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# Is 15 the average (arithmetic mean) of x, y, and 15?

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Math Expert
Joined: 02 Sep 2009
Posts: 51100
Is 15 the average (arithmetic mean) of x, y, and 15?  [#permalink]

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15 Feb 2018, 07:46
00:00

Difficulty:

25% (medium)

Question Stats:

97% (00:59) correct 3% (01:31) wrong based on 42 sessions

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Is 15 the average (arithmetic mean) of x, y, and 15?

(1) x + y= 30

(2) x - y = 4

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Joined: 21 Aug 2013
Posts: 1412
Location: India
Re: Is 15 the average (arithmetic mean) of x, y, and 15?  [#permalink]

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15 Feb 2018, 23:42
Bunuel wrote:
Is 15 the average (arithmetic mean) of x, y, and 15?

(1) x + y= 30

(2) x - y = 4

Average of x, y and 15 is = (x+y+15)/3. If this is equal to 15, then we will have:
x+y+15 = 45 OR x+y = 30
So if we can determine whether x+y is 30 or not (with surety) then we will be able to answer.

Statement 1
This gives x+y = 30. Sufficient. This gives us YES as an answer to the question asked.

Statement 2
x-y = 4. This does not help us in determining whether sum of x & y is 30 or not. So not sufficient.

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Re: Is 15 the average (arithmetic mean) of x, y, and 15?  [#permalink]

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17 Feb 2018, 04:13
Bunuel wrote:
Is 15 the average (arithmetic mean) of x, y, and 15?

(1) x + y= 30

(2) x - y = 4

Question : Is (x+y+15)/3 = 15?

Question : Is (x+y) = 30?

Statements 1: x + y= 30

Sufficient

Statements 2: x - y= 4

NOT SUFFICIENT

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Is 15 the average (arithmetic mean) of x, y, and 15?  [#permalink]

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19 Feb 2018, 16:56
Bunuel wrote:
Is 15 the average (arithmetic mean) of x, y, and 15?

(1) x + y= 30

(2) x - y = 4

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the question as follows.

The question asks if $$(x+y+15)/3 = 15$$.

$$(x+y+15)/3 = 15$$ ?
$$⇔ x + y + 15 = 45$$ ?
$$⇔ x + y = 30$$ ?

The equivalent question "$$x + y = 30$$ ?" is same as the condition 1).

The condition 1) is sufficient.

Condition 2)
$$x = 17, y = 13$$ : Yes
$$x = 5, y = 1$$ : No
Since we don't have a unique answer, the condition 2) is not sufficient.

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Is 15 the average (arithmetic mean) of x, y, and 15? &nbs [#permalink] 19 Feb 2018, 16:56
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