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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
pigi512 wrote:
Sorry, I mean that statements 1 & 2 are sufficient separately. My answer is D. Is there any further official explanation?
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
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 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!
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.
_________________
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!
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.
_________________
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
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!
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.
Bunuel I think on a deeper level, the mistake that person made when analyzing statement 1 is subconsciously assuming that the solution to r - s = 8 must necessarily equate to r + s =18 - sometimes when you're not careful you assume the truth of the premise you're attempting to falsify or prove correct-
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
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).
_________________
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
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).
Alright, so here is my shortcoming! Thanks Bunuel for making it simple
Sorry, I mean that statements 1 & 2 are sufficient separately. My answer is D. Is there any further official explanation?
The questions states Does 3^(r+s) = 27^6 ? That means we have to answer in Yes, 3^(r+s) = 27^6 or No, 3^(r+s) = 27^6. We don't have to find the exact value.
Statement 1 says r-s = 8 R and S can be any value with the absolute difference of 8 . example (8,0) (9,1) and so on. So there is no unique value. Hence Statement I alone is insufficient
Statement 2 says 5r = 13s Again, we can not find any unique value. example R =13 and S = 5 OR R = 26 and S = 10 and so on.
So if you see, some values can satisfy the equations but some can not . So we can't mark option D as the values may or may not satisfy the equation.
But if we combine We get R=13 and s = 5 Now this is a unique value. This is what we need to answer if 3^(r+s) = 27^6. The answer can be Yes/No.
I hope my explanation helps you. _________________ Kindly click on +1Kudos if my post helps you...