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GMAT/Data Sufficiency - Variable Inequalities
Variable Inequalities
Nina and Teri are playing a dice game. Each girl rolls a pair of 12-sided dice, numbered with the integers from -6 through 5, and receives a score that is equal to the negative of the sum of the two die. (E.g., If Nina rolls a 3 and a 1, her sum is 4, and her score is -4.) If the player who gets the highest score wins, who won the game?
(1) The value of the first die Nina rolls is greater than the sum of both Teri's rolls.
(2) The value of the second die Nina rolls is greater than the sum of both Teri's rolls.
(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) Statements (1) and (2) TOGETHER are NOT sufficient.
| ОТВЕТЫ И КОММЕНТАРИИ |
| Решение |
Begin by rephrasing, or simplifying, the original question. Since the rules of the game involve the negative of the sum of two dice, one way of restating this problem is that whoever gets the higher sum LOSES the game. Thinking about the sum of the two dice is easier than thinking about the negative of the sum of the two dice. Thus, let's rephrase the question as: Who lost the game? (Knowing this will obviously allow us to answer the original question, who won the game.)
Statement (1) gives us information about the first of Nina's dice, but it does not tell us anything about the second. Consider the following two possibilities:
| | Nina's First Roll | Nina's Second Roll | Teri's Sum | Higher Sum = Loser |
| CASE ONE | 3 | 5 | –1 | Nina |
| CASE TWO | 3 | –5 | –1 | Teri |
Notice that in both cases, Nina's first roll is greater than Teri's Sum. However, in Case One Nina loses, but in Case Two Teri loses. Thus, this information is not sufficient to answer the question.
Statement (2) gives us information about the second of Nina's dice, but it does not tell us anything about the first. Using the same logic as for the previous statement, this is not sufficient on its own to answer the question.
Combining the information contained in both statements, one may be tempted to conclude that Nina's sum must be higher than Teri's sum. However, one must test scenarios involving both positive and negative rolls. Consider the following two possibilities.
| | Nina's First Roll | Nina's Second Roll | Teri's Sum | Higher Sum = Loser |
| CASE ONE | 3 | 4 | –5 | Nina |
| CASE TWO | –3 | –4 | –5 | Teri |
Notice that in both cases, Nina's first roll is greater than Teri's Sum and Nina's second roll is greater than Teri's sum. However, in Case One Nina loses, but in Case Two Teri loses. Thus, this information is not sufficient to answer the question.
The correct answer is E: Statements (1) and (2) TOGETHER are NOT sufficient.
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Prima 57
If x, y, and z are positive integers such that x < y < z, is x a factor of the
odd integer z?
(1) x and y are prime numbers, whose sum is a factor of 57
(2) z is a factor of 57
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2)
alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1)
alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the
question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question.
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Вверх 
