What is the average (arithmetic mean) of x, y, and z?
(1) -x − 4y + 3z = 14
(2) 5x + 8y + z = 26
What is the average (arithmetic mean) of x, y, and z?
This topic has expert replies
-
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Statement 1
$$-x-4y+3z=14$$ =
Values of x, y and z are unknown, so we can't arrive at a definite answer hence, Statement 1 is INSUFFICIENT.
Statement 2
$$5x+8y+z=26$$
Value of x, y and z are unknown, so we can't arrive at a definite answer. Hence, Statement 2 is INSUFFICIENT.
Combining statements 1 and 2 together
Adding Statement 1 and 2 together
$$-x-4y+3z=14$$ ..............................1
$$5x+8y+z=26$$ ...............................2
We obtain
$$4x+4y+4z=40$$
Dividing both sides of the equation by 4, we obtain
$$\frac{\left(4x+4y+4z\right)}{4}=\frac{40}{4}$$
$$\left(x+y+z\right)=10$$
$$Average\ arithemetic\ mean=\frac{EFX}{EF}=\frac{10}{3}$$
both statement together is SUFFICIENT.
$$answer\ is\ Option\ C$$
$$-x-4y+3z=14$$ =
Values of x, y and z are unknown, so we can't arrive at a definite answer hence, Statement 1 is INSUFFICIENT.
Statement 2
$$5x+8y+z=26$$
Value of x, y and z are unknown, so we can't arrive at a definite answer. Hence, Statement 2 is INSUFFICIENT.
Combining statements 1 and 2 together
Adding Statement 1 and 2 together
$$-x-4y+3z=14$$ ..............................1
$$5x+8y+z=26$$ ...............................2
We obtain
$$4x+4y+4z=40$$
Dividing both sides of the equation by 4, we obtain
$$\frac{\left(4x+4y+4z\right)}{4}=\frac{40}{4}$$
$$\left(x+y+z\right)=10$$
$$Average\ arithemetic\ mean=\frac{EFX}{EF}=\frac{10}{3}$$
both statement together is SUFFICIENT.
$$answer\ is\ Option\ C$$
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
You should always start by REPHRASING any DS question to determine: what's the minimum information that would be sufficient to answer this question?
Our question is "what is the average of x, y, and z?" First, rephrase algebraically:
(x + y + z)/3 = ?
What would we need in order to find that? Just the sum (x + y + z). We don't necessarily need the values of the variables individually.
Target question: what is the value of x + y + z?
(1) -x - 4y + 3z = 14
We cannot rearrange or simplify this to get a value for x + y + z. Insufficient.
(2) 5x + 8y + z = 26
We cannot rearrange or simplify this to get a value for x + y + z. Insufficient.
(1) and (2) together:
If we combine the 2 equations, we get:
-x - 4y + 3z = 14
+ 5x + 8y + z = 26
____________________
4x + 4y + 4z = 40
Divide both sides by 4 and we get a value for x + y + z. Sufficient. (We don't actually need to do the work to solve, or to find the average. We know that our target question is answerable, so that's enough).
The answer is C.
Our question is "what is the average of x, y, and z?" First, rephrase algebraically:
(x + y + z)/3 = ?
What would we need in order to find that? Just the sum (x + y + z). We don't necessarily need the values of the variables individually.
Target question: what is the value of x + y + z?
(1) -x - 4y + 3z = 14
We cannot rearrange or simplify this to get a value for x + y + z. Insufficient.
(2) 5x + 8y + z = 26
We cannot rearrange or simplify this to get a value for x + y + z. Insufficient.
(1) and (2) together:
If we combine the 2 equations, we get:
-x - 4y + 3z = 14
+ 5x + 8y + z = 26
____________________
4x + 4y + 4z = 40
Divide both sides by 4 and we get a value for x + y + z. Sufficient. (We don't actually need to do the work to solve, or to find the average. We know that our target question is answerable, so that's enough).
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
$$? = \frac{{x + y + z}}{3}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\boxed{\,? = x + y + z\,}$$DivyaD wrote:What is the average (arithmetic mean) of x, y, and z?
(1) -x − 4y + 3z = 14
(2) 5x + 8y + z = 26
$$\left( 1 \right)\,\, - x - 4y + 3z = 14\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y,z} \right) = \left( { - 14,0,0} \right)\,\,\,\, \Rightarrow \,\,\,? = - 14 \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y,z} \right) = \left( { - 10, - 1,0} \right)\,\,\,\, \Rightarrow \,\,\,? = - 11 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{\rm{INSUFF}}.$$
$$\left( 2 \right)\,\,5x + 8y + z = 26\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y,z} \right) = \left( {0,0,26} \right)\,\,\,\, \Rightarrow \,\,\,? = 26 \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y,z} \right) = \left( {4,0,6} \right)\,\,\,\, \Rightarrow \,\,\,? = 10 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$
$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\, - x - 4y + 3z = 14 \hfill \cr
\,5x + 8y + z = 26 \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,4\left( {x + y + z} \right) = 40\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br