Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
In the figure above, which quadrants contain pairs (x comma y) that satisfy the condition x over y = 1?
(A) roman numeral 1 only
(B) roman numeral 1 and roman numeral 2 only
(C) roman numeral 1 and roman numeral 3 only
(D) roman numeral 2 and roman numeral 4 only
(E) roman numeral 1, roman numeral 2, roman numeral 3, and roman numeral 4
The correct answer is C
Explanation
In order for (x comma y) to satisfy x over y = 1, it must be true that x and y are equal to each other and not equal to zero. An example of such a pair is (3 comma 3), which is in quadrant roman numeral 1.
In quadrant roman numeral 2, all the x values are negative and all the yvalues are positive, so in quadrant roman numeral 2, x and y cannot be equal. For example, the pair (minus 3 comma 3) does not satisfy the condition, since (negative 3 over 3) = negative 1, not 1.
In quadrant roman numeral 3, the x values and the y values are both negative, so it is possible for x and y to be equal. For example, the pair (minus 3 comma minus 3) is in quadrant roman numeral 3 and minus 3 over minus 3 = 1.
In quadrant roman numeral 4, x and y cannot be equal because the x values are positive and the y values are negative. For example, the pair (3 comma minus 3) does not satisfy the condition, since 3 over minus 3 = minus 1.
The quadrants that contain pairs (x comma y) that satisfy the given condition are quadrants roman numeral 1 and roman numeral 3 only.