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If the average (arithmetic mean) of p, q, and r is 6, what i

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by Max@Math Revolution » Fri Nov 02, 2018 12:20 am

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[Math Revolution GMAT math practice question]

If the average (arithmetic mean) of p, q, and r is 6, what is the value of r?

1) p=-r
2) p=-q
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Nov 02, 2018 5:27 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If the average (arithmetic mean) of p, q, and r is 6, what is the value of r?
1) p = -r
2) p = -q
Given: The average (arithmetic mean) of p, q, and r is 6
We can write: (p + q + r)/3 = 6
This means: p + q + r = 18

Target question: What is the value of r?

Statement 1: p = -r
Given: p + q + r = 18
Replace p with -r to get: -r + q + r = 18
Simplify: q = 18
What about the value of r?
All we know is that p = -r (which also means r = -p), which doesn't help us much.
There are several values of r and p (and q) that satisfy statement 1 (and the given information). Here are two cases:
Case a: r = 1, p = -1 and q = 18. In this case, the answer to the target question is r = 1
Case b: r = 2, p = -2 and q = 18. In this case, the answer to the target question is r = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p = -q
Given: p + q + r = 18
Replace p with -q to get: -q + q + r = 18
Simplify: r = 18
So, the answer to the target question is r = 18
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Nov 04, 2018 6:56 pm
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The question asks for the value of r, where r = 18 - ( p + q ). If we know the value of p + q, then we can determine the value or r. Condition 2) implies that p + q = 0. Therefore, r = 0 + r = ( p + q ) + r = 18, and condition 2) is sufficient.



Condition 1)
If p = -1, q =18, and r = 1, then p + q + r = 18 and r = 1.
If p = -2, q =18, and r = 2, then p + q + r = 18 and r = 2.
Since it doesn't give a unique value of r, condition 1) is not sufficient.

Therefore, B is the answer.
Answer: B
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by fskilnik@GMATH » Mon Nov 05, 2018 3:54 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If the average (arithmetic mean) of p, q, and r is 6, what is the value of r?

1) p=-r
2) p=-q
$$p + q + r = 18\,\,\,\,\left( * \right)$$
$$? = r$$

Embrace math! The homogeneity nature of the average (*) trivializes this problem!

$$\left( 1 \right)\,\,p + r = 0\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,q = 18\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {q,p,r} \right) = \left( {18,0,0} \right)\,\,\,\, \Rightarrow \,\,\,? = 0 \hfill \cr
\,\,{\rm{Take}}\,\,\left( {q,p,r} \right) = \left( {18,1, - 1} \right)\,\,\,\, \Rightarrow \,\,\,? = - 1\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,p + q = 0\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,? = r = 18$$

This solution follows 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
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