Although large mammals like elephants and whales tend to live longer than small ones like mice, larger breeds of dogs...
GMAT Two Part Analysis : (TPA) Questions
Although large mammals like elephants and whales tend to live longer than small ones like mice, larger breeds of dogs have shorter life spans, on average, than smaller breeds. A researcher studying the relationship between average body mass and average life span in breeds of dogs concluded that, for every \(2\) kilograms of body mass, life span is \(1\) month less.
According to this conclusion, the average life span of a breed with an average body mass of \(\mathrm{x}\) kg is \(\mathrm{y}\) months less than the average life span of a breed with an average body mass of \(10\) kg. Select for x and for y values that are jointly consistent with the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Understanding the Relationship
The researcher found that for every 2 kg of body mass, life span decreases by 1 month. Let's visualize this on a number line:
Body Mass (kg): 0 -------- 10 -------- 20 -------- 30 -------- 40
Life Span Change: Base -5 months -10 months
(from 10 kg) (from 10 kg)This linear relationship means:
- If we move from 10 kg to 12 kg (+2 kg), life span decreases by 1 month
- If we move from 10 kg to 20 kg (+10 kg), life span decreases by 5 months
- The formula: Life span change = \(-\frac{\mathrm{Body\ mass\ change}}{2}\) months
Phase 2: Understanding the Question
The question states: "the average life span of a breed with an average body mass of x kg is y months less than the average life span of a breed with an average body mass of 10 kg."
Breaking this down:
- We have a reference breed at 10 kg
- We have another breed at x kg
- The x kg breed lives y months less than the 10 kg breed
From our relationship, if a breed weighs x kg instead of 10 kg:
- The mass difference is \((\mathrm{x} - 10)\) kg
- The life span difference is \(\frac{(\mathrm{x} - 10)}{2}\) months
Therefore: \(\mathrm{y} = \frac{(\mathrm{x} - 10)}{2}\)
Phase 3: Finding the Answer
We need to find values from our choices [10, 15, 20, 25, 30, 35] where \(\mathrm{y} = \frac{(\mathrm{x} - 10)}{2}\).
Starting systematically:
- If x = 10: \(\mathrm{y} = \frac{(10-10)}{2} = 0\) (not in choices)
- If x = 15: \(\mathrm{y} = \frac{(15-10)}{2} = 2.5\) (not in choices)
- If x = 20: \(\mathrm{y} = \frac{(20-10)}{2} = 5\) (not in choices)
- If x = 25: \(\mathrm{y} = \frac{(25-10)}{2} = 7.5\) (not in choices)
- If x = 30: \(\mathrm{y} = \frac{(30-10)}{2} = 10\) ✓ (10 is in choices!)
Stop here - we found our answer.
Let's verify: A breed with 30 kg average body mass has 20 kg more mass than a 10 kg breed. Since life span decreases by 1 month per 2 kg increase, the life span difference is \(20 \div 2 = 10\) months.
Phase 4: Solution
x = 30
y = 10
A breed with an average body mass of 30 kg has an average life span that is 10 months less than a breed with an average body mass of 10 kg, perfectly matching the researcher's conclusion.