Study the information given below and answer the questions that follow:
S scored higher marks than Q but lower than U.
P scored higher than S but lower than R and U.
T scored higher than R. The third lowest marks are 56. R scored 12 marks more than P.
U scored less than 69 marks.
If Q + R = 111 and P + T = 137, then fnd out Q + T.
Explanation:
Let’s break down the information:
- S: S > Q, S < U
- P: P > S, P < R, P < U
- T: T > R
- The marks in ascending order: Q < S < P < R < T/U/U/R/T ?
- U < 69
- Third lowest marks = 56
- R = P + 12
- Q + R = 111
- P + T = 137
Let's assign the order:
Q < S < P < R < T (since P < R < T and S < P < R)
U: U is higher than S and P, but below 69. Since U could be above R or below T, but it's not the highest (cannot be T).
Let’s use variables:
Q, S, P, R, T, U
Assume numbers:
Since third lowest is 56, order is:
(1) Q
(2) S
(3) P = 56
(4) R
(5) T
(U somewhere above S and below 69, and above P)
Let’s step by step:
- If P = 56, R = 56 + 12 = 68
- Q + R = 111 ? Q + 68 = 111 ? Q = 43
- P + T = 137 ? 56 + T = 137 ? T = 81
- Now S is between Q and P, so S = x where 43 < x < 56, pick S = 50
Let’s check U:
- S < U, P < U
- U < 69 ? so U = 67 (since R = 68, U < R)
- Final Order:
Q (43), S (50), P (56), U (67), R (68), T (81)
Sum Q + T: 43 + 81 = 124
So, Option 1: 124 is correct.
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- Q scored the lowest, 43 marks.
- S scored higher than Q but lower than P, 50 marks.
- P scored the third lowest, 56 marks.
- R, who is higher than P, got 68 marks (12 more than P).
- U is higher than S and P but lower than 69, so 67.
- T has the highest marks at 81 (higher than R).
- Q + R = 111 is satisfied.
- P + T = 137 is satisfied.
- Correct answer is: Option 1: 124