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

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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10 Jan 2019, 23:24
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Difficulty:

25% (medium)

Question Stats:

76% (01:17) correct 24% (01:54) wrong based on 24 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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Status: It always seems impossible until it's done.
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Posts: 661
Re: If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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10 Jan 2019, 23:35
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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“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Intern
Joined: 30 Oct 2018
Posts: 49
Re: If 3x + y = 14, and x and y are positive integers, each of the followi  [#permalink]

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10 Jan 2019, 23:37
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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Joined: 18 Aug 2017
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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, 01:39
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 &nbs [#permalink] 11 Jan 2019, 01:39
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