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# If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)

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Joined: 02 Sep 2009
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If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)  [#permalink]

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15 Jul 2019, 23:51
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89% (01:36) correct 11% (02:41) wrong based on 53 sessions

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If $$2x \neq y$$ and $$5x \neq 4y$$, what is the value of $$\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}$$ ?

A. $$\frac{1}{2}$$

B. $$\frac{3}{2}$$

C. $$\frac{5}{2}$$

D. $$\frac{7}{2}$$

E. $$\frac{9}{2}$$

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Re: If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)  [#permalink]

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16 Jul 2019, 08:19
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Let us assume x = 1 and y = 1

Numerator = $$\frac{5-4}{2-1}$$ = $$\frac{1}{1}$$ = 1
Denominator = 3/1-2 + 5 = -3+5 = 2

Therefore. $$\frac{numerator}{denominator}$$ = $$\frac{1}{2}$$ (the answer is A)
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Re: If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)  [#permalink]

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16 Jul 2019, 00:06
Bunuel wrote:
If $$2x \neq y$$ and $$5x \neq 4y$$, what is the value of $$\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}$$ ?

A. $$\frac{1}{2}$$

B. $$\frac{3}{2}$$

C. $$\frac{5}{2}$$

D. $$\frac{7}{2}$$

E. $$\frac{9}{2}$$

$$\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}$$
=$$\frac{\frac{5x-4y}{2x-y}}{\frac{8y-10x}{y-2x}}$$
=$$\frac{\frac{5x-4y}{2x-y}}{\frac{10x-8y}{2x-y}}$$
=$$\frac{5x-4y}{10x-8y}$$
=$$\frac{1}{2}$$

IMO A
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Re: If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)  [#permalink]

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16 Jul 2019, 00:08
Bunuel wrote:
If $$2x \neq y$$ and $$5x \neq 4y$$, what is the value of $$\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}$$ ?

A. $$\frac{1}{2}$$

B. $$\frac{3}{2}$$

C. $$\frac{5}{2}$$

D. $$\frac{7}{2}$$

E. $$\frac{9}{2}$$

$$\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}$$
$$=\frac{\frac{5x-4y}{2x-y}}{\frac{8y-10x}{y-2x}}$$
$$=\frac{\frac{5x-4y}{2x-y}}{\frac{10x-8y}{2x-y}}$$
$$=\frac{5x-4y}{10x-8y}$$
$$=\frac{1}{2}$$

IMO A
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Re: If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)  [#permalink]

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16 Jul 2019, 00:35
This is A when we reduce the equation we get y - 2x which has to be replaced with -(2x-y) and the denominator similarly is replaced with -2 (5x- 4y) this brings us to 1/2 A
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Re: If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)  [#permalink]

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16 Jul 2019, 11:36
bebs wrote:
Let us assume x = 1 and y = 1

Numerator = $$\frac{5-4}{2-1}$$ = $$\frac{1}{1}$$ = 1
Denominator = 3/1-2 + 5 = -3+5 = 2

Therefore. $$\frac{numerator}{denominator}$$ = $$\frac{1}{2}$$ (the answer is A)

I followed the same approach
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Re: If 2x ≠ y and 5x ≠ 4y, what is the value of (5x - 4y)/(2x - y)/(3y/y-)   [#permalink] 16 Jul 2019, 11:36
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