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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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Intern
Joined: 02 Feb 2018
Posts: 36
How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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27 Nov 2018, 11:21
1
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:59) correct 43% (01:49) wrong based on 46 sessions

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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
Intern
Joined: 19 Jun 2017
Posts: 10
Re: How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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27 Nov 2018, 19:30
1
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.

Intern
Joined: 08 Jan 2018
Posts: 17
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
Re: How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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27 Nov 2018, 21:28
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
Intern
Joined: 10 Nov 2018
Posts: 33
Location: France
GMAT 1: 600 Q48 V25
GMAT 2: 680 Q49 V34
GRE 1: Q163 V161
GPA: 3.6
Re: How many pairs (x,y) are there for which y>x when x and y each can  [#permalink]

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30 Nov 2018, 11:50
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.
Re: How many pairs (x,y) are there for which y>x when x and y each can   [#permalink] 30 Nov 2018, 11:50
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