PROMISEDPAGE

Inequality Reasoning Questions

Questions 11-15 with visual inequality representations

Directions:

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Question 11

Statements:

Y ≥ P = O, P < R ≤ J

Conclusions:

R > Y, J > O

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusion I and II follow

D. Neither conclusion I nor conclusion II follows

E. Either conclusion I or conclusion II follows

Correct Answer: B. Only conclusion II follows

Explanation:

From the statements: Y ≥ P = O and P < R ≤ J

We can combine: Y ≥ P < R ≤ J

Conclusion I: R > Y → Cannot be determined as we have Y ≥ P < R (no direct relation between R and Y)

Conclusion II: J > O → Since P = O and P < R ≤ J, we have O = P < J, so J > O is true.

Visual Representation:

Y

≥

P

=

O

P

<

R

≤

J

Y

≥

P

<

R

≤

J

✗ Conclusion I: R > Y → Cannot be determined

✓ Conclusion II: J > O → True (since O = P < J)

Question 12

Statements:

T > D ≥ P, F ≥ P = R

Conclusions:

T > R, D > F

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusion I and II follow

D. Neither conclusion I nor conclusion II follows

E. Either conclusion I or conclusion II follows

Correct Answer: A. Only conclusion I follows

Explanation:

From the statements: T > D ≥ P and F ≥ P = R

We can combine: T > D ≥ P = R and F ≥ P = R

Conclusion I: T > R → Since T > D ≥ P = R, we have T > R (true)

Conclusion II: D > F → We have D ≥ P and F ≥ P, but no direct relation between D and F (cannot be determined)

Visual Representation:

T

>

D

≥

P

=

R

F

≥

P

=

R

✓ Conclusion I: T > R → True (T > D ≥ P = R)

✗ Conclusion II: D > F → Cannot be determined

Question 13

Statements:

C < D, E ≥ B, B > D, A = E

Conclusions:

B > C, A < D

A. Either C1 or C2 follows

B. Only C1 follows

C. Only C2 follows

D. Both C1 and C2 follow

E. Neither C1 nor C2 follows

Correct Answer: B. Only C1 follows

Explanation:

From the statements: C < D, E ≥ B, B > D, A = E

We can combine: C < D < B ≤ E = A

Conclusion I: B > C → Since C < D < B, we have B > C (true)

Conclusion II: A < D → From C < D < B ≤ E = A, we have D < A, so A < D is false

Visual Representation:

C

<

D

<

B

≤

E

=

A

✓ Conclusion I: B > C → True (C < D < B)

✗ Conclusion II: A < D → False (actually D < A)

Question 14

Statement:

M = X < Z ≥ W = N ≤ Q < T ≤ V = U

Conclusions:

I. V ≥ W, II. T ≯ U

A. Only C2 follows

B. Only C1 follows

C. Neither C1 nor C2 follows

D. Both C1 and C2 follow

E. Either C1 or C2 follows

Correct Answer: A. Only C2 follows

Explanation:

From the statement: M = X < Z ≥ W = N ≤ Q < T ≤ V = U

Conclusion I: V ≥ W → We have Z ≥ W and T ≤ V = U, but no direct relation between V and W (cannot be determined)

Conclusion II: T ≯ U → Since T ≤ V = U, we have T ≤ U, so T is not greater than U (true)

Visual Representation:

M

=

X

<

Z

≥

W

=

N

≤

Q

<

T

≤

V

=

U

✗ Conclusion I: V ≥ W → Cannot be determined

✓ Conclusion II: T ≯ U → True (T ≤ V = U)

Question 15

Statement:

P ≤ Q < S = T ≥ U ≥ W < Z

Conclusions:

I. S > W, II. W = T

A. Only I follows

B. Only II follows

C. Both I and II follows

D. Either I or II follows

E. Neither I nor II follows

Correct Answer: A. Only I follows

Explanation:

From the statement: P ≤ Q < S = T ≥ U ≥ W < Z

Conclusion I: S > W → Since S = T ≥ U ≥ W, we have S ≥ W. But we need to check if S > W is always true.

If T = U = W, then S = W, so S > W is not always true. Wait, let's reconsider: S = T ≥ U ≥ W means S ≥ W, but we cannot say S > W with certainty.

Actually, looking more carefully: S = T ≥ U ≥ W means S ≥ W. But since we have W < Z at the end, this doesn't affect the S-W relationship.

Let me correct: S = T ≥ U ≥ W means S ≥ W. This could be S > W or S = W. So conclusion I (S > W) is not necessarily true.

Conclusion II: W = T → From T ≥ U ≥ W, we have T ≥ W, but not necessarily T = W.

Actually, neither conclusion follows definitively. Let me check the answer again.

Upon re-examination: S = T ≥ U ≥ W means S ≥ W. Since the relationship is ≥ (not >), we cannot definitively say S > W. Similarly, we cannot say W = T.

So the correct answer should be E. Neither I nor II follows.

Visual Representation:

P

≤

Q

<

S

=

T

≥

U

≥

W

<

Z

✗ Conclusion I: S > W → Not necessarily true (could be S = W)

✗ Conclusion II: W = T → Not necessarily true