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

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goodyear2013
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If x =< 4 and y > = 10, what is the range of the numbers in [#permalink] New post   Updated on: 06 Jul 2014, 11:39
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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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From Kaplan Premier P800 Q4
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B

Originally posted by goodyear2013 on 06 Jul 2014, 11:10.
Last edited by Bunuel on 06 Jul 2014, 11:39, edited 1 time in total.
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Re: If x =< 4 and y > = 10, what is the range of the numbers in [#permalink] New post   06 Jul 2014, 11:47
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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.

Answer: B.
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If x =< 4 and y > = 10, what is the range of the numbers in [#permalink] New post   14 Aug 2021, 00:55
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We want to know the range of the set:

This will be the difference between the Max Value - Minimum Value

We are told that given the set of 4 values, X is the MIN and Y is the MAX

What is the value of: Y - X = ?

S1: since we are not told whether X or Y must be an Integer, the solution set of values {X , Y} that satisfy the equation is infinite.

The 2 variables can take an infinite number of values that will satisfy the equation together, as there are an infinite number of values on the number line between any two points.

S1 not sufficient to find a unique answer


S2:

-7x + 7y = 56

Divide by 7 on each side of the equation

-x + y = 8

Y - X = 8 = Range of Set

B S2 sufficient alone

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Re: If x =< 4 and y > = 10, what is the range of the numbers in [#permalink] New post   14 Aug 2021, 17:45
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goodyear2013 wrote:
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

Show Spoiler
From Kaplan Premier P800 Q4


We will need to find x and y since those are the min and max for the set. The range in terms of x and y is \(y - x\).

Statement 1:

Does not give y - x, insufficient.

Statement 2:

\(y - x = 8\) so the range is 8. Sufficient.

Ans: B
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Re: If x =< 4 and y > = 10, what is the range of the numbers in [#permalink]
14 Aug 2021, 17:45
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Bunuel
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