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When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?
We need to find the exact number of boxes in the warehouse.
We need to find ONE specific value for the number of boxes. Let's see what values are possible:
For sufficiency, we need information that narrows these five possibilities down to exactly ONE value.
Statement 1: If boxes were arranged in stacks of 9, there would be no remainder.
This means the number must be divisible by 9. Let's check which of our possible values {84, 92, 100, 108, 116} are divisible by 9:
Quick divisibility test for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Only 108 is divisible by 9.
Since Statement 1 narrows our answer to exactly one value (108 boxes), it is sufficient.
[STOP - Sufficient!]
This eliminates choices B, C, and E. The answer must be A or D.
Now let's forget Statement 1 completely and analyze Statement 2 independently.
Statement 2: If boxes were arranged in stacks of 12, there would be no remainder.
This means the number must be divisible by 12. Let's check our possible values {84, 92, 100, 108, 116}:
We have TWO values that work: 84 and 108.
Since we can't determine which one is the actual number of boxes, Statement 2 alone is NOT sufficient.
This eliminates choices B and D.
Answer Choice A: "Statement 1 alone is sufficient, but Statement 2 alone is not sufficient."