PROMISEDPAGE

Reasoning Inequalities Questions

Questions 6-10 with visual inequality chains

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 6

Statements:

L ≥ Y ≥ A < R, S > Q = A ≥ I

Conclusions:

I. S > Y

II. R > Q

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusions follow

D. Either conclusion I or conclusion II follows

E. Neither conclusion I nor II follows

Correct Answer: B. Only conclusion II follows

Inequality Chain:

S

>

Q

=

A

≤

Y

≤

L

Q

=

A

<

R

✗

Conclusion I (S > Y): Cannot be determined. We know S > Q = A ≤ Y, so S could be greater than, equal to, or less than Y.

✓

Conclusion II (R > Q): Follows. Since Q = A < R, we can conclude R > Q.

Explanation: From the statements, we have Q = A < R, so R > Q definitely follows. However, for S > Y, we only know S > Q = A ≤ Y, which doesn't guarantee S > Y.

Question 7

Statements:

M < A ≤ P > X, P ≥ B = C < Y, C ≥ D > F = L

Conclusions:

I. P ≥ D

II. M < C

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusions follow

D. Either conclusion I or conclusion II follows

E. Neither conclusion I nor II follows

Correct Answer: A. Only conclusion I follows

Inequality Chain:

M

<

A

≤

P

≥

B

=

C

≥

D

✓

Conclusion I (P ≥ D): Follows. From P ≥ B = C ≥ D, we get P ≥ D.

✗

Conclusion II (M < C): Cannot be determined. We know M < A ≤ P ≥ B = C, but the relationship between M and C is uncertain.

Explanation: From P ≥ B = C ≥ D, we can conclude P ≥ D. However, for M < C, we have M < A ≤ P ≥ C, which doesn't establish a definite relationship between M and C.

Question 8

Statements:

J = X ≤ U > Z, M = N ≥ U = P, L = O < N ≥ T

Conclusions:

I. J < N

II. O > U

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusions follow

D. Either conclusion I or conclusion II follows

E. Neither conclusion I nor II follows

Correct Answer: A. Only conclusion I follows

Inequality Chain:

J

=

X

≤

U

=

P

≤

N

=

M

L

=

O

<

N

✓

Conclusion I (J < N): Follows. From J = X ≤ U = P ≤ N, we get J ≤ N. Since J = X ≤ U and U > Z, J could be equal to N only if all are equal, but U > Z prevents that, so J < N.

✗

Conclusion II (O > U): Does not follow. We know O < N ≥ U, which doesn't establish a relationship between O and U.

Explanation: From J = X ≤ U = P ≤ N, we get J ≤ N. Since U > Z, not all elements can be equal, so J < N follows. For O > U, we only know O < N ≥ U, which doesn't give us a definite relationship.

Question 9

Statements:

H ≥ V = O > R, X ≤ D > Y > R, Y > N = L < Z

Conclusions:

I. O < D

II. R > N

A. Neither conclusion I nor II follows

B. Only conclusion I follows

C. Both conclusions I and II follow

D. Only conclusion II follows

E. Either conclusion I or II follows

Correct Answer: D. Only conclusion II follows

Inequality Chain:

H

≥

V

=

O

>

R

<

Y

<

D

R

<

Y

>

N

✗

Conclusion I (O < D): Cannot be determined. We know O > R < Y < D, but this doesn't establish a relationship between O and D.

✓

Conclusion II (R > N): Follows. From R < Y > N, we cannot directly compare R and N. Actually, let's check: We have O > R and Y > N, but no direct relationship between R and N. Wait, let me recheck...

Explanation: For conclusion I (O < D), we have O > R < Y < D, which doesn't establish a relationship between O and D. For conclusion II (R > N), we have R < Y > N, which also doesn't establish a relationship between R and N. Let me verify the correct answer...

Actually, looking at the statements: H ≥ V = O > R and X ≤ D > Y > R. We can see O > R and D > Y > R, but no direct comparison between O and D. For R and N: R < Y > N, so we cannot determine if R > N or R < N. The correct answer should be A. Neither conclusion I nor II follows.

Question 10

Statements:

C < R = X; M = L > O = C; X > L = I

Conclusions:

I. O = X

II. I < R

A. Neither conclusion I nor II follows

B. Only conclusion I follows

C. Both conclusions I and II follow

D. Only conclusion II follows

E. Either conclusion I or II follows

Correct Answer: D. Only conclusion II follows

Inequality Chain:

O

=

C

<

R

=

X

>

L

=

I

<

M

✗

Conclusion I (O = X): Does not follow. We have O = C < R = X, so O < X.

✓

Conclusion II (I < R): Follows. From R = X > L = I, we get R > I, so I < R.

Explanation: From O = C < R = X, we get O < X, so conclusion I is false. From R = X > L = I, we get R > I, so conclusion II is true.