How many pairs (x,y) exist for which yx when x and y each can take th

Question

How many pairs (x,y) exist for which y>x when x and y each can take the integer values from -10 to 9 inclusive?

(A) 180
(B) 190
(C) 200
(D) 210
(E) 220

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Bunuel · Accepted Answer

How many pairs (x,y) exist for which y>x when x and y each can take the integer values from -10 to 9 inclusive?

(A) 180 
 (B) 190 
 (C) 200 
 (D) 210 
 (E) 220

There are 20 integers from -10 to 9. If we pick two different integers from that set, one will always be greater than the other. We can then assign the greater one to y and the smaller one to x, giving us the desired pair where y > x.

Since we are simply choosing 2 different integers from 20, the total number of pairs is 20C2 = 190.

Answer: B.

JerryAtDreamScore · Answer

Breaking Down the Info:

When y = -10, there are 0 x values.

When y = -9, there is 1 x value.

.....

When y = 10, there are 19 x values.

So we are adding 1, 2, 3, ..., 18, 19. That is  \frac{1 + 19}{2}*19 = 190

Answer: B

CEO2021 · Answer

i think the above highlighted should be
 "When y = 9, there are 19 x values"

stne · Answer

CEO2021 ,

You are correct, minor typo by Jerry

Lets expand it.

9,8,7,6,5,4,3,2,1,0,-1,-2, -3,-4,-5,-6,-7,-8,-9,-10

So when  y=9  there are indeed  19  values of  x   from  x=8  to  x= -10   inclusive

8-(-10)+1 =19

AJSIPA · Answer

Bunuel  can you provide the solution for this one?

How many pairs (x,y) exist for which y>x when x and y each can take th

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