Practice GMAT Data Sufficiency Question

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After a long career, John C. Walden is retiring. If there are 25 associates who contribute equally to a parting gift for John in an amount that is an integer, what is the total value of the parting gift?

If four associates were fired for underperformance, the total value of the parting gift would have decreased by $200
The value of the parting gift is greater than $1,225 and less than $1,275

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: D

Simplify the question by translating it into algebra.
Let P = the total value of John's parting gift
Let E = the amount each associate contributed
Let N = the number of associates
P = NE = 25E
With this algebraic equation, if you find the value of either P or E, you will know the total value of the parting gift.
Evaluate Statement (1) alone.
1. Two common ways to evaluate Statement (1) alone:
Statement 1: Method 1
1. Since the question stated that each person contributed equally, if losing four associates decreased the total value of the parting gift by $200, then the value of each associate's contribution was $50 (=$200/4).
2. Consequently, P = 25E = 25(50) = $1,250.
Statement 1: Method 2
1. If four associates leave, there are N - 4 = 25 - 4 = 21 associates.
2. If the value of the parting gift decreases by $200, its new value will be P - 200.
3. Taken together, Statement (1) can be translated:
  P - 200 = 21E
  P = 21E + 200
4. You now have two unique equations and two variables, which means that Statement (1) is SUFFICIENT.
5. Although you should not spend time finding the solution on the test, here is the solution.
  Equation 1: P = 21E + 200
  Equation 2: P = 25E
  P = P
  25E = 21E + 200
  4E = 200
  E = $50
6. P = NE = 25E = 25($50) = $1250
Evaluate Statement (2) alone.
1. Statement (2) says that $1,225 < P < $1,275. It is crucial to remember that the question stated that "25 associates contribute equally to a parting gift for John in an amount that is an integer." In other words P / 25 must be an integer. Stated differently, P must be a multiple of 25.
2. There is only one multiple of 25 between 1,225 and 1,275. That number is $1,250. Since there is only one possible value for P, Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.

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