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

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New post 03 Jan 2018, 01:43
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  35% (medium)

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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. \(240\)

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

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New post 03 Jan 2018, 02:55
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
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Math Revolution GMAT Instructor
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Re: In how many ways can two integers x and y (with x>y) be selected from [#permalink]

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New post 05 Jan 2018, 00:57
=>

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 = \(\frac{21*20}{(1*2)}\) = \(21 * 10\) = \(210\)

Therefore, the answer is D.

Answer: D
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Re: In how many ways can two integers x and y (with x>y) be selected from [#permalink]

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New post 05 Jan 2018, 01:13
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

Hence answer: D
Re: In how many ways can two integers x and y (with x>y) be selected from   [#permalink] 05 Jan 2018, 01:13
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