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rss GMAT Practice Question (One of Hundreds)
Determine which of the ordered pairs listed below satisfies both of the following inequalities:
Y1 < 7
Y2 > 3x-1
Correct Answer: C
Any point with y greater than 7 can be eliminated immediately.
  1. Construct a truth table, testing the ordered pairs against the individual inequalities. Any pair that is true for both inequalities satisfies both, and is a solution to the given problem. One such table appears below.
  2. In order to determine the truth value of an ordered pair in the context of an inequality, we substitute the X quantity of the pair in question into the inequality, then compute the output Y value and compare it to the inequality itself. In the case where no such operation is possible, such as with inequality Y1, we simply compare the Y component of the pair being considered with the inequality. These steps will be specifically detailed immediately following the table.
      Y1 Y2
    A(2,9) F T
    B(3,8) F F
    C(1,3) T T
    D(2,4)
    E(2,3) T F
  3. The ordered pair (2,9) fails to satisfy the first inequality, Y1 < 7, because its Y coordinate, 9, is greater than 7. However, (2,9) does satisfy the second inequality because the substitution of X = 2 into Y2 > 3X-1 yields Y2 > 5, which is true as 9 is greater than 5.
  4. The ordered pair (3,8) has a Y coordinate greater than 7, thus failing to satisfy Y1 < 7. When the X value of 3 is substituted into Y2, the result is 8, which means that we have also failed to satisfy Y2 (remember that Y2 specifies a value greater than 3x-1, whereas 8 is equal to 3x-1 when X = 3).
  5. The ordered pair (1,3) satisfies the first inequality, Y1 < 7, as 3 is less than 7. It also satisfies the second inequality, Y2 > 3X -1, as substitution of the X value 1 gives the output value 2, and 3 is larger than 2. Since both values are true, both inequalities are satisfied. However, in the spirit of complete work, we will consider the next pair.
  6. The ordered pair (2,4) has a Y coordinate less than 7, and so satisfies Y1 < 7. However, substitution of X = 2 into Y2 > 3x-1 yields 5, and since the pair's Y coordinate is less than 5, we fail this test.
  7. The ordered pair (2,3) has a Y coordinate less than 7, and so satisfies Y1 < 7. However, substitution of X = 2 into Y2 > 3x-1 yields 5, and since the pair's Y coordinate is less than 5, we fail this test.