beatgmatny1 wrote:Can someone please explain the appropriate method to solve the following question?
if -4<x<7 and -6<y<3, which of the following specifies all the possible values of xy?
a. -42<xy<21
b. -42<xy<24
c. -28<xy<18
d. -24<xy<21
e. -24<xy<24
Ans: B
To combine ranges with respect to a given operation, perform the given operation using EVERY COMBINATION OF ENDPOINTS.
Here, the given operation is MULTIPLICATION.
Calculating the value of xy using every combination of endpoints, we get:
(-4)(-6) = 24.
(-4)(3) = -12.
(7)(-6) = -42.
(7)(3) = 21.
The SMALLEST result gives us the LOWER limit of xy: -42.
The GREATEST result gives us the UPPER limit of xy: 24.
Thus:
-42 < xy < 24.
The correct answer is
B.
Another example:
If -4<x<7 and -6<y<3, which of the following specifies all the possible values of x-y?
Here, the given operation is SUBTRACTION.
Calculating the value of x-y using every combination of endpoints, we get:
-4 - (-6) = 2.
-4 - 3 = -7.
7 - (-6) = 13.
7 - 3 = 4.
Thus:
-7 < x-y < 13.
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