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# If y > 2 and = y, for which of the following expressions can a single

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If y > 2 and = y, for which of the following expressions can a single [#permalink]

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10 Jun 2016, 03:36
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If y > 2 and $$\frac{x}{6}$$= y, for which of the following expressions can a single numerical value be determined?

I.$$\frac{x-2}{y-2}$$

II.$$\frac{x^2}{y}$$

III.$$\frac{91x}{y}$$

(A) I only

(B) II only

(C) III only

(D) I and III only

(E)I, II, and III
[Reveal] Spoiler: OA

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Md. Abdur Rakib

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Re: If y > 2 and = y, for which of the following expressions can a single [#permalink]

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11 Jun 2016, 05:04
i got it wrong , as i considered single numercal value as 1 digit value , to which i assume y=3 x18
but latter by looking at the answer , i guess it is asking for sure short value, whch will not deponds on y
PLease correct me if i m wrong

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Re: If y > 2 and = y, for which of the following expressions can a single [#permalink]

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10 Sep 2017, 00:52
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If y > 2 and = y, for which of the following expressions can a single [#permalink]

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11 Sep 2017, 18:06
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AbdurRakib wrote:
If y > 2 and $$\frac{x}{6}$$= y, for which of the following expressions can a single numerical value be determined?

I.$$\frac{x-2}{y-2}$$

II.$$\frac{x^2}{y}$$

III.$$\frac{91x}{y}$$

(A) I only

(B) II only

(C) III only

(D) I and III only

(E)I, II, and III

I am out on a limb here.

I picked ANSWER C. You can factor out the variable(s) and get a "single numeric value" for the expression in III. That is not true of the other two.

I could be completely off the mark. The phrase "single numeric value" is usually associated with random variables, probability functions, and outcomes (though usually random variables are capitalized).

If that is the case, someone please post as much asap and stop reading.

Here is how I solved:

If $$\frac{x}{6}$$= y, then $$x = 6y$$.

Substitute 6y for x in each expression. The only one that yields a single numeric value is III.

I.$$\frac{x-2}{y-2}$$

$$\frac{6y-2}{y-2}$$: The variable cannot be factored out. The numerator can be factored to 2(3y -1), which does not allow a variable to be factored out. If y is 3, the answer is 16. If y is 7, the answer is 8. Number of answers is infinite as long as y > 3

II.$$\frac{x^2}{y}$$

$$\frac{(6y)^2}{y}$$ =

$$\frac{(36)y^2}{y}$$= $$36y$$

Possible answers are infinite, as long as y > 3

III.$$\frac{91x}{y}$$

$$\frac{(91)(6y)}{y}$$ =

$$91 * 6 =$$ 546

I factored out the y. Having defined x in terms of y, I effectively factored x out as well.

AbdurRakib , or anyone: Is this reasoning correct?

I cannot quite articulate the distinguishing factor in III.

Maybe this: I can get a single numeric value in III, because . . .III emulates the original expression: x is a multiple of y, and that relationship is unaltered by arithmetic (as in the other two expressions), such that the 6:1 ratio is preserved?
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If y > 2 and = y, for which of the following expressions can a single   [#permalink] 11 Sep 2017, 18:06
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