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# If x =< 4 and y > = 10, what is the range of the numbers in

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Joined: 21 Oct 2013
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If x =< 4 and y > = 10, what is the range of the numbers in [#permalink]

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06 Jul 2014, 10:10
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If $$x\leq{4}$$ and $$y\geq{10}$$, what is the range of the numbers in the set {5, 8, x, y}?

(1) 3x + 5y = 72

(2) -7x + 7y = 56

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Last edited by Bunuel on 06 Jul 2014, 10:39, edited 1 time in total.
Edited the question.

Kudos [?]: 1857 [2], given: 289

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Kudos [?]: 135384 [2], given: 12691

Re: If x =< 4 and y > = 10, what is the range of the numbers in [#permalink]

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06 Jul 2014, 10:47
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If $$x\leq{4}$$ and $$y\geq{10}$$, what is the range of the numbers in the set {5, 8, x, y}?

The range is the difference between the largest and smallest elements of a set. Since we know that $$x\leq{4}$$ and $$y\geq{10}$$, then the range of {x, 5, 8, y} is y - x.

(1) 3x + 5y = 72. If x = 0 < 4 and y = 72/5 > 10, then the range is 72/5 - 0 but if x = 1 < 4 and y = 69/5 > 10, then the range is 69/5 - 1. Not sufficient.

(2) -7x + 7y = 56 --> reduce by 7 and re-arrange: y - x = 8. Sufficient.

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Kudos [?]: 135384 [2], given: 12691

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Re: If x =< 4 and y > = 10, what is the range of the numbers in [#permalink]

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12 Oct 2017, 09:17
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Kudos [?]: 287 [0], given: 0

Re: If x =< 4 and y > = 10, what is the range of the numbers in   [#permalink] 12 Oct 2017, 09:17
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# If x =< 4 and y > = 10, what is the range of the numbers in

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