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# In how many ways can two integers x and y (with x>y) be selected from

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4716
GPA: 3.82
In how many ways can two integers x and y (with x>y) be selected from [#permalink]

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03 Jan 2018, 00:43
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Difficulty:

35% (medium)

Question Stats:

67% (00:58) correct 33% (00:45) wrong based on 46 sessions

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[GMAT math practice question]

In how many ways can two integers $$x$$ and $$y$$ (with $$x>y$$) be selected from $$-10$$ to $$10$$ (inclusive)?

A. $$150$$
B. $$180$$
C. $$190$$
D. $$210$$
E. $$240$$
[Reveal] Spoiler: OA

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 838
Location: India
GPA: 3.82
In how many ways can two integers x and y (with x>y) be selected from [#permalink]

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03 Jan 2018, 01:55
MathRevolution wrote:
[GMAT math practice question]

In how many ways can two integers $$x$$ and $$y$$ (with $$x>y$$) be selected from $$-10$$ to $$10$$ (inclusive)?

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

from $$-10$$ to $$10$$ there are $$21$$ numbers.

if $$x$$ & $$y$$ are represented on a number line from $$-10$$ to $$10$$, then here order matters as $$y$$ has to be lower than $$x$$

So total number of selection = (total number of ways of arranging $$x$$ & $$y$$)$$/2$$ (because in half the cases $$y$$ will be higher than $$x$$ and we need to exclude those cases)

$$=> \frac{21_P_2}{2} = 210$$

Option D
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4716
GPA: 3.82
Re: In how many ways can two integers x and y (with x>y) be selected from [#permalink]

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04 Jan 2018, 23:57
=>

This is the number of ways of selecting two different numbers from a set of 21 numbers. The order of choosing the numbers does not matter: we simply assign the larger number to x once the choice has been made. So, the number of ways of choosing the two numbers is
21C2 = $$\frac{21*20}{(1*2)}$$ = $$21 * 10$$ = $$210$$

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Intern
Joined: 30 Jan 2017
Posts: 3
Re: In how many ways can two integers x and y (with x>y) be selected from [#permalink]

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05 Jan 2018, 00:13
total cases: 21c1 * 21c1 ---> 441

number of cases with x=y: 21

cases with x not equal to y: 441-21 ----> 420
As x and y have the same domain, the cases with x>y and x<y will be equal in number.
So cases with x>y are: 420/2 ---> 210

Re: In how many ways can two integers x and y (with x>y) be selected from   [#permalink] 05 Jan 2018, 00:13
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