Solution: Determine a) the value of antique as on Jan 1 and Dec 31
or b) ratio of value as on Jan 1 and Dec 31

Statement 1: The value of the antique on January 1, 1981, was $3,000
We only know the value as on Jan 1, but not as on Dec 31 - Insufficient

Statement 2: The value of the antique on December 31, 1981, was double the value of the antique on January 1,1981
We know the ratio of value as on Jan 1 and Dec 31 (100% rise) - Sufficient

Answer B

Note we need to calculate %increase and not value of the object.

S(1): Gives value at the beginning. No way to calculate value at the end. Hence Not Sufficient.

S(2): Tell us that the value doubled. Hence we know the % increase i.e 100%. Hence Suff.

Answer B.

St-1 not sufficient as value or ratio/percentage at Dec 31, 1981 is not present
St-2 is sufficient. Amount doubled means 100% increase.

Ans - B

1. We dont know the value on Dec 31 - Not sufficient to find the percent increase
2. Since it is double during the time frame, the percent increase is 100% - Sufficient

Ans B
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The correct answer is B.
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Target question: What was the percent increase in the value of a certain antique from January 1, 1981, to December 31, 1981?

Percent increase = 100(new - old)/old
So, we can answer the target question if we have the OLD value and the NEW value.

Statement 1: The value of the antique on January 1, 1981, was $3,000.
Okay, so we have the OLD value, but we don't know the NEW value.
So, we don't have enough info to answer the target question
Statement 1 is NOT SUFFICIENT

Statement 2: The value of the antique on December 31, 1981, was double the value of the antique on January 1, 1981.
Although we aren't given specific numbers for the OLD value and NEW value, we still have enough information. Here's why:
Let x = the value of December 31, 1981
This means 2x = the value on January 1, 1981

When we apply the above formula, we get: percent increase = 100(2x - x)/x = 100x/x = 100
So, the answer to the target question is 100 percent
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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