The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are...

Understanding the Question

We need to determine whether any students of the same gender born in the same month have the same GMAT score.

Given Information

• GMAT scores range from \(200\) to \(800\) in \(10\)-point increments (valid scores: \(200, 210, 220, \ldots, 790, 800\))
• This gives us exactly \(61\) possible GMAT scores
• The first-year class has \(478\) students

What We Need to Determine

This is a yes/no question. We need to establish whether we can definitively answer:

• YES: At least two students of the same gender born in the same month have the same GMAT score
• NO: No such students exist

Key Insight

Since there are \(2\) genders and \(12\) months, we have \(24\) different gender-month combinations. This is a classic setup for the Pigeonhole Principle: if we can show that any gender-month group has more students than available GMAT scores, then some students in that group must share the same score.

Analyzing Statement 1

Statement 1 tells us that GMAT scores in the class range from \(600\) to \(780\).

What Statement 1 Tells Us

This dramatically reduces our available GMAT scores:

• Valid scores in this range: \(600, 610, 620, \ldots, 770, 780\)
• Number of possible scores = \((780 - 600) \div 10 + 1 = 19\) scores only

Applying the Pigeonhole Principle

With \(478\) students distributed across \(24\) gender-month combinations:

• Average students per gender-month group = \(478 \div 24 \approx 19.92\) students

Here's the crucial realization: we have an average of about 20 students per group, but only 19 possible GMAT scores.

By the Pigeonhole Principle, at least one gender-month group must have 20 or more students. Since there are only 19 possible scores available for that group, at least two students in that group must have the same GMAT score.

Conclusion for Statement 1

Statement 1 is sufficient to answer the question. The answer is definitively YES.

[STOP - Statement 1 is Sufficient!]

This eliminates choices B, C, and E. We only need to check if Statement 2 alone is also sufficient.

Analyzing Statement 2

Important: We now forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us that \(60%\) of the students are male.

What Statement 2 Provides

• Male students: \(60% \times 478 = 287\) males (rounding \(286.8\))
• Female students: \(478 - 287 = 191\) females

Testing the Distribution

Now we have all \(61\) possible GMAT scores available (\(200\) to \(800\)), and:

• \(287\) males across \(12\) months: average of \(287 \div 12 \approx 24\) males per month
• \(191\) females across \(12\) months: average of \(191 \div 12 \approx 16\) females per month

Even with an average of 24 males per month, we have 61 possible GMAT scores - more than enough to give each male born in any given month a different score. The same logic applies to females.

Without knowing the actual distribution or score range, we cannot definitively conclude that duplicates must exist.

Conclusion for Statement 2

Statement 2 is NOT sufficient to answer the question.

This eliminates choices B and D.

The Answer: A

Since only Statement 1 is sufficient to determine that some students of the same gender born in the same month must have the same GMAT score, the answer is A.

Answer Choice A: "Statement 1 alone is sufficient, but Statement 2 alone is not sufficient."