How many Rs. Would Shalini need to spend to buy 11 pencils and 14 pens.…
2024
How many Rs. Would Shalini need to spend to buy 11 pencils and 14 pens.
Shalini spent an amount of Rs. 201 to buy 15 pencils and 12 pens.
Shalini spent an amount of Rs. 121 to buy 7 pencils and 9 pens.
- A.
if the question can be answered by using one of the statements.
- B.
if the question can be answered by using either statement alone.
- C.
if the question can be answered by using both statements together.
- D.
if the question cannot be answered even by using both statements together.
Attempted by 693 students.
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Correct answer: C
Let p = price of one pencil and q = price of one pen.
From the first statement: 15p + 12q = 201.
From the second statement: 7p + 9q = 121.
Key point: two linear equations in two unknowns determine a unique solution if they are independent.
Compute the determinant of the coefficient matrix: 15*9 - 12*7 = 135 - 84 = 51.
Because the determinant is not zero, the two equations are independent and the system has a unique solution for p and q.
Therefore, both statements together are sufficient to find the prices and to compute 11p + 14q. Each statement alone is insufficient because a single linear equation with two unknowns does not give a unique solution.
Note: For a data-sufficiency answer you only need to state that both statements together suffice; computing the numeric value is not required here.