# GRE® Quantitative Comparison Q5

#### GRE Practice Questions | Ratio and Proportion, Number Systems

The GRE maths sample question given below is a Quantitative Comparison Question in ratio and proportion. This GRE Math question also tests the fundamentals of Modulus, and Number Systems. While a GRE problem solving question and a GRE Quantitative Comparison question may test the same math concept, the analysis required to get the answer right is more in a GRE Quantitative Comparison question.

Question 5: If a, b, and c are numbers such that (a + b) : (b + c) : (c + a) is 15 : 11 : 12, then

Quantity A Quantity B
a c

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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### Explanatory Answer | GRE Practice Question 5

Given Data
(a + b) : (b + c) : (c + a) = 15 : 11 : 12
To compare a and c, it is sufficient if we compare the first two components of this ratio.
(a + b) : (c + b) = 15 : 11
Since b is a constant present in both the components, we can find the greater of the two terms, a and c, by equating the above ratio.
However, the caveat is that the ratio a + b : c + b is 15 : 11. Either both a and c are positive or are negative.

#### Case 1: Both a and c are positive

Let the value of (a + b) be 15x, and (c + b) be 11x.
If x is positive it is evident that 15x > 11x.
∴ (a + b) > (c + b)
Based on Case 1, we can deduce that a > c.

#### Case 2: Both a and c are negative

Let the value of (a + b) be 15x, and (c + b) be 11x.
If x is negative it is evident that 15x < 11x.
∴ (a + b) < (c + b)
Based on Case 2, we can deduce that a < c.

Because both possibilities exist, we are not able to deduce which of the two quantities a or c is greater based on the information given in the question. The key to getting the answer right is to remember that 15 : 11 need not always result in the two quantities being positive.

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