BTGmoderatorDC wrote: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

OA B

Source: GMAT Prep

Given that -4 < x < 7 and -6 < y < 3, we see that x and y can be negative, positive or even 0. To find out all the possible values of xy, we must consider the smallest negative number for the lower range and the greatest positive number for the upper range.

Since -4 for -4 < x < 7 and -6 for -6 < y < 3 would render xy = 24, greatest possible positive value, the upper range for xy would be 24; note that 7*3 = 21 is less than 24.

Let's come to the lower range of xy. The lowest possible negative value would be 7*-6 = -42. Thus, the range that specifies all the possible range of xy would be -42 < xy < 24.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote: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

OA B

Source: GMAT Prep

To determine the largest possible value of xy, we either multiply together the two smallest negative values or the two largest positive values. Since (-4)(-6) = 24 and (7)(3) = 21, and 24 > 21, we see that the largest possible product of x and y is less than 24.

To determine the smallest value of xy, we multiply the largest positive number by the smallest negative number. Thus, the product of x and y must be greater than (7)(-6) = -42. Thus:

-42 < xy < 24

Answer: B