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

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

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New post Updated on: 05 Aug 2018, 02:12
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A
B
C
D
E

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Question Stats:

81% (01:21) correct 19% (02:44) wrong based on 24 sessions

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In the system of equations above, what is the value of b?
a+b+c/2=60
-a-b+c/2=-10

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

Source: Nova's GMAT Prep Course

Originally posted by Xin Cho on 05 Aug 2018, 01:22.
Last edited by Xin Cho on 05 Aug 2018, 02:12, edited 3 times in total.
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Re: In the system of equations above, what is the value of b?  [#permalink]

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New post 05 Aug 2018, 01:37
Please reformat the question so it is easy to understand.

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

\(a + b + \frac{c}{2} = 60\)
\(-a - b + \frac{c}{2} = 10\)

It's clearly visible that by adding them, you will eliminate a and b and thus can solve for C. This leads to C= 70. Now solve for:

\(a + b = 25\)
\(-a - b = -25\)

The above equation does not allow us to solve for a or b; hence, the answer is C.
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Re: In the system of equations above, what is the value of b?  [#permalink]

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New post 05 Aug 2018, 02:04
strivingFor800 wrote:
Please reformat the question so it is easy to understand.

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

\(a + b + \frac{c}{2} = 60\)
\(-a - b + \frac{c}{2} = 10\)

It's clearly visible that by adding them, you will eliminate a and b and thus can solve for C. This leads to C= 70. Now solve for:

\(a + b = 25\)
\(-a - b = -25\)

The above equation does not allow us to solve for a or b; hence, the answer is C.


The same format is presented in the book.

Adding equations:
a-a+b-b+(c/2)+(c/2)=60-10
2*(c/2)=50
c= 50

If C = 50 then first equation:
a+b+25=60
a+b=35

The second equation:
-a-b+25=-10
-a-b=-35
a+b=35

Thus, equation two appears to be tautological statement, not proving any extra information. Thus, 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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New post 06 Aug 2018, 10:37
Xin Cho wrote:
In the system of equations above, what is the value of b?
a+b+c/2=60
-a-b+c/2=-10

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

Source: Nova's GMAT Prep Course


OA: E

\(a+b+c/2=60 ...(1)\)
\(-a-b+c/2=-10...(2)\)
Adding both equation, we get \(c=50\)
Putting value of c into \((1)\) and \((2)\), we get
\(a+b=35\)
\(-a-b=-35\)
both are same equation , we will get infinite solution.
So value of\(b\) or \(a\) cannot be found out from these \(2\) equations
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Re: In the system of equations above, what is the value of b?   [#permalink] 06 Aug 2018, 10:37
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