Two Students Appeared At An Examination. One of Them Secured 9 Marks GMAT Problem Solving

Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

1. 39, 30
2. 41, 32
3. 42, 33
4. 43, 34
5. 41, 36

‘Two students appeared at an examination.’ –  is the topic from the GMAT Quantitative problem set. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

There is only one way to solve this problem.
This problem can best be solved while considering the required number to be x.
Let's consider x to be the smaller score
So, x + 9 to be the larger score.
According to the question,
The larger score is 56% of the sum of the two scores.
So it can written as:
x + 9 = 56% of [x + (x + 9)]
Solving further x + 9 = 0.56(2x + 9)
implies that x + 9 = 1.12x + 5.04
Subtracting 5.04 from both sides: x + 3.96 = 1.12x
Subtract x from both sides: 3.96 = 0.12x
Solving we get, x = 3.96/0.12 = 396/12 = 33
Therefore, 33 is the smaller score, and 42 is the larger score.
Correct Answer: C

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