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What is the arithmetic mean of 3x and 4y? (1) y/3 - x/4 = 4/3

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What is the arithmetic mean of 3x and 4y? (1) y/3 - x/4 = 4/3  [#permalink]

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New post 12 Mar 2018, 04:26
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A
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Difficulty:

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Question Stats:

64% (01:25) correct 36% (01:22) wrong based on 119 sessions

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What is the arithmetic mean of 3x and 4y?

(1) y/6 - x/8 = 2/3

(2) y/6 + x/8 = 5/3
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Re: What is the arithmetic mean of 3x and 4y? (1) y/3 - x/4 = 4/3  [#permalink]

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New post 12 Mar 2018, 06:30
amanvermagmat wrote:
What is the arithmetic mean of 3x and 4y?

(1) y/6 - x/8 = 2/3

(2) y/6 + x/8 = 5/3


Question : (3x+4y)/2 = ?

Statement 1: y/6 - x/8 = 2/3
Since there is -ve sign in the given equation therefore 3x+4y can't be calculated using this statement Hence
NOT SUFFICIENT

Statement 2: y/6 + x/8 = 5/3

i.e. (4y+3x)/24 = 5/3

i.e. (3x+4y) can be calculated hence

SUFFICIENT

Answer: option B
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What is the arithmetic mean of 3x and 4y? (1) y/3 - x/4 = 4/3  [#permalink]

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New post 19 Mar 2018, 12:15

SOLUTION



We are given:
    • Two numbers, \(3x\) and \(4y\).

We need to find:
    • Arithmetic mean of \(3x\) and \(4y\).
      o Thus, we need to find the value of \(\frac{(3x + 4y)}{2}\).

Let us analyze both the statements one by one.

Statement-1: \(\frac{y}{6}\)-\(\frac{x}{8}\)=\(\frac{2}{3}\)

Simplifying the above equation, we can write:
    • \(\frac{(8y-6x)}{48}\)=\(\frac{2}{3}\)
    • \(\frac{(4y-3x)}{16}\)=\(1\)
    • \(4y-3x\)=\(16\)

Since we cannot find the value of \((3x+4y)\) from the above expression, hence statement 1 is not sufficient to answer the question.

Statement-2: \(\frac{y}{6}\) + \(\frac{x}{8}\) = \(\frac{5}{3}\)

Simplifying the above equation, we can write:
    • \(\frac{(8y+6x)}{48}\)=\(\frac{2}{3}\)
    • \(\frac{(4y+3x)}{16}\)=\(1\)
    • \(4y+3x\)=\(16\)
Since we are getting a unique value of \(4y+3x\). Hence, we can easily find the value of \(\frac{(4y+3x)}{2}\) from this information.

Therefore, Statement 2 ALONE is sufficient to answer the question.

Answer: B
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Re: What is the arithmetic mean of 3x and 4y? (1) y/3 - x/4 = 4/3  [#permalink]

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New post 06 Nov 2018, 02:43
Can it be solved by linear system equation and why the result is different?

(1) y/6 - x/8 = 2/3
+
(2) y/6 + x/8 = 5/3

y = 7 and x = 4

Substitute an initial variables

(7*4+3*4)/2=20

The answer is C
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Re: What is the arithmetic mean of 3x and 4y? (1) y/3 - x/4 = 4/3   [#permalink] 06 Nov 2018, 02:43
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