GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2019, 17:50

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57155
In the system of equations above, what is the value of b?  [#permalink]

Show Tags

07 Aug 2019, 00:46
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:25) correct 6% (01:58) wrong based on 32 sessions

HideShow timer Statistics

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

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

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.

_________________
Senior Manager
Joined: 16 Jan 2019
Posts: 409
Location: India
Concentration: General Management
WE: Sales (Other)
Re: In the system of equations above, what is the value of b?  [#permalink]

Show Tags

07 Aug 2019, 01:12
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

Posted from my mobile device
Intern
Joined: 15 Dec 2011
Posts: 1
Re: In the system of equations above, what is the value of b?  [#permalink]

Show Tags

07 Aug 2019, 08:56
To find values of three distinct variables, we need three distinct equations, so the answer is (E).
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7399
Location: United States (CA)
Re: In the system of equations above, what is the value of b?  [#permalink]

Show Tags

12 Aug 2019, 11:51
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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In the system of equations above, what is the value of b?   [#permalink] 12 Aug 2019, 11:51
Display posts from previous: Sort by