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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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12 Mar 2018, 04:26
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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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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

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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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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.

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

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