a certain fixed length leans against a wall forming a 60° angle between
the ground and the ladder. If the bottom of the ladder is 10 feet away from the
wall, how long is the ladder?
A. 20 feet
B. 10 feet
C. 5 feet
D. 1.54 feet
Correct Answer: A – 20 feet
Explanation: The ladder forms a right triangle with the wall and ground. The angle
at the ground is 60°. The distance from the wall to the ladder bottom (10 ft) is the
adjacent side to the 60° angle. Cosine = adjacent/hypotenuse. cos60° = 0.5 = 10 /
ladder length → ladder length = .5 = 20 feet. Option B (10) would be
cos60°=1, impossible. Option C (5) would give cos=2. Option D (1.54) is cos≈6.5,
incorrect.
Question 4
An angle is equal to one fourth of its supplement. What would be the measure of
that angle?
A. 18
B. 36
C. 45
D. 72
,Correct Answer: B – 36
Explanation: Let the angle be x. Its supplement is 180° - x. The equation is x =
¼(180 - x) → multiply by 4: 4x = 180 - x → 5x = 180 → x = 36°. Check: supplement
= 144°, 144/4 = 36°. Correct. Option A (18) would give supplement 162,
162/4=40.5, not 18. Option C (45): supplement 135, 135/4=33.75. Option D (72):
supplement 108, 108/4=27.
Question 5
The complement of an angle exceeds the angle by 60°. Then the angle would be?
A. 30
B. 15
C. 35
D. 90
Correct Answer: B – 15
Explanation: Let the angle be x. Its complement is 90° - x. The equation: (90 - x) =
x + 60 → 90 - x = x + 60 → 90 - 60 = 2x → 30 = 2x → x = 15°. Check: complement =
75°, which exceeds 15° by 60°. Correct. Option A (30): complement 60, exceeds by
30. Option C (35): complement 55, exceeds by 20. Option D (90): complement 0,
exceeds by -90.
Question 6
If the difference between the two acute angles of a right triangle is 10°, what will
be the measure of the smaller one?
A. 50
B. 40
C. 80
D. 70
Correct Answer: B – 40
, Explanation: In a right triangle, the two acute angles sum to 90°. Let smaller = x,
larger = x + 10. Then x + (x + 10) = 90 → 2x + 10 = 90 → 2x = 80 → x = 40°. Smaller
angle = 40°, larger = 50°. Option A (50) is the larger. Option C (80) is too large.
Option D (70) is too large.
Question 7
A circle is inscribed in a square of area 4. What will be the area of the circle?
A. 2π
B. π
C. 16π
D. π/2
Correct Answer: B – π
Explanation: Square area = 4, so side length = √4 = 2. A circle inscribed in a square
has diameter equal to the side of the square, so radius = 2/2 = 1. Area of circle =
πr² = π(1)² = π. Option A (2π) would be radius √2 ≈1.414. Option C (16π) would be
radius 4. Option D (π/2) would be radius √0.5 ≈0.707.
Question 8
The circumference of a circle is xπ units and the area of the circle is yπ units. If x =
y, what would be the radius of the circle?
A. 1
B. 3
C. π
D. 2
Correct Answer: D – 2
Explanation: Circumference = 2πr = xπ → x = 2r. Area = πr² = yπ → y = r². Given x =
y, so 2r = r² → r² - 2r = 0 → r(r - 2) = 0 → r = 0 or r = 2. Radius = 2. Check:
circumference = 4π, area = 4π, x=y=4. Option A (1): circumference=2π, area=π, not
