If the Celsius temperature of Object X is C and the equivalent Fahrenheit temperature of Object X is F, then...

Understanding the Question

We need to determine whether the Celsius temperature of Object X is greater than 50°C.

Given the relationship \(\mathrm{F} = \frac{9}{5}\mathrm{C} + 32\), let's find a key reference point: when \(\mathrm{C} = 50\), we get \(\mathrm{F} = \frac{9}{5}(50) + 32 = 90 + 32 = 122°\mathrm{F}\).

So our question essentially becomes: Is F > 122°F?

For this yes/no question to be sufficient, we need information that definitively tells us either:

• YES, C is always greater than 50, or
• NO, C is always 50 or less

Analyzing Statement 1

Statement 1 tells us: \(\mathrm{F} > 120\)

Let's test specific scenarios to see if this guarantees \(\mathrm{C} > 50\):

Test Case 1: What if \(\mathrm{F} = 121°\mathrm{F}\)?

• This satisfies \(\mathrm{F} > 120\) ✓
• But since 121 < 122, this would mean \(\mathrm{C} < 50\)
• Answer to our question: NO

Test Case 2: What if \(\mathrm{F} = 125°\mathrm{F}\)?

• This satisfies \(\mathrm{F} > 120\) ✓
• Since 125 > 122, this would mean \(\mathrm{C} > 50\)
• Answer to our question: YES

Since we can get different answers (both YES and NO are possible), 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: \(\mathrm{F} - \mathrm{C} > 72\)

Here's the key insight: Let's examine what happens to the difference \((\mathrm{F} - \mathrm{C})\) as C changes.

When \(\mathrm{C} = 50\), we know \(\mathrm{F} = 122\), which means \(\mathrm{F} - \mathrm{C} = 122 - 50 = 72\) exactly.

The crucial observation: As C increases, the gap \((\mathrm{F} - \mathrm{C})\) also increases. Why? Because when converting from Celsius to Fahrenheit, we multiply by 9/5 (which is 1.8, greater than 1) before adding 32. This multiplication creates an ever-widening gap.

Therefore:

• If \(\mathrm{F} - \mathrm{C} = 72\), then \(\mathrm{C} = 50\)
• If \(\mathrm{F} - \mathrm{C} > 72\), then \(\mathrm{C} > 50\)

Since Statement 2 tells us \(\mathrm{F} - \mathrm{C} > 72\), we can definitively conclude \(\mathrm{C} > 50\).

[STOP - Sufficient!] Statement 2 is sufficient.

This eliminates choices C and E.

The Answer: B

Since Statement 2 alone is sufficient but Statement 1 alone is not sufficient, the answer is B.

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