Does 3^(r + s) = 27^6 ? (1) r s = 8 (2) 5r = 13s

Question

Does  3^{r+s} = 27^6  ?

(1)  r – s = 8

(2)  5r = 13s

Bunuel · Accepted Answer

No that's not correct.

Does 3^(r + s) = 27^6 ?

Does  3^{(r + s)} = 3^{18} ?

Does r + s = 18.

(1) r – s = 8. Both r + s = 18 and r – s = 8 can be true simultaneously for r = 13 and s = 5 (answer YES) but if say r = 10 and s =2, then r + s does not equal to 18 (answer NO). Not sufficient.

(2) 5r = 13s. Again, both r + s = 18 and 5r = 13s can be true simultaneously for r = 13 and s = 5 (answer YES) but if say r = 0 and s = 0, then r + s does not equal to 18 (answer NO). Not sufficient.

(1)+(2) r – s = 8 and 5r = 13s gives r = 13 and s = 5 --> r + s = 18. Sufficient.

Answer: C.

P.S. You can check OA (Official Answer) under the spoiler in the original post.

KrishnakumarKA1 · Answer

in order to answer the question, we need:
1# exact value of r and s
2# two equations in r and s
3# any other information to predict the value of r and s
4# the value of the expression r+s

St 1: one equation 2 variable. INSUFFICIENT
St 2: one equation 2 variable. INSUFFICIENT

St 1 & St 2: two equations, two variable. SUFFICIENT

Option C

Sajjad1994 · Answer

Official Explanation

This is a  “Yes/No”  data sufficiency question. Begin by assessing the question. Start by rewriting the equation in the question stem using common bases, to find that 3^(r + s) =  (3^3) 6 = 3^18. Since the bases are the same, the exponent expressions can be set as equal. So the question is really asking “Is  r + s = 18? ” Now evaluate the statements to see if the information is sufficient to answer the question.

To evaluate Statement (1) ,  r – s = 8 , plug in numbers for r and s. If  r = 13  and  s = 5 , then the statement is satisfied. These numbers also produce a  “Yes”  answer to the question because  13 + 5 = 18 . Now, see if there is a way to get a  “No”  answer. If  r = 9  and  s = 1 , then the statement is still satisfied but the answer to the question “Is  r + s = 18?”  is now  “No.”   Statement (1) is insufficient , so write down BCE as the possible answer choices.

Statement (2)  is  5r = 13s . Plug in again. If  r = 13  and  s = 5 , then the statement is satisfied and the answer to the question Is  r + s = 18? ” is  “Yes.”  Now, see if there is a way to get a  “No”  answer. If  r = 0  and  s = 0 , then the answer to the question is now  “No.”   Eliminate choice (B).

Look at both statements together  and recycle any values that were already used. If  r = 13  and  s = 5 , then both statements are satisfied and the answer to the question “Is  r + s = 18 ?” is “ Yes.”  Since there is no other possible combination that satisfies both statements.

correct answer is (C)  .

Hope it helps

MaximD · Answer

SajjadAhmad I don't agree in total, if i may.

The question is 3^(r + s) = 27^6.

We know that that's the same as 3^r * 3^s = 3^18

So you get a formula from the question: r+s=18
In statement 1 you get the formula: r-s=8
Now we have 2 different formula's, with just the first statement. Since we have 2 formula's, we can exactly identify r and s.

So the answer should be A, in my opinion!

chetan2u · Answer

Hi,
You do not know that r+s=18... Rather you have to answer IS r+s=18?

So you have to find value of R and s OR r+s to check the equation.
Statement I just gives you one equation...
You don't have second equation.

BrentGMATPrepNow · Answer

Target question :    Does 3^(r + s) = 27^6 ?  
This is a good candidate for  rephrasing the target question.  
To get the same base on both sides, rewrite 27 as 3^3. 
We get:  3^(r + s) = (3^3)^6  
Apply power of power rule to get:  3^(r + s) = 3^18  
Now that the bases are the same, we can conclude that:  r + s = 18  
So, we can REPHRASE the target question....

REPHRASED target question :    Does r + s = 18?

Statement 1 : r – s = 8   
Does this provide enough information to answer the  REPHRASED target question ? No. 
There are several values of r and s that satisfy statement 1. Here are two: 
Case a: r = 8 and s = 0, in which case  r + s = 8 + 0 =  8  
Case b: r = 13 and s = 5, in which case  r + s = 13 + 5 =  18  
Since we cannot answer the  REPHRASED target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : 5r = 13s  
There are several values of r and s that satisfy statement 2. Here are two: 
Case a: r = 0 and s = 0, in which case  r + s = 0 + 0 =  0  
Case b: r = 13 and s = 5, in which case  r + s = 13 + 5 =  18  
Since we cannot answer the  REPHRASED target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that r – s = 8
Statement 2 tells us that 5r = 13s
So, we have a system of two  different  linear equations with 2 different variables. 
Since we COULD solve this system for r and s, we could determine whether or not  r + s = 18 , which means we COULD answer the  REPHRASED target question  with certainty. 
So,the combined statements are SUFFICIENT

Answer: C

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Shef08 · Answer

I don’t understand why can’t we take each statement seperately and tackle them. Cutting down the question, it asks does r+s= 18?

S1: r-s=8, so r=s+8 (equation 1)
Now substitute this equation 1 in the question does r+s=18? We get the answer as yes.

S2: 5r=13s, so r=13/5s (equation 2)
Now same way when substituted in question stem, we get an answer as yes.

Yet the answer is C and not D

Posted from my mobile device

Bunuel · Answer

The problem with your approach is that we don't know from the stem that r + s = 18. The question asks DOES r + s = 18? So, you cannot use r + s = 18 with r - s = 8 to solve (again because we are not given that r+s=18).

Shef08 · Answer

Alright, so here is my shortcoming! Thanks Bunuel for making it simple

achloes · Answer

Bunuel   BrentGMATPrepNow   KarishmaB   chetan2u

Since the question does not present any constraints, can we test negative cases too?

1. r-s = 8 
2. 5r = 13s

Combining both statements:

Let's take r to be -5 and s to be -13. In which case:

1. r-s = 8 
-5-(-13) 
= -5+13 
= 8

2. 5r = 13s 
 5(-13) = 13 (-5).

Is the case above valid as well? If so, since the question doesn't ask for a unique value, are both statements together still sufficient?

Please let me know if my understanding is correct. Thanks in advance!

Bunuel · Answer

When evaluating each statement individually, negative values can be used to eliminate them. However, when considering the statements together, we have a system of equations r - s = 8 and 5r = 13s. This system yields exact values: r = 13 and s = 5. Thus, when examining (1) + (2), plugging in specific values doesn't really make sense, as we can directly determine the exact values of the variables involved.

The error you are making is that if r = -5 and s = -13, then 5r should be calculated as 5*(-5), not 5*(-13), and 13s should be computed as 13*(-13), not 13*(-5).

Does 3^(r + s) = 27^6 ? (1) r s = 8 (2) 5r = 13s

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GMAT Data Sufficiency (DS) Questions

Does 3^(r + s) = 27^6 ? (1) r s = 8 (2) 5r = 13s

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