GRE Quant | Ratios - Quantitative Comparison | GRE Math Practice Questions

GRE Quant | Ratios - Quantitative Comparison | GRE Math Practice Questions

This is a medium-difficulty GRE quant tutorial on quantitative comparison from the topic ratios. Solving this question requires knowing the properties of ratios and numbers.

Question:
If a, b, and c are numbers such that (a + b) : (b + c) : (c + a) is 15 : 11 : 12, then which one of the following is true?

Answer Options:
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. Cannot be determined

Chapter
00:00 Intro
00:30 Question
01:00 Solution - Case (i)
02:09 Solution - Case(ii)
03:42 Summary

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[matveykokin]

Hey, I got A by powering thought the algebra. Any ideas why is this also wrong
Solution:

Given the ratio:
Solution:

1. Given the ratio:
a + b : b + c : c + a = 15 : 11 : 12

2. Set up the equations:
- a + b = 15 → b = 15 - a
- c + a = 12 → c = 12 - a
- b + c = 11

3. Substitute b and c into the third equation:
(15 - a) + (12 - a) = 11

4. Simplify the equation:
27 - 2a = 11

5. Solve for a:
16 = 2a → a = 8

6. Find c:
c = 12 - a = 12 - 8 = 4

Conclusion:
Since a = 8 and c = 4, a > c. Therefore, Quantity A is greater.

Answer: A