Q.1 If A > B, B > C, and C > D, which of the following is true?
A > D
A < D
B < D
C > A
Explanation - Since A > B > C > D, A is definitely greater than D.
Correct answer is: A > D
Q.2 If P ≤ Q, Q < R, then which of the following is always correct?
P < R
P > R
Q ≥ P
R ≤ P
Explanation - Since P ≤ Q and Q < R, the maximum P can be is just less than R, so P < R is always true.
Correct answer is: P < R
Q.3 If X + Y > Z and Z > 0, which of the following is correct?
X + Y > 0
X + Y < 0
X + Y = Z
X + Y ≤ Z
Explanation - Since Z > 0 and X + Y > Z, X + Y must also be greater than 0.
Correct answer is: X + Y > 0
Q.4 If M > N, N = O, O < P, then which of the following is correct?
M < P
M > P
M = P
Cannot be determined
Explanation - M > N and O < P but relationship between M and P is unknown, so cannot be determined.
Correct answer is: Cannot be determined
Q.5 If A ≥ B, B ≥ C, C ≥ D, which of the following is false?
A ≥ D
B ≥ D
C ≥ A
A ≥ C
Explanation - C is less than or equal to B and B is less than or equal to A, so C ≥ A is false.
Correct answer is: C ≥ A
Q.6 If 3X + 2 > 11, then X is:
X > 3
X < 3
X = 3
X ≥ 3
Explanation - 3X + 2 > 11 ⇒ 3X > 9 ⇒ X > 3.
Correct answer is: X > 3
Q.7 If 5A - 3 < 12, then A is:
A < 3
A > 3
A = 3
A ≤ 3
Explanation - 5A - 3 < 12 ⇒ 5A < 15 ⇒ A < 3.
Correct answer is: A < 3
Q.8 If X - Y > 4 and Y > 2, then X is:
X > 6
X < 6
X = 6
X ≤ 6
Explanation - X - Y > 4 and Y > 2 ⇒ X > 4 + Y ⇒ X > 6.
Correct answer is: X > 6
Q.9 If A + B < 10 and B > 3, which of the following is true?
A < 7
A > 7
A = 7
A ≥ 7
Explanation - A + B < 10 and B > 3 ⇒ A < 10 - B < 7.
Correct answer is: A < 7
Q.10 If P < Q, Q ≤ R, P + R = 10, which of the following is correct?
P < 5
R > 5
P > 5
Cannot be determined
Explanation - Exact values of P and R are unknown; only the sum is given.
Correct answer is: Cannot be determined
Q.11 If 2X + 3 ≤ 7, then X is:
X ≤ 2
X ≥ 2
X < 2
X = 2
Explanation - 2X + 3 ≤ 7 ⇒ 2X ≤ 4 ⇒ X ≤ 2.
Correct answer is: X ≤ 2
Q.12 If A > B and B < C, then:
A < C
A > C
Cannot be determined
B > A
Explanation - No direct comparison between A and C is given, so cannot be determined.
Correct answer is: Cannot be determined
Q.13 If X/2 > 4, then X is:
X > 8
X < 8
X = 8
X ≥ 8
Explanation - Dividing inequality: X/2 > 4 ⇒ X > 8.
Correct answer is: X > 8
Q.14 If 3A - 5 < 7, then A is:
A < 4
A > 4
A ≤ 4
A ≥ 4
Explanation - 3A - 5 < 7 ⇒ 3A < 12 ⇒ A < 4.
Correct answer is: A < 4
Q.15 If P + Q ≥ 12 and Q ≤ 5, then P is:
P ≥ 7
P ≤ 7
P > 7
P < 7
Explanation - P + Q ≥ 12 and Q ≤ 5 ⇒ P ≥ 12 - 5 ⇒ P ≥ 7.
Correct answer is: P ≥ 7
Q.16 If X - 3 ≥ 5, then X is:
X ≥ 8
X ≤ 8
X > 8
X < 8
Explanation - X - 3 ≥ 5 ⇒ X ≥ 8.
Correct answer is: X ≥ 8
Q.17 If A < B < C and C - A = 10, which is possible?
A = 2, B = 5, C = 12
A = 3, B = 7, C = 13
A = 0, B = 5, C = 10
A = 1, B = 5, C = 10
Explanation - All inequalities are satisfied: A < B < C and C - A = 10.
Correct answer is: A = 1, B = 5, C = 10
Q.18 If 4X + 1 > 9, then X is:
X > 2
X < 2
X = 2
X ≥ 2
Explanation - 4X + 1 > 9 ⇒ 4X > 8 ⇒ X > 2.
Correct answer is: X > 2
Q.19 If A ≥ B and B > C, which of the following is true?
A > C
A < C
B < A
C ≥ A
Explanation - Since A ≥ B and B > C, A > C is always true.
Correct answer is: A > C
Q.20 If X + 2 < 7, then X is:
X < 5
X > 5
X ≤ 5
X ≥ 5
Explanation - X + 2 < 7 ⇒ X < 5.
Correct answer is: X < 5
Q.21 If P < Q < R < S, which is false?
P < S
Q < R
R < Q
P < R
Explanation - Given Q < R, so R < Q is false.
Correct answer is: R < Q
Q.22 If 2A - 3 ≤ 5, then A is:
A ≤ 4
A ≥ 4
A < 4
A > 4
Explanation - 2A - 3 ≤ 5 ⇒ 2A ≤ 8 ⇒ A ≤ 4.
Correct answer is: A ≤ 4
Q.23 If X + Y > 0 and Y < 0, which is true?
X > -Y
X < -Y
X = -Y
Cannot be determined
Explanation - X + Y > 0 ⇒ X > -Y.
Correct answer is: X > -Y
Q.24 If M ≥ N ≥ O, then which is false?
M ≥ O
N ≤ M
O ≤ N
O ≥ M
Explanation - O ≤ N ≤ M, so O ≥ M is false.
Correct answer is: O ≥ M
Q.25 If 5X + 2 ≥ 12, then X is:
X ≥ 2
X ≤ 2
X > 2
X < 2
Explanation - 5X + 2 ≥ 12 ⇒ 5X ≥ 10 ⇒ X ≥ 2.
Correct answer is: X ≥ 2