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How many pairs (x,y) are there for which y>x when x and y each can

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How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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New post 27 Nov 2018, 10:21
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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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Re: How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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New post 27 Nov 2018, 18:30
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barryseal wrote:
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


Its a nice question.My explanation is as follows:

Given range of x and y integers is -10 to 9.so total of 20 integers.
Now we start with Y value of 9.so the possible combinations(y,x) are:(9,8)(9,7)(9,6).....(9,-1)...(9,-10)- so total combinations-19
repeat with Y value of 8,so the possible combinations (y,x) are:(8,7)(8,6)....(8,-1)...(8,-10)-so total combinations-18
same with Y value of 7,so possible Combinations are:(7,6)(7,5),..total combinations-17
now we can observe a cycle of decreasing in numbers so next possible combinations will be 16,15,14,13,12,......1.
So total possible combinations are sum of numbers ranging from 1 to 19 inclusive i.e is 190.so answer is B.


please kudos if this helps.
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Re: How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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New post 27 Nov 2018, 20:28
Range for x,y = [-10,9] -----Total of 20# No's
Condt. y>x

If x= -10 , y= [ -9,-8, .............. ,9 ] = 19# No's {19 Pairs Possible }
lly, if x= -9 , y=[ -8, -7, .........., 9]= 18# No's {18 Pairs Possible }
..............
last, if x= 8, y= [9 ]= 1# No.

Total Possible pairs= Sum [ 19+18+.........+2+1 ]= 19*20/2= 190
Ans. B
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Re: How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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New post 30 Nov 2018, 10:50
barryseal wrote:
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


A simpler way how i figured this was : the pair (x, y) can have 20X20 possible combinations, hence total 400. Out of these, there would be 20 pairs that would have the same values for x and y [ (-10, -10) , (-9, -9), (-8, -8) ....]. Now divide the total number of combinations (400) by two, to have the half where y>x and remove half of the combinations that would have same values : 400/2 -10 = 190.
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Re: How many pairs (x,y) are there for which y>x when x and y each can &nbs [#permalink] 30 Nov 2018, 10:50
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How many pairs (x,y) are there for which y>x when x and y each can

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