Multiple choice

The following question accompanied by three statements I, II and III. We have to determine which statements is/are sufficient to answer the question. What is the sum of two numbers? I. The bigger of these two numbers is $6$ more than the smaller number. II. $40\%$ of the smaller number is equal to $30\%$ of the bigger number. III. The ratio between half of the bigger number and one-third of the smaller number is $2:1.$

  1. Only II and II are sufficient

  2. Only I and II are sufficient

  3. I and either II or III is sufficient

  4. All, I, II, and III together are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the difference between the numbers. Statement II gives their ratio as 4:3, and statement III also gives the same ratio. Combining the difference with either ratio determines both numbers and their sum.

AI explanation

From statement I, let the numbers be x and y, giving the equation x - y = 6. From statement II, substituting y + 6 for x gives 0.40y = 0.30(y + 6), which solves to y = 18 and x = 24. Statement III simplifies to 3x = 4y, which is exactly equivalent to statement II, meaning either one can be used with statement I to find the sum. Therefore, statement I combined with either statement II or statement III is sufficient to answer the question.

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