First-time computer buyers buying PXC home computers typically buy models that cost much less and have a smaller profit margin...

GMAT Critical Reasoning : (CR) Questions

Source: Official Guide

Critical Reasoning

Inference

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Notes

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First-time computer buyers buying PXC home computers typically buy models that cost much less and have a smaller profit margin per computer than do PXC computers bought by people replacing their computers with more powerful models. Last year PXC's profits from computer sales were substantially higher than the previous year, although about the same number of PXC computers were sold and the prices and profit margins for each computer model that PXC sells remained unchanged.

If the statements above are true, which of the following is most strongly supported by them?

PXC's competitors raised the prices on their computers last year, making PXC computers more attractive to first-time computer buyers.

The number of people buying PXC computers who also bought PXC computer-related products, such as printers, was larger last year than the previous year.

Among computer buyers who bought a PXC computer to replace their existing computer, the proportion who were replacing a computer made by a competitor of PXC was greater last year than the previous year.

The proportion of PXC computers bought by first-time computer buyers was smaller last year than the previous year.

PXC's production costs for its computers were lower last year than they had been the previous year.

Solution

Passage Visualization

Passage Statement	Visualization and Linkage
First-time computer buyers buying PXC home computers typically buy models that cost much less and have a smaller profit margin per computer than do PXC computers bought by people replacing their computers with more powerful models.	Establishes: Customer segmentation and profit patterns Key Pattern: Two distinct buyer types with different purchasing behaviors Concrete Example: First-time buyers: Purchase $800 computers with \(\$80\) profit margin (\(10\%\)) Replacement buyers: Purchase $2,000 computers with \(\$400\) profit margin (\(20\%\)) Critical Insight: Customer type directly correlates with profit per unit
Last year PXC's profits from computer sales were substantially higher than the previous year, although about the same number of PXC computers were sold and the prices and profit margins for each computer model that PXC sells remained unchanged.	Establishes: The profit paradox - higher profits without typical drivers Constraints Given: Total units sold: Same (e.g., 10,000 both years) Prices per model: Unchanged Profit margins per model: Unchanged Result: Substantially higher total profits Example: Previous year profit: \(\$2,000,000\) Last year profit: \(\$2,800,000\) (\(+40\%\)) What didn't change: Unit economics, total volume
Overall Implication	The Composition Shift Paradox: Since total units and per-unit economics remained constant, but total profits increased substantially, the only explanation is a shift in the mix of customers. Logical Resolution: Year 1: 7,000 first-time buyers + 3,000 replacement buyers = \(\$1,760,000\) profit Year 2: 4,000 first-time buyers + 6,000 replacement buyers = \(\$2,720,000\) profit Same 10,000 total units, but higher proportion of high-margin replacement buyers

Passage Statement

Visualization and Linkage

Establishes: Customer segmentation and profit patterns

Key Pattern: Two distinct buyer types with different purchasing behaviors

Concrete Example:

First-time buyers: Purchase $800 computers with $\$80$ profit margin ($10\%$)
Replacement buyers: Purchase $2,000 computers with $\$400$ profit margin ($20\%$)

Critical Insight: Customer type directly correlates with profit per unit

Last year PXC's profits from computer sales were substantially higher than the previous year, although about the same number of PXC computers were sold and the prices and profit margins for each computer model that PXC sells remained unchanged.

Establishes: The profit paradox - higher profits without typical drivers

Constraints Given:

Total units sold: Same (e.g., 10,000 both years)
Prices per model: Unchanged
Profit margins per model: Unchanged

Result: Substantially higher total profits

Example:
Previous year profit: $\$2,000,000$
Last year profit: $\$2,800,000$ ($+40\%$)

What didn't change: Unit economics, total volume

Overall Implication

The Composition Shift Paradox:

Since total units and per-unit economics remained constant, but total profits increased substantially, the only explanation is a shift in the mix of customers.

Logical Resolution:

Year 1: 7,000 first-time buyers + 3,000 replacement buyers = $\$1,760,000$ profit
Year 2: 4,000 first-time buyers + 6,000 replacement buyers = $\$2,720,000$ profit
Same 10,000 total units, but higher proportion of high-margin replacement buyers

Valid Inferences

Inference: Last year, a higher proportion of PXC computer sales were to people replacing their computers rather than to first-time buyers compared to the previous year.

Supporting Logic: Since the passage establishes that replacement buyers purchase higher-margin computers than first-time buyers, and since total profits increased substantially while total units sold and per-unit margins remained unchanged, the only way for total profits to increase is if the sales mix shifted toward the more profitable customer segment (replacement buyers).

Clarification Note: The passage supports a change in customer composition, not necessarily a change in absolute numbers of each customer type. What matters is the relative proportion of high-margin replacement buyers versus low-margin first-time buyers.

Answer Choices Explained

PXC's competitors raised the prices on their computers last year, making PXC computers more attractive to first-time computer buyers.

This choice suggests that competitor price increases made PXC more attractive to first-time buyers. However, this would actually contradict what we need to explain. If more first-time buyers were attracted to PXC, that would decrease average profit per sale (since first-time buyers purchase lower-margin computers), which would make total profits go down, not up as stated in the passage.

The number of people buying PXC computers who also bought PXC computer-related products, such as printers, was larger last year than the previous year.

This choice introduces computer-related products like printers, but the passage specifically states that the profit increase came from "computer sales." The passage gives us no information about related products, so we cannot infer anything about printer sales or other accessories from the given information.

This choice focuses on whether replacement buyers were switching from competitors versus upgrading PXC computers, but this distinction doesn't matter for explaining the profit increase. Whether replacement buyers previously owned PXC or competitor computers, they're still purchasing the same high-margin PXC models, so this wouldn't affect the profit pattern described.

The proportion of PXC computers bought by first-time computer buyers was smaller last year than the previous year.

This is strongly supported by the passage. We know that first-time buyers purchase lower-margin computers while replacement buyers purchase higher-margin computers. Since total profits increased substantially while total units sold and per-unit margins remained the same, the only way this could happen is if the sales mix shifted toward more profitable replacement buyers. This necessarily means the proportion of less profitable first-time buyers decreased.

PXC's production costs for its computers were lower last year than they had been the previous year.

This choice suggests lower production costs increased profits, but the passage specifically states that "profit margins for each computer model remained unchanged." If production costs had decreased while selling prices stayed the same, profit margins would have increased, contradicting the given information.

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