Coded Inequality questions with solutions

1. Question 1Moderate

   In the following, '&' means 'greater than', '@' means 'greater than or equal to', '*' means 'less than', '#' means 'less than or equal to' and '$' means 'equal to'. Statements: P & Q, Q @ R, R & S Conclusions: I. P is greater than S II. Q is greater than S

   • A.Only conclusion I follows
   • B.Only conclusion II follows
   • C.Both conclusions followCorrect
   • D.Neither conclusion follows
   • E.Either conclusion I or II follows
   Show solution

   Decoding gives P > Q, Q >= R and R > S, which chains to P > Q >= R > S. From this P is greater than S and Q, being at least R which is greater than S, is also greater than S. Both conclusions follow.

2. Question 2Moderate
   In these questions the symbols are used with the following meanings: A @ B means A is greater than B. A # B means A is greater than or equal to B. A $ B means A is smaller than B. A & B means A is smaller than or equal to B. A * B means A is equal to B.

   Statements: A $ B, B & C, C @ D. Conclusions: I. A $ C. II. D @ B.

   • A.Only conclusion I is trueCorrect
   • B.Only conclusion II is true
   • C.Either I or II is true
   • D.Neither I nor II is true
   • E.Both I and II are true
   Show solution

   Decoding: A < B, B is at most C, and C > D. From A < B and B at most C, A < C - conclusion I is true. For II, C > D and B at most C leave D and B unordered, so D > B is not established. Only I is true.

3. Question 3Moderate
   In these questions the symbols are used with the following meanings: A @ B means A is greater than B. A # B means A is greater than or equal to B. A $ B means A is smaller than B. A & B means A is smaller than or equal to B. A * B means A is equal to B.

   Statements: M # N, N * O, O $ P. Conclusions: I. M # O. II. P @ N.

   • A.Only conclusion I is true
   • B.Only conclusion II is true
   • C.Either I or II is true
   • D.Neither I nor II is true
   • E.Both I and II are trueCorrect
   Show solution

   Decoding: M is greater than or equal to N, N equals O, and O < P. Since N equals O, M is greater than or equal to O - conclusion I. And P > O equals N, so P > N, that is P @ N - conclusion II. Both are true.

4. Question 4Moderate
   In the questions below, the symbols are used with the following meanings. A @ B means A is not smaller than B. A # B means A is neither greater than nor equal to B. A $ B means A is neither smaller than nor greater than B. A % B means A is not greater than B. A & B means A is neither smaller than nor equal to B.

   Statements: P @ Q, Q & R, R $ S Conclusions: I. P & S II. S @ Q

   • A.Only conclusion I followsCorrect
   • B.Only conclusion II follows
   • C.Either conclusion I or conclusion II follows
   • D.Neither conclusion I nor conclusion II follows
   • E.Both conclusion I and conclusion II follow
   Show solution

   Decode first: P @ Q is P >= Q, Q & R is Q > R, and R $ S is R = S. Conclusion I asks whether P > S. Since P >= Q > R = S, it does. Conclusion II asks whether S >= Q. But S equals R, and Q is strictly greater than R, so S is strictly less than Q and the conclusion fails. Only I follows. Write the decoded chain out before touching the conclusions, because reading the symbols one at a time while testing is where these go wrong.

5. Question 5Moderate
   In these questions the symbols are used with the following meanings: A @ B means A is greater than B. A # B means A is greater than or equal to B. A $ B means A is smaller than B. A & B means A is smaller than or equal to B. A * B means A is equal to B.

   Statements: P @ Q, Q # R, R @ S. Conclusions: I. P @ S. II. Q @ S.

   • A.Only conclusion I is true
   • B.Only conclusion II is true
   • C.Either I or II is true
   • D.Neither I nor II is true
   • E.Both I and II are trueCorrect
   Show solution

   Decoding: P > Q, Q is greater than or equal to R, and R > S. So Q is at least R, which is above S, giving Q > S - conclusion II. And P > Q > S gives P > S - conclusion I. Both are true.

6. Question 6Hard
   In the questions below, the symbols are used with the following meanings. A @ B means A is not smaller than B. A # B means A is neither greater than nor equal to B. A $ B means A is neither smaller than nor greater than B. A % B means A is not greater than B. A & B means A is neither smaller than nor equal to B.

   Statements: L % M, M # N, N @ O Conclusions: I. O # M II. L $ N

   • A.Only conclusion I follows
   • B.Only conclusion II follows
   • C.Either conclusion I or conclusion II follows
   • D.Neither conclusion I nor conclusion II followsCorrect
   • E.Both conclusion I and conclusion II follow
   Show solution

   Decoded, the statements read L <= M, M < N and N >= O. Conclusion I asks whether O < M. O is only known to be at most N, and M is below N as well, so O could fall on either side of M and nothing is established. Conclusion II asks whether L equals N. That is not merely unproven but impossible, since L <= M and M < N force L < N. Neither follows. Note the difference between the two failures: one conclusion is undetermined, the other is ruled out, and both count as not following.

These are 6 of 8 coded inequality questions in the bank. Attempt the rest with instant feedback in the practice drills, or under a clock in the mock tests.