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# If two integers x and y such x>y are selected at random between -8 and

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If two integers x and y such x>y are selected at random between -8 and  [#permalink]

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16 May 2017, 00:33
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:49) correct 25% (02:18) wrong based on 86 sessions

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If two integers x and y such x>y are selected at random between -8 and 11, inclusive, how many cases are possible?

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

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Re: If two integers x and y such x>y are selected at random between -8 and  [#permalink]

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16 May 2017, 13:48
If X is -8, then the possible values for y are (-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11)

So there are 19 combinations possible, when x is -8

Similarly, if x is -7, then y can take 18 values.

So the total number of combinations = 19+18+17+16+15+..+3+2+1 = 19/2 * (19+1) = 19 * 10 = 190

Math Revolution GMAT Instructor
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Re: If two integers x and y such x>y are selected at random between -8 and  [#permalink]

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18 May 2017, 00:08
==> Since two integers from -8 to 11 are being randomly selected and x>y, you use combination. Thus, the number of integers from -8 to 11 becomes 11-(-8)+1=20, so 20, then 20C2=(20)(19)/2!=190.

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Re: If two integers x and y such x>y are selected at random between -8 and  [#permalink]

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22 May 2017, 02:24

see we need to select two integers between -8 to 11( inclusive) that are total 20 integers there where x>y , so we can choose like this 20ways(y) * 19 ways(X) =380ways but the order does not matter here means whether we choose x first or y first the order is same so divide with 2 such as 380/2= 190 ways to select .

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Re: If two integers x and y such x>y are selected at random between -8 and  [#permalink]

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04 Jul 2018, 12:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If two integers x and y such x>y are selected at random between -8 and &nbs [#permalink] 04 Jul 2018, 12:40
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