Town X has 50,000 residents, some of whom were born in Town X. What percent of the residents of Town...

Understanding the Question

We need to find what percent of Town X's 50,000 residents were born in Town X.

What We Need to Determine

Since this is a value question, finding the specific percentage requires either:

• The exact number of residents born in Town X, or
• Enough information about population subgroups to calculate this number

Key Insight from Our Approach Analysis

The approach analysis revealed a powerful pattern: when all subgroups of a population share the same percentage, the overall percentage must equal that common percentage. Let's see if this pattern applies here.

Analyzing Statement 1

Statement 1 tells us: Of the male residents, 40% were NOT born in Town X.

This means 60% of male residents WERE born in Town X. However, we're missing crucial information:

• We don't know how many residents are male
• We don't know anything about female residents

Why This Matters

Let's visualize with concrete examples:

• Example 1: If there are 20,000 males and 30,000 females, and 90% of females were born in Town X:
  • Males born in Town X: \(20,000 \times 60\% = 12,000\)
  • Females born in Town X: \(30,000 \times 90\% = 27,000\)
  • Total born in Town X: 39,000 out of 50,000 = 78%
• Example 2: Same gender split, but only 30% of females were born in Town X:
  • Males born in Town X: \(20,000 \times 60\% = 12,000\)
  • Females born in Town X: \(30,000 \times 30\% = 9,000\)
  • Total born in Town X: 21,000 out of 50,000 = 42%

Since different scenarios lead to different answers, Statement 1 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 tells us: Of the female residents, 60% were born in Town X.

Again, we're missing key information:

• We don't know how many residents are female
• We don't know anything about male residents

The same logic applies. Without knowing the male percentage or the gender distribution, we cannot determine the overall percentage. Different male percentages would yield different total percentages.

Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Statements

Now let's use both statements together:

• 60% of males were born in Town X (from Statement 1)
• 60% of females were born in Town X (from Statement 2)

The Key Recognition

Here's where our pattern delivers the answer! When every subgroup has the same percentage (60%), the overall percentage must equal that common percentage—regardless of how the population is split.

Think of it this way:

• If Town X has 10,000 males and 40,000 females → 60% of total were born in Town X
• If Town X has 25,000 males and 25,000 females → 60% of total were born in Town X
• If Town X has 40,000 males and 10,000 females → 60% of total were born in Town X

No matter what the gender split is, when both groups have 60%, the total must be 60%.

Quick Verification

For any split where M + F = 50,000:

• Total born in Town X = \(0.6\mathrm{M} + 0.6\mathrm{F} = 0.6(\mathrm{M} + \mathrm{F}) = 0.6(50,000) = 30,000\)
• Percentage = \(30,000/50,000 = 60\%\)

The statements together are sufficient.

[STOP - Sufficient!] This eliminates choice E.

The Answer: C

Both statements together tell us that 60% of all residents were born in Town X, but neither statement alone provides enough information.

Answer Choice C: "Both statements together are sufficient, but neither statement alone is sufficient."