Finding of a survey of Systems magazine subscribers: Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year were placed by subscribers under age thirty-five. Finding of a survey of advertisers in Systems magazine: Most of the merchandise orders placed in response to advertisements in Systems last year were placed by people under age thirty-five.
For both of the findings to be accurate, which of the following must be true?
- A. More subscribers to Systems who have never ordered merchandise in response to advertisements in the magazine are age thirty-five or over than are under age thirty-five.
- B. Among subscribers to Systems , the proportion who are under age thirty-five was considerably lower last year than it is now.
- C. Most merchandise orders placed in response to advertisements in Systems last year were placed by Systems subscribers over age thirty-five.
- D. Last year, the average dollar amount of merchandise orders placed was less for subscribers under age thirty-five than for those age thirty-five or over.
- E. Last year many people who placed orders for merchandise in response to advertisements in Systems were not subscribers to the magazine.
Solution
Passage Visualization
| Passage Statement | Visualization and Linkage |
|---|---|
| Finding of a survey of Systems magazine subscribers: Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year were placed by subscribers under age thirty-five. | Establishes: Proportion of subscriber orders from under-35 age group Key insight: Only 30% of subscriber orders came from under-35 Concrete example: If subscribers placed 1,000 total orders300 orders from subscribers under 35700 orders from subscribers 35 and olderScope: Limited to magazine subscribers only |
| Finding of a survey of advertisers in Systems magazine: Most of the merchandise orders placed in response to advertisements in Systems last year were placed by people under age thirty-five. | Establishes: Majority of all orders (>50%) came from under-35 age group Key insight: Most (>50%) of ALL orders came from under-35 Concrete example: If total orders were 2,0001,100+ orders from people under 35900- orders from people 35 and olderScope: Includes ALL people who ordered (subscribers + non-subscribers) |
| Overall Implication | PARADOX REVEALED: Under-35 subscribers represent only 30% of subscriber orders, but under-35 people represent majority of ALL orders Mathematical requirement: If subscribers under 35 = 300 orders (30% of 1,000)But total under 35 = 1,100+ orders (>50% of 2,000)Then non-subscriber under 35 orders = 800+ ordersCritical insight: Non-subscribers under 35 must heavily outorder subscribers under 35 |
Valid Inferences
Inference: A significant number of merchandise orders must have been placed by non-subscribers under age thirty-five.
Supporting Logic: Since subscribers under 35 placed only 30% of subscriber orders, but people under 35 placed most (>50%) of all orders, the majority of under-35 orders must have come from non-subscribers. This mathematical relationship requires that non-subscribers under 35 placed substantially more orders than subscribers under 35 did.
Clarification Note: The passage establishes that there must be a large population of non-subscriber customers under 35, but does not explain why this age group orders more frequently when they’re not magazine subscribers versus when they are subscribers.
Answer Choices Explained
A. More subscribers to Systems who have never ordered merchandise in response to advertisements in the magazine are age thirty-five or over than are under age thirty-five.
This focuses on subscribers who have never ordered merchandise, which is completely irrelevant to our analysis. We’re trying to reconcile data about people who did place orders. The age distribution of non-ordering subscribers doesn’t help explain the discrepancy between 30% (subscriber orders from under-35) and majority (all orders from under-35). This choice is a distractor that shifts focus away from the actual ordering patterns we need to explain.
B. Among subscribers to Systems , the proportion who are under age thirty-five was considerably lower last year than it is now.
This discusses changes in subscriber demographics over time (“last year” vs “now”), but our argument only deals with data from last year. We have no information about current subscriber demographics, and changes over time wouldn’t explain the simultaneous findings from the same time period. The discrepancy exists within last year’s data alone, not across different time periods.
C. Most merchandise orders placed in response to advertisements in Systems last year were placed by Systems subscribers over age thirty-five.
This directly contradicts the second finding. The advertisers’ survey clearly states that most orders came from people under 35, not over 35. If most orders were from people over 35, then the second finding would be false, which violates our requirement that both findings must be accurate. This choice makes the findings inconsistent rather than reconciling them.
D. Last year, the average dollar amount of merchandise orders placed was less for subscribers under age thirty-five than for those age thirty-five or over.
The dollar amount per order is irrelevant to explaining the numerical discrepancy we identified. Whether under-35 customers spent more or less per order doesn’t change the fact that they represented 30% of subscriber orders but majority of all orders. We’re dealing with order counts and proportions, not order values. This is a classic GMAT distractor that introduces irrelevant financial information.
E. Last year many people who placed orders for merchandise in response to advertisements in Systems were not subscribers to the magazine.
This is the key insight that resolves our mathematical puzzle. If many non-subscribers placed orders, then the total customer base includes both subscribers and non-subscribers. Subscribers under 35 could represent only 30% of subscriber orders, while the larger pool of under-35 non-subscribers could push the overall under-35 percentage above 50%. For example: if subscribers placed 1000 orders (300 from under-35) and non-subscribers placed 1500 orders (1000 from under-35), then under-35 customers would represent 1300 of 2500 total orders (52%), while still being only 30% of subscriber orders. This perfectly reconciles both findings.
