Multiple choice

Passage

Directions: In this problem, a question is followed by three statements, labelled as (A), (B) and (C). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question.

Find the monthly incomes of XYZ and PQR. (A) XYZ saves Rs. 2500 per month and PQR saves Rs. 5000 per month. (B) The monthly incomes of XYZ and PQR are in the ratio of 4 : 5. (C) The ratio of the expenses of XYZ and PQR is 5 : 6.

  1. Only A and B together are sufficient.

  2. All of them together are necessary.

  3. All of them together are not sufficient.

  4. Any one of A, B and C is sufficient.

  5. Any two of A, B and C are sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be 4x and 5x, and expenses be 5y and 6y. Savings are Income - Expense. So, 4x - 5y = 2500 and 5x - 6y = 5000. We have two equations with two variables (x, y), which is sufficient to find x and y. Statement A gives savings, B gives income ratio, C gives expense ratio. We need all three to form the system of equations.

AI explanation

Using the combination of all three statements, let the monthly incomes of XYZ and PQR be 4x and 5x, and let their expenses be 5y and 6y. From statement A, we can formulate two equations: 4x minus 5y equals 2500 and 5x minus 6y equals 5000. Solving this system of linear equations yields the values of x and y, which in turn gives the exact monthly incomes for both individuals. Therefore, all three statements together are necessary to answer the question.

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