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# If in set S above, x is an integer x is an integer greater than one

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Director
Joined: 11 Feb 2015
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If in set S above, x is an integer x is an integer greater than one  [#permalink]

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15 Oct 2018, 08:51
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Difficulty:

35% (medium)

Question Stats:

66% (01:22) correct 34% (02:22) wrong based on 30 sessions

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Set S = {$$x$$, $$\frac{x}{4}$$ , $$y^2$$, $$5y$$, $$x^2$$, $$y$$}

If in set S above, $$x$$ is an integer greater than one and $$0 < y ≤ 0.7$$, which of the following represents the range of the set S?

A) $$(x + y)(x − y)$$

B) $$x^2 ​– 3y$$

C) $$y^2$$

D) $$x – y$$

E) $$x^2 − y$$

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Re: If in set S above, x is an integer x is an integer greater than one  [#permalink]

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15 Oct 2018, 09:43
According to the constraints of the variables, $$x^2$$ will be the greatest value and $$y^2$$ - the lowest
So the range we have got $$x^2-y^2$$

IMO
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Re: If in set S above, x is an integer x is an integer greater than one  [#permalink]

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15 Oct 2018, 10:01
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Top Contributor
CAMANISHPARMAR wrote:
Set S = {$$x$$, $$\frac{x}{4}$$ , $$y^2$$, $$5y$$, $$x^2$$, $$y$$}

If in set S above, $$x$$ is an integer greater than one and $$0 < y ≤ 0.7$$, which of the following represents the range of the set S?

A) $$(x + y)(x − y)$$

B) $$x^2 ​– 3y$$

C) $$y^2$$

D) $$x – y$$

E) $$x^2 − y$$

Nice question!

In order to determine the range, we must determine the greatest and smallest values in the set.

Let's start with the expressions with x in them: x, x/4 and x²
Since x > 1, we know that x/4 < x < x²

Now the expressions with y in them: y, 5y and y²
Since 0 < y ≤ 0.7 y² < y < 5y

From these two inequalities, we must determine the greatest and smallest values
We'll do so by finding some EXTREME values.

First, since x is an INTEGER greater than 1, the smallest possible value of x is 2
So, the smallest possible value of x/4 = 2/4 = 1/2

Next, since y ≤ 0.7, the greatest possible value of y is 0.7
So, the greatest possible value of y² = (0.7)² = 0.49

Notice that the greatest possible value of y² is still less than the smallest possible value of x/4
Since y² < y < 5y, we can conclude that y² is the SMALLEST value in the set.
----------------------------------------

Since x is an INTEGER greater than 1, the smallest possible value of x is 2
So, the smallest possible value of x² = 2²= 4
Next, since y ≤ 0.7, the greatest possible value of 5y is 3.5

Notice that the smallest possible value of x² is still greater than the greatest possible value of 5y
Since x/4 < x < x², we can conclude that x² is the GREATEST value in the set.
----------------------------------------

Range = GREATEST value - SMALLEST value
= x² - y²
= (x + y)(x - y)

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Re: If in set S above, x is an integer x is an integer greater than one   [#permalink] 15 Oct 2018, 10:01
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