If 5

Question

If 5 < x < 9 and -4 < y < 15, which of the following gives all possible values of xy?

(A) -36 < xy < 20

(B) -36 < xy < 75

(C) -36 < xy < 135

(D) 20 < xy < 75

(E) -20 < xy < 135

niks18 · Answer

We need to know the two extremes of xy if x=9 & y=-4 , then xy=-36 . But we know that x<9 and y>-4 , hence the lowest value of xy will be greater than -36 So we have xy>-36 Now x<9 & y<15 , multiply both to get xy<135 . Hence -36

Bunuel · Answer

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hero_with_1000_faces · Answer

The value of X is less than less than 9 and not less than  equal to   9.
So I think, if we take extremes of XY it should be 8*-3 = -24

Can someone explain, I do not get the Idea that 9*-4 has to be calculated and then their lower values need to be considered.

Is it because, all values include fractions/decimals too ?

niks18 · Answer

hi  hero_with_1000_faces

Pls note that x & y are not integers. hence x can be 8.99999999999 (a value extremely close to 9) and y can be -3.99999999999(a value extremely close to -4)

hence the lowest value will be extremely close to -36 but not equal to -36

hero_with_1000_faces · Answer

Thanks for confirmation niks18

JeffTargetTestPrep · Answer

The minimum product of x and y is greater than 9 x -4 = -36

The maximum product of x and y is less than 9 x 15 = 135
Thus,

-36 < xy < 135

Answer: C/3

luisdicampo · Answer

Deconstructing the Question

We are given open intervals:
 5<x<9,\quad -4<y<15

So the endpoints are not included.

Step-by-step

The extreme products are:

9\cdot(-4)=-36  
 9\cdot 15=135

But  x=9 ,  y=-4 , and  y=15  are not allowed.

So these values are never actually reached.

Thus:

-36<xy<135

Answer: C

If 5 < x < 9 and -4 < y < 15, which of the following gives

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