If 2 < x < 5 and 3 < y < 10, which of the following expresses the poss

The question stem does not specify x or y as integers, therefore they could be 2.01, 3.01, 9.99, etc. for example.

1) Plug in the highest and lowest possible values.
2) To keep it simple, have x as 2 and y as 10
x-y = 2 - 10 = -8
-8 is the lowest possible number

Now have x = 5 and y = 3
x-y = 5 - 3 = 2
2 is the highest possible number.

3) The possible range is -8 < x - y < 2

D

imo,
lowest and highest value of X = 2 and 4
lowest and highest value of Y = 4 and 9
so the range should be -7 < X-Y < 0

@bunnuel Please help
thank you!

4 values are possible in this kinda question.

5- 10 = -5

2 - 10 = -8

5 - 3 = 2

3 -2=1.

Max = 2
min = -8

-8<x<2

all the values fall into this range.

To determine the smallest difference of x and y, we want x to be as small as possible and y to be as large as possible. Thus, the smallest difference of x and y is 2 - 10 = -8.

To determine the largest difference of x and y, we want x to be as large as possible and y to be as small as possible. Thus, the largest difference of x and y is 5 - 3 = 2.

Thus, -8 < x - y < 2.

Answer: D

Make sure the signs of both the equations are the same. In this case, both of the equation has the same sign. ie, < symbol

Now, place the equations in the following format

since we need (X-Y), we will keep the X equation above and Y equation below.

2<X<5
3<Y<10

Now, perform the operation to get maximum and minimum values. There will be 4 answers and from that, we will select the max value and min value

Performing the action (X-Y)
2-3 = -1
2-10 = -8 (Min)
5-3 = 2 (Max)
5-10 = -5

So, the possible range will be -8<X-Y<2

Answer D

(1st) all of the X and Y values must be (+)Positive Values


(2nd) MIN Value of (X - Y)

in order to Minimize (X - Y): we want to take the Lowest Possible +Pos. Value that X can Take and Subtract the HIGHEST Possible +Pos. Value that Y can take

X ----> Lower Bound is 2
Y ----> Upper Bound is 10

therefore, (X - Y) > (2 - 10) > -8


(3rd) MAX Value of (X - Y)

we want to take the HIGHEST Possible +Pos. Value that X can Take and Subtract the SMALLEST Possible +Pos. Value that Y can take

X ----> Upper Bound is 5
Y -----> Lower Bound is 3

(X - Y) < (5 - 3) < +2


-8 < (X - Y) < +2

-D-


Other Method, when the question ONLY Involves MAX/MIN the Addition or Subtraction of Variables -----> you can ADD or SUBTRACT the Inequalities and get the Same Answer

2 < X < 5

- (10 > Y > 3)
___________________

2 - 10 < (X - Y) < 5 -3

-8 < (X - Y) < 2

-D-

2 < x < 5
3 < y < 10

x – y:


Case I: 2 - 3 < x - y < 5 - 10

=> -1 < x - y < -5 Not Possible

Case II: 2 - 10 < x - y < 5 - 3

=> -8 < x - y < 2 Possible

Answer D

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