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# In the system of equations above, what is the value of b?

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Math Expert
Joined: 02 Sep 2009
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In the system of equations above, what is the value of b?  [#permalink]

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06 Aug 2019, 23:46
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15% (low)

Question Stats:

84% (01:21) correct 16% (01:27) wrong based on 45 sessions

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$$a+b+\frac{c}{2}=60$$

$$-a-b+\frac{c}{2}=-10$$

In the system of equations above, what is the value of b?

(A) 8
(B) 20
(C) 35
(D) 50
(E) Not enough information to decide.

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Re: In the system of equations above, what is the value of b?  [#permalink]

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07 Aug 2019, 00:12
Adding the two equations we get c=50 and so,

a+b=35
-a-b=-35 which is again a+b=35

So the two are essentially the same equation.

We have one equation and two unknowns so there is not enough information to decide

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Re: In the system of equations above, what is the value of b?  [#permalink]

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07 Aug 2019, 07:56
To find values of three distinct variables, we need three distinct equations, so the answer is (E).
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Re: In the system of equations above, what is the value of b?  [#permalink]

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12 Aug 2019, 10:51
Bunuel wrote:
$$a+b+\frac{c}{2}=60$$

$$-a-b+\frac{c}{2}=-10$$

In the system of equations above, what is the value of b?

(A) 8
(B) 20
(C) 35
(D) 50
(E) Not enough information to decide.

Adding the two equations, we have:

c = 50

Substituting, the two equations become:

a + b + 25 = 60

a + b = 35

and

-a - b + 25 = -10

-a - b = -35

a + b = 35

We see that the two equations reduce to a single equation of a + b = 35. Since there are infinitely many values of b which will satisfy this equation, we don’t have enough information to decide on a single value of b which will satisfy this equation.

Alternative solution:

If we subtract the two equations (e.g., subtract the second equation from the first), we have:

2a + 2b = 70

a + b = 35

Since there are infinitely many values of b which will satisfy this equation, we don’t have enough information to decide on a single value of b which will satisfy this equation.

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Re: In the system of equations above, what is the value of b?   [#permalink] 12 Aug 2019, 10:51