Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. The ratio of the salaries of John and Sam is 3 : 4 and that of their expenditures is 4 : 5, respectively. Find the ratio of saving of John and Sam. 1. The saving of Sam is 25% of his salary. 2. The salary of Sam is Rs. 5000.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statement (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
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A Correct answer
Explanation

Let John's salary be 3x and Sam's be 4x. Let John's expenditure be 4y and Sam's be 5y. Savings = Salary - Expenditure. Statement 1 says Sam's savings (4x - 5y) = 25% of his salary (4x). So 4x - 5y = x, which means 3x = 5y, or y = 0.6x. Now we can find the ratio of savings: John's savings = 3x - 4y = 3x - 4(0.6x) = 0.6x. Sam's savings = 4x - 5y = 4x - 5(0.6x) = x. The ratio is 0.6x : x = 3 : 5. Statement 1 is sufficient. Statement 2 only gives a specific value for Sam's salary, which is not enough to find the ratio.

AI explanation

Let John's salary be 3x and Sam's be 4x; their expenditures are 4y and 5y, making their savings (3x - 4y) and (4x - 5y). Statement (1) says Sam's saving is 25% of his salary, which creates the equation 4x - 5y = 0.25(4x), simplifying to 4x - 5y = x, so 3x = 5y. Substituting this relationship back into the ratio of their savings yields (3x - 4y)/(4x - 5y) = 1. Statement (2) only provides the absolute value of Sam's salary (4x = 5000), which does not help find the expenditures or the savings ratio without more information. Therefore, statement (1) alone is sufficient, but statement (2) alone is not.

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