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If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how

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If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how  [#permalink]

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New post 09 Feb 2016, 17:16
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If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?

A. 150
B. 180
C. 190
D. 210
E. 240


* A solution will be posted in two days.

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Re: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how  [#permalink]

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New post 09 Feb 2016, 17:57
MathRevolution wrote:
If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?

A. 150
B. 180
C. 190
D. 210
E. 240


* A solution will be posted in two days.


Since x>y
let us first choose y
then , we will choose x . because x is greater than y
Our choice of numbers are
-9 -8 -7 -6 ............................... 9 = total 9-(-10)+1 = 20 numbers

Now for every y that we choose ,x will always be to the right of y in the number line because x is greater

So we start from the left ,
If y = -9 , x can be chosen from 19 number in the right = > 19C1 = 19 ways
IF y= -8 , x can be chosen from 18 number in the right = > 18C1 = 18 ways
If y = -7 , x can be chosen from 17 number in the right = > 17C1 = 17 ways
.... ..... ......... ..... ......... ..... ......... ..... ......... ..... ......... ..... ......... ..... .....
.... ..... ......... ..... ......... ..... ......... ..... ......... ..... ......... ..... ......... ..... .....
If y = 8 , x can be chosen from 1 number in the right = >only 9 Left =1 way
___________________________________________________________
Total = 19+18+17+..........................................1 = n(n+1)/2=(19.20)/2 = 190

Hence the answer is (C)
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Re: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how  [#permalink]

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New post 11 Feb 2016, 21:52
If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?

A. 150
B. 180
C. 190
D. 210
E. 240


--> 20C2=20*19/2=190. Therefore, the answer is C.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

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Re: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how  [#permalink]

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New post 15 Oct 2018, 01:42
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Re: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how   [#permalink] 15 Oct 2018, 01:42
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