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A certain pizzeria has more than fifty types of pizzas on its menu. The chart shows the revenue share, in...

GMAT Data Sufficiency : (DS) Questions

Source: Official Guide
Data Sufficiency
DS - Money
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A certain pizzeria has more than fifty types of pizzas on its menu. The chart shows the revenue share, in the pizzeria's total revenue in the last month, of its four most popular pizza types. Each pizza type has only a single size and a single price. Which was their best-selling pizza last month in terms of number of pizzas sold?

  1. The number of customers who ordered at least one Pep-Peroni pizza last month was greater than the number of customers who ordered at least one of any other pizza type last month.
  2. The lowest-priced pizza type on the pizzeria's menu is Tomato Blast, followed by VegCheese.
A
Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B
Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D
EACH statement ALONE is sufficient.
E
Statements (1) and (2) TOGETHER are not sufficient.
Solution
## Understanding the Question

We need to determine which pizza had the highest unit sales (number of pizzas sold) last month.

### Given Information
- The pizzeria has more than 50 types of pizzas
- We have a chart showing revenue share of the four most popular pizza types
- Each pizza type has only a single size and a single price
- Revenue = Price × Quantity

### What We Need to Determine
To find which pizza sold the most units, we need to convert revenue shares into actual quantities sold. Since revenue depends on both price and quantity, a pizza with high revenue share could either have:
- High price with moderate sales volume
- Low price with high sales volume

The key insight: **without knowing relative prices, we cannot determine which pizza had the highest unit sales from revenue data alone**.

## Analyzing Statement 1

**Statement 1**: The number of customers who ordered at least one Pep-Peroni pizza last month was greater than the number of customers who ordered at least one of any other pizza type last month.

This tells us Pep-Peroni had the most customers, but **having the most customers doesn't guarantee the most pizzas sold**. 

### Why Customer Count ≠ Pizza Count

Let's test two scenarios to see if different outcomes are possible:

**Scenario 1: Each customer orders exactly one pizza**
- 100 customers order Pep-Peroni → 100 pizzas sold
- 80 customers order VegCheese → 80 pizzas sold
- **Result**: Pep-Peroni has the highest unit sales

**Scenario 2: Customers order different quantities**
- 100 customers each order 1 Pep-Peroni → 100 pizzas sold
- 50 customers each order 3 VegCheese → 150 pizzas sold
- **Result**: VegCheese has the highest unit sales

Since different scenarios lead to different answers about which pizza sold the most units, we cannot determine the best-selling pizza.

Statement 1 alone is **NOT sufficient**.

**[STOP - Not Sufficient!]** This eliminates choices A and D.

## Analyzing Statement 2

**Now let's forget Statement 1 completely and analyze Statement 2 independently.**

**Statement 2**: The lowest-priced pizza type on the pizzeria's menu is Tomato Blast, followed by VegCheese.

This gives us a partial price ranking: Tomato Blast is cheapest, VegCheese is second-cheapest.

### What We Still Don't Know

Critical gaps remain:
- We don't know if Tomato Blast or VegCheese are among the four pizzas shown in the revenue chart
- We don't know the actual prices or price ratios
- We don't know the prices of Pep-Peroni and PizzAzza

Without knowing which pizzas are in the chart and their exact price relationships, we cannot convert revenue shares to unit sales. For instance, even if we knew Tomato Blast was in the chart with 20% revenue share, without its exact price relative to others, we couldn't calculate its unit sales.

Statement 2 alone is **NOT sufficient**.

**[STOP - Not Sufficient!]** This eliminates choices B and D.

## Combining Both Statements

Using both statements together:
- From Statement 1: Pep-Peroni had the most customers
- From Statement 2: Tomato Blast is lowest-priced, VegCheese is second-lowest

### Why Together They're Still Not Sufficient

Even with both pieces of information, we still cannot determine unit sales because:

1. **Unknown chart composition**: We don't know if Tomato Blast or VegCheese are among the four pizzas in the revenue chart

2. **Missing price ratios**: Without knowing exact price relationships, we can't convert revenue to quantity. For example, if Pep-Peroni costs $20 and VegCheese costs $10, then VegCheese needs only half Pep-Peroni's revenue to achieve equal unit sales—but we don't have these price ratios.

3. **Variable ordering patterns**: Having the most customers doesn't determine total units when customers can order multiple pizzas

The combined statements are **NOT sufficient**.

**[STOP - Still Not Sufficient!]** This eliminates choices A, B, C, and D.

## The Answer: E

We cannot determine which pizza had the highest unit sales because we lack the price information needed to convert revenue shares into quantities sold.

**Answer Choice E**: "The statements together are not sufficient."
Answer Choices Explained
A
Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
B
Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D
EACH statement ALONE is sufficient.
E
Statements (1) and (2) TOGETHER are not sufficient.
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