Practice GMAT Data Sufficiency Question

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As a result of dramatic changes in the global currency market, the value of every item in Country X plummeted by 50% from 1990 to 1995. What was the value of a copy of St. Augustine's Confessions in Country X's currency in 1990? (Assume that the only variable influencing changes in the value of the book is the value of Country X's currency.)

The value of St. Augustine's Confessions at the end of 1993 was $30
If the value of every item in Country X had plummeted by 50% from 1995 to 2000, the value of St. Augustine's Confessions in 2000 would have been $25

A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)	EACH statement ALONE is sufficient.
E)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: B

If "the value of every item in Country X plummeted by 50% from 1990 to 1995," the value in 1995 would be 100%-50% = 50% of the value in 1990.
Translate the information in the question into an algebraic equation.
P₉₅ = (.5)P₉₀; P₉₀ = ?
Evaluate Statement (1) alone.
1. Statement (1) says that P₉₃ = $30.
2. It may be tempting to assume that the value of the book changed the same amount each year. If this were true, Statement (1) would be sufficient since $30 would be the result of the value falling an equal percent for a known number of years. But, you cannot make this assumption. All you know is that the value in 1995 was half the value in 1990 and the value in 1993 was $30. It is possible that the value could have risen substantially from 1990 to 1993, only to fall dramatically enough during 1993, 1994, and 1995 that the value decreased by 50% from 1990 to 1995.
3. Consider the following two examples, which are both possible under the constraints of Statement (1) yet give different values for P₉₀.
  (1) P₉₀ = $15 and the value doubled to P₉₃ = $30, only to fall to P₉₅ = $7.5
  (2) P₉₀ = $25 and the value grew 20% to P₉₃ = $30, only to fall to P₉₅ = $7.5
  Since both examples satisfy the conditions (i.e., P₉₃ = $30 and P₉₅ = (.5)P₉₀) yet produce different values for P₉₀, Statement (1) is not definitive.
4. Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. Translate Statement (2) into algebra.
  (.5)P₉₅ = P₂₀₀₀
  (.5)P₉₅ = $25
  Therefore: P₉₅ = $50
2. The original question states the following relationship:
  P₉₅ = (.5)P₉₀
  Since we know that P₉₅ = $50, by substitution, we also know that:
  $50 = (.5)P₉₀
  Therefore: P₉₀ = $100
  Statement (2) is SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.

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