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
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.
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Evaluate Statement (1) alone.
- Two common ways to evaluate Statement (1) alone:
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Statement 1: Method 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).
- Consequently, P = 25E = 25(50) = $1,250.
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Statement 1: Method 2
- If four associates leave, there are N - 4 = 25 - 4 = 21 associates.
- If the value of the parting gift decreases by $200, its new value will be P - 200.
- Taken together, Statement (1) can be translated:
P - 200 = 21E
P = 21E + 200
- You now have two unique equations and two variables, which means that Statement (1) is SUFFICIENT.
- 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
- P = NE = 25E = 25($50) = $1250
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Evaluate Statement (2) alone.
- 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.
- 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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