Inequalities

1. 1

   Statement: R < T > A = X > P
   Conclusions: I. X ≤ T   II. P ≤ A

   Question 1

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer EE

   X and T: the chain gives X < T, so X ≤ T is definitely true. P and A: the chain gives P < A, so P ≤ A is definitely true. So: Both conclusions follow.

2. 2

   Statement: N > H < J ≥ B = Z
   Conclusions: I. J = Z   II. J > Z

   Question 2

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer CC

   J and Z: the chain gives J ≥ Z, so J = Z is not definitely true. J and Z: the chain gives J ≥ Z, so J > Z is not definitely true. Together the two cover every possibility the chain allows. So: Either conclusion I or II follows.

3. 3

   Statement: H ≤ C ≥ N ≥ R < S
   Conclusions: I. R = C   II. R < C

   Question 3

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer CC

   R and C: the chain gives R ≤ C, so R = C is not definitely true. R and C: the chain gives R ≤ C, so R < C is not definitely true. Together the two cover every possibility the chain allows. So: Either conclusion I or II follows.

4. 4

   Statement: T < D ≤ N ≥ Y ≥ U
   Conclusions: I. N = U   II. N > U

   Question 4

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer CC

   N and U: the chain gives N ≥ U, so N = U is not definitely true. N and U: the chain gives N ≥ U, so N > U is not definitely true. Together the two cover every possibility the chain allows. So: Either conclusion I or II follows.

5. 5

   Statement: J > V > T > K > L
   Conclusions: I. V ≥ K   II. V ≥ L

   Question 5

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer EE

   V and K: the chain gives V > K, so V ≥ K is definitely true. V and L: the chain gives V > L, so V ≥ L is definitely true. So: Both conclusions follow.

6. 6

   Statement: Z > U > D > F > Q
   Conclusions: I. F ≤ U   II. Z ≥ D

   Question 6

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer EE

   F and U: the chain gives F < U, so F ≤ U is definitely true. Z and D: the chain gives Z > D, so Z ≥ D is definitely true. So: Both conclusions follow.

7. 7

   Statement: X = V = S ≤ C < R
   Conclusions: I. R < X   II. V ≤ R

   Question 7

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer BB

   R and X: the chain gives R > X, so R < X is not definitely true. V and R: the chain gives V < R, so V ≤ R is definitely true. So: Only conclusion II follows.

8. 8

   Statement: Q < T < G ≤ R > H
   Conclusions: I. H ≤ T   II. G ≥ Q

   Question 8

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer BB

   H and T: the signs between them point both ways, so no relation can be fixed, so H ≤ T is not definitely true. G and Q: the chain gives G > Q, so G ≥ Q is definitely true. So: Only conclusion II follows.

9. 9

   Statement: U = Y ≥ R ≥ Z ≥ N
   Conclusions: I. Y = Z   II. Y > Z

   Question 9

   AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

   Answer and working

   Answer CC

   Y and Z: the chain gives Y ≥ Z, so Y = Z is not definitely true. Y and Z: the chain gives Y ≥ Z, so Y > Z is not definitely true. Together the two cover every possibility the chain allows. So: Either conclusion I or II follows.

10. 10

    Statement: S ≥ U > Q > G ≤ A
    Conclusions: I. Q = S   II. Q ≤ S

    Question 10

    AOnly conclusion I follows BOnly conclusion II follows CEither conclusion I or II follows DNeither conclusion follows EBoth conclusions follow

    Answer and working

    Answer BB

    Q and S: the chain gives Q < S, so Q = S is not definitely true. Q and S: the chain gives Q < S, so Q ≤ S is definitely true. So: Only conclusion II follows.

More reasoning: Number and letter series, Coding and decoding, Analogies, Odd one out, Blood relations, Direction sense.