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# If 3x + y = 14, and x and y are positive integers, each of the followi

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Joined: 02 Sep 2009
Posts: 55803
If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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11 Jan 2019, 00:24
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25% (medium)

Question Stats:

74% (01:45) correct 26% (01:56) wrong based on 45 sessions

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If 3x + y = 14, and x and y are positive integers, each of the following could be the value of x + y EXCEPT

A. 12
B. 10
C. 8
D. 6
E. 4

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Re: If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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11 Jan 2019, 00:35
We know that x and y are positive integers so minimum value they can take is 1.

Also,
$$3x + y = 14$$
Giving y the minimum value of 1... it turns out x will not be an integer

Hence minimum value of y possible is 2
$$3x + 2 = 14$$
$$3x = 12$$
$$x = 4$$

So minimum value of x + y is 4 + 2 = 6

Anything lower than this is not possible - So Option (E) is the first one out.

Also, we know only one of the options can be correct. Therefore we can afford to not check any of the other options and go with (E).
Bunuel wrote:
If 3x + y = 14, and x and y are positive integers, each of the following could be the value of x + y EXCEPT

A. 12
B. 10
C. 8
D. 6
E. 4

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Re: If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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11 Jan 2019, 00:37
option A-> x=1, y=11
option B-> x=2, y=8
option C-> x=3, y=5
option D-> x=4, y=2

hence option E is not possible and is the answer.
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Re: If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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11 Jan 2019, 02:39
Bunuel wrote:
If 3x + y = 14, and x and y are positive integers, each of the following could be the value of x + y EXCEPT

A. 12
B. 10
C. 8
D. 6
E. 4

3x+y=14
would stand true
@x=1,2,3,4 where y = 11,8,5,2
x+y= 12,10,8,6
IMO E ;4 stands out
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Re: If 3x + y = 14, and x and y are positive integers, each of the followi   [#permalink] 11 Jan 2019, 02:39
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