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# If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma  [#permalink]

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25 Jul 2016, 04:55
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:36) correct 40% (01:47) wrong based on 118 sessions

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If two integers x,y (x>y) are selected from -5 to 4(inclusive), how many cases are there?
A. 15
B. 18
C. 36
D. 45
E. 90

*An answer will be posted in 2 days.

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Re: If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma  [#permalink]

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25 Jul 2016, 06:09
Top Contributor
MathRevolution wrote:
If two integers x,y (x>y) are selected from -5 to 4(inclusive), how many cases are there?
A. 15
B. 18
C. 36
D. 45
E. 90

There are 10 integers from -5 to 4 inclusive.
Choose ANY 2 integers and make x = the larger integer and make y = the smaller integer.
Since the order in which we select the two numbers does not matter, we can use COMBINATIONS.
We can select 2 integers from 10 integers in 10C2 ways
10C2 = 45

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Joined: 22 Jun 2016
Posts: 245
Re: If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma  [#permalink]

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25 Jul 2016, 06:17
two integers x,y (x>y) are selected from -5 to 4(inclusive)

So two integers can be -5,-4,-3,-2,-1,0,1,2,3 or 4.

If x = -5, y cannot be any integer in the given range as x>y.
If x = -4, y can have only 1 value -5.
If x = -3, y can have 2 values -5 and -4.

and so on till

x = 4, where y can have 9 values -5 to 3.

sum of consecutive integers = n*(n+1)/2

sum of 1 to 9 = 9*10/2 = 45

Hence, D will be the answer!
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Math Revolution GMAT Instructor
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Re: If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma  [#permalink]

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26 Jul 2016, 17:24
10C2=45. Hence, the correct answer is D.
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Re: If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma  [#permalink]

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27 Oct 2016, 11:13
Use combinatorics to solve:

We have 10 numbers because 5--4+1 = 10
& we are trying to make two combinations, hence why we have 2! in the denominator.

10!/[2!8!] = 45
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Re: If two integers x,y (x>y) are selected from -5 to 4(inclusive), how ma  [#permalink]

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11 Jul 2018, 22:52
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,y (x>y) are selected from -5 to 4(inclusive), how ma &nbs [#permalink] 11 Jul 2018, 22:52
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