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

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Intern
Joined: 29 May 2016
Posts: 9
In the system of equations above, what is the value of b?  [#permalink]

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Updated on: 05 Aug 2018, 02:12
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15% (low)

Question Stats:

100% (01:15) correct 0% (00:00) wrong based on 12 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.
Manager
Joined: 29 Sep 2017
Posts: 113
Location: United States
GMAT 1: 720 Q49 V39
GPA: 3.3
WE: Consulting (Consulting)
Re: In the system of equations above, what is the value of b?  [#permalink]

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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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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.

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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Joined: 18 Jun 2018
Posts: 96
Re: In the system of equations above, what is the value of b?  [#permalink]

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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
Re: In the system of equations above, what is the value of b? &nbs [#permalink] 06 Aug 2018, 10:37
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