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1) C

Recall that the sum of the 3 accounts is $3 million. If the largest is $1.3 million, then the sum of the other two accounts must be $1.7 million. Since the second-largest account could be $1.29 million, then the smallest account could be $0.41 million, which is less than $0.5 million. Hence, Statement 1 by itself is insufficient.

However, if we know the value of 2 of the variables (as we do if we read statements 1 and 2 together), and the average value of all three variables (as we do from reading the question), then we can determine the value of the third variable. If the largest account is worth $1.3 million and the smallest is worth $0.7 million, then the third variable must be $1.0 million. With the value of all 3 variables, we can quickly determine the value of the smallest variable. Statements 1 and 2 together give us the information needed to answer the question.

2) C

Statement 1 by itself is not sufficient. One of the two variables could be a small fraction. (Think of 500 and 0.01.) Statement 2 by itself could yield the product of 3 and 4. However, the information from both statements is taken together, we can definitively state that the answer to this question is “true.”

3) A

Statement 1 is sufficient to determine that x equals 5. Statement 2 only tells us that x could be +5 or -5.

4) E

The statements, together as well as alone, do not give enough information to answer the question. To determine the percent change, we would need one of the additional pieces of information:

  1. The beginning stock price for the month.
  2. The ending stock price for the month.
  3. The percent change in the stock for the second half of the month.

5) E

The question can not be answered with the statements provided. The question asks which company’s earnings increased by more dollars, not which company’s earnings increased by a greater percentage. The different percentage rates of increase tell us nothing about either company’s actual (dollar) increase in sales unless we know each firm’s starting baseline.

6) E

The question can not be answered with the statements provided. Because x can be an even number and still be prime (2 is a prime number), statement 1 is insufficient. Additionally, x might be divisible by even numbers, so statement 2 is also insufficient.

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