The table shows the distribution of scores on a typing test for a group of 84 trainees. Is the range...

Understanding the Question

We need to determine whether the range of scores for 84 trainees is greater than 34.

The range is simply: \(\mathrm{Greatest\ score - Least\ score}\)

So we're asking: Is \((\mathrm{Greatest\ score - Least\ score}) > 34\)?

This is a yes/no question. To answer it definitively, we need to calculate the exact range and compare it to 34.

What Makes This Sufficient?

For this question to be answerable, we need to know BOTH:

• The greatest score
• The least score

Without both values, we cannot calculate the range.

Analyzing Statement 1

Statement 1 tells us: The greatest score is 90.

Now we know one piece of the range formula, but we're missing the least score. Without it, we can't determine the range. Let's test different scenarios to see if we can answer our question:

• If the least score = 50, then range = \(90 - 50 = 40\), which is > 34 → Answer: YES
• If the least score = 60, then range = 90 - 60 = 30, which is < 34 → Answer: NO

Since we can get both YES and NO depending on the unknown least score, Statement 1 alone is 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: The least score is 50.

This gives us the other piece of the range formula, but now we're missing the greatest score. Let's test scenarios:

• If the greatest score = 85, then range = \(85 - 50 = 35\), which is > 34 → Answer: YES
• If the greatest score = 80, then range = \(80 - 50 = 30\), which is < 34 → Answer: NO

Again, we can get both YES and NO depending on the unknown greatest score, so Statement 2 alone is NOT sufficient.

This eliminates choice B.

Combining Statements

Using both statements together, we now have:

• Greatest score = 90 (from Statement 1)
• Least score = 50 (from Statement 2)

Therefore: Range = \(90 - 50 = 40\)

Since \(40 > 34\), we can definitively answer YES to our question.

[STOP - Sufficient!] The statements together are sufficient.

This eliminates choice E.

The Answer: C

Both statements together give us the exact range (40), which we can compare to 34. Neither statement alone provides enough information because each provides only one boundary value needed for the range calculation.

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