Let x and y be numbers such that −y 0 III. y > 0

Correct Answer is : I and III only

SAT Mathematics Practice Test 4

Question : 46 of 58

Marks: +1, -0

Let x and y be numbers such that

−y < x < y

Which of the following must be true?
I.

|x|< y

II.

x > 0

III.

y > 0

I only
I and II only
I and III only
I,II, and III

Validate

Solution:

−y < x < y

, the value of x is either between

−y

and

0

or between 0 and y, so statement I,

|x| < y

is true. It is possible that the value of x is greater than zero, but x could be negative. For example, a counterexample to statement II,

x > 0

, is

x=−2

and

y=3,

yielding

−3 < −2 < 3,

so the given condition is satisfied. Statement III must be true since

−y < x < y

implies that

−y < y,

so y must be greater than 0. Therefore, statements I and III are the only statements that must be true.
Choices A, B, and D are incorrect because each of these choices either omits a statement that must be true or includes a statement that could be false.

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