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What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are

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Bunuel
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What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are [#permalink] New post   17 Jan 2024, 10:45
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61% (01:20) correct 39% (01:27) wrong based on 72 sessions
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What is the average of x and y?

(1) 2x + 3y = 12
(2) x and y are positive integers.
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C
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pk2023
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Re: What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are [#permalink] New post   17 Jan 2024, 23:45
2x+3y=12 by first statement we get many values , by second statement we get x=0 y=4, x=6 y=0 thus not getting definite answer so data in either statement is insufficient
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Re: What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are [#permalink] New post   26 Feb 2024, 06:32
pk2023 wrote:
2x+3y=12 by first statement we get many values , by second statement we get x=0 y=4, x=6 y=0 thus not getting definite answer so data in either statement is insufficient


Staement 2 says it X and Y are postive integers , 0 is not an postive integers  therefore only 2 values exist X = 3 and Y = 2

 

­The ZERO does not have any postive value
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Re: What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are [#permalink] New post   08 Mar 2024, 13:17
(1) is insufficient because there can be several values

(2) is insufficient as we do not know the exact numbers set and their value

(1+2) Is sufficient because if from (2) we know that x and y are positive values, x or y cannot be 0 therefore the only numbers that x = 3 and y = 2
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Re: What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are [#permalink] New post   09 Mar 2024, 21:38
What is the average of x and y?
(1) 2x + 3y = 12
(2) x and y are positive integers.

So we need to find the average of x and y (x+y/2), but here from the question stem we don't know if x & y are integers or fractions or decimals.

From St 1. 2x+3y=12 put x=3 and y=2 => satisfies the equations. we can get an av. (2.5)
one more possibility is, putting x=0 and y=4 => satisfies the equations. we will get a different av. value. (2)

this is insufficient.. We can also check fraction values by putting x=11/2 and y= 1/3 => satisfies the equations. we will get a different av. value.

St 2. is not of any use as a stand alone statement, but it is just giving us a vital info.
this is insufficient..

combing St. 1 & 2, discard are fractions and decimals values and stick with integers only.

only x=3 and y=2 will answer the main stem question.
Discard x=0 and y=4 as 0 is neither positive nor negative but is considered even in GMAT.

Therefore, answer is C.

Hope it is clear now.

Also, in such type of questions, directly start from statement 2 and save yourself some time and then we can check different combinations of st 1 and only one condition will get satisfied.­­
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Re: What is the average of x and y? (1) 2x + 3y = 12 (2) x and y are [#permalink]
09 Mar 2024, 21:38
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Bunuel
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