Inequality Quiz: Direct and Coded Reasoning Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. Statement: P > Q >= R = S < T. Conclusions: I. P > S II. T > R

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Both I and II follow. P > Q >= R = S gives P > S. T > S and S = R give T > R. Both follow.

2. Statement: J >= K > L = M <= N. Conclusions: I. J > M II. N > L

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Only I follows. J >= K > L = M gives J > M. But N >= M = L only gives N >= L, so N > L is not certain.

3. Statement: A <= B = C >= D > E. Conclusions: I. C > A II. C = A

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Both I and II follow

   Answer: Either I or II follows. C = B >= A, so C >= A. Neither I nor II is certain alone, but together they cover >= and exactly one must be true: either I or II follows.

4. Statement: W > X < Y >= Z > V. Conclusions: I. W > Y II. V < X

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Neither I nor II follows

   Answer: Neither I nor II follows. W and Y are both greater than X, so they cannot be compared. X and V are both smaller than Y, so they cannot be compared either. Neither follows.

5. Statements: F = G > H >= I; J > G. Conclusions: I. F > J II. I < F

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Only II follows. J > G = F means F < J, so I is false. I <= H < G = F gives I < F, so II follows.

6. Statements: P >= Q > R; S <= R = T; U > T. Conclusions: I. P > S II. U > S

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Both I and II follow

   Answer: Both I and II follow. Join the statements at R: P >= Q > R >= S gives P > S, and U > T = R >= S gives U > S. Both follow.

7. 'P # Q' means P is greater than Q; 'P @ Q' means P is smaller than Q; 'P $ Q' means P is equal to Q; 'P % Q' means P is either greater than or equal to Q; 'P & Q' means P is either smaller than or equal to Q. Statements: A # B, B % C, C $ D. Conclusions: I. A # D II. D # B

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Only I follows. Decoded: A > B >= C = D. So A > D (I follows), while D <= B, so D > B (II) is false.

8. 'A * B' means A is not smaller than B; 'A @ B' means A is neither smaller than nor equal to B; 'A $ B' means A is not greater than B; 'A & B' means A is neither greater than nor smaller than B. Statements: K @ L, L & M, M $ N. Conclusions: I. N @ K II. K @ M

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Neither I nor II follows

   Answer: Only II follows. Decoding: * is >=, @ is >, $ is <= and & is =. So K > L = M <= N. K > M follows (II); K > M and N >= M put both K and N above M, so K and N cannot be compared and I is uncertain.

9. 'A * B' means A is not smaller than B; 'A @ B' means A is neither smaller than nor equal to B; 'A & B' means A is neither greater than nor smaller than B. Statements: X * Y, Y & Z. Conclusions: I. X @ Z II. X & Z

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Neither I nor II follows

   Answer: Either I or II follows. Decoded: X >= Y = Z, so X >= Z. I (X > Z) and II (X = Z) are not certain alone, but one of them must be true: either I or II follows.

10. In which of the following expressions does 'M > Q' definitely hold?

    • M >= N > O <= Q
    • M > N = O >= Q
    • M = N < O > Q
    • M >= N = O <= Q

    Answer: M > N = O >= Q. In M > N = O >= Q every sign points the same way, and one is strict, so M > Q. In the others the chain changes direction, so M and Q cannot be compared.