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# If 3x – 2y = 7, what is the value of x ? x and y are positive integer

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If 3x – 2y = 7, what is the value of x ? x and y are positive integer  [#permalink]

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27 Nov 2019, 23:32
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35% (medium)

Question Stats:

71% (01:13) correct 29% (01:10) wrong based on 28 sessions

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If 3x – 2y = 7, what is the value of x ?

1) x and y are positive integers.

2) x = y − 1

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Re: If 3x – 2y = 7, what is the value of x ? x and y are positive integer  [#permalink]

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28 Nov 2019, 11:24
If 3x – 2y = 7, what is the value of x ?

1) x and y are positive integers.

3x= 7 +2y
x = 1/3(7+2y)

y = 1 --> x=1/3(9) x=3
y = 4 --> x=1/3(15) x= 5
y = 10 --> x=1/3(27) x=9

Not Sufficient

2) x = y − 1
3(y-1) – 2y = 7
3y-3 -2y =7
y=10

for y =10 x =9 Sufficient

Ans B
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Re: If 3x – 2y = 7, what is the value of x ? x and y are positive integer  [#permalink]

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29 Nov 2019, 12:40
CAMANISHPARMAR wrote:
If 3x – 2y = 7, what is the value of x ?

1) x and y are positive integers.

2) x = y − 1

Statement 1:
The statement is not constricting enough, we have many combinations of x and y that can solve this. x = 3 and y = 1, or x = 5 and y = 4. Insufficient.

Statement 2:
We have two equations with two variables that are linear and independent. That allows us to solve for a unique solution so this is sufficient.

Ans: B
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Re: If 3x – 2y = 7, what is the value of x ? x and y are positive integer  [#permalink]

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29 Nov 2019, 23:51
CAMANISHPARMAR wrote:
If 3x – 2y = 7, what is the value of x ?

1) x and y are positive integers.

2) x = y − 1

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Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Possbile pairs of (x,y) are x = 3, y = 1 and x = 5, y = 4.

Since condition 1) does not yield a unique solution, it is not sufficient

Condition 2)
We have y = x + 1 and 3x - 2y = 3x -2(x+1) = x - 2 = 7 or x = 9.

Since condition 2) yields a unique solution, it is sufficient

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: If 3x – 2y = 7, what is the value of x ? x and y are positive integer   [#permalink] 29 Nov 2019, 23:51
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