The ratio of R to S is 3 to 5, what is the value of the rati

Question

The ratio of R to S is 3 to 5, what is the value of the ratio (R + K)/(S + K)?

(1) R = 12
(2) K = 7

Bunuel · Answer

The ratio of R to S is 3 to 5, what is the value of the ratio (R + K)/(S + K)?

R:S = 3:5.

(1) R = 12 --> S = 20. We need K. Not sufficient.

(2) K = 7 --> (R + K)/(S + K) = (R + 7)/(5R/3 + 7). The ratio will change depending on R. Not sufficient.

(1)+(2) We know the values of all variables, thus we can get the desired ratio. Sufficient.

Answer: C.

buddyisraelgmat · Answer

Hi Bunuel,

Just a silly basic question...

Given that ratio of R to S is 3 to 5, We cannot compute this as 3+7 / 5+7 Correct? Hence "B" would be wrong.

Pls clarify my doubt as in why we cannot compute this as 3+7 / 5+7.

Thanks

Bunuel · Answer

Yes, you are right we cannot do that way.

The ratio of R to S is 3 to 5, does not mean that R is 3 and S is 5, they can be (6, 10), (9, 15), (12, 20)...

pradeepss · Answer

1. R = 12 that gives us S but we do not know K. NS
2. K = 7 but we do not know what is S, S can be 5, 10 15 so no.. NS

1&2. we get R, S and K Sufficient.

Answer: C

Reaper · Answer

Folks,

Since R:S::3:5, why can't we use R=3K and S=5K then we don't need information from 1. and 2. 
Then shouldn't D. be the answer?

-Thanks

EgmatQuantExpert · Answer

Hi  Reaper  - if R & S are in a ratio of 3:5, we can surely write them as 3x and 5x respectively. However, in this case we do not know whether x = K. Hence your interpretation of answer being D will not hold.

Let me also explain this with an example. Assume R = 12 and S = 20, then R & S are in the ratio of 3:5. So, R & S can be written as 3x and 5x respectively for x =4. Depending upon the values of R & S, the value of x would vary. For R = 15 & S = 25, value of x would be 5 and so on.

Since we do not know the value of K, we can't say for sure if R=3K and S=5k respectively.

Hope this helps!

Regards
Harsh

EMPOWERgmatRichC · Answer

Hi All,

This DS question can be dealt with in a couple of different ways. You can use "math theory" on this prompt, but unless your understanding of the concepts is PERFECT, you might make a little mistake and select an incorrect answer (and not even know it). By TESTing VALUES, you can PROVE the correct answer (and do so with a certain amount of ease).

We're told that the ratio of R to S is 3 to 5. We're asked for the value of (R + K)/(S + K).

Fact 1: R = 12

With the given ratio (R:S = 3:5), we now know that S = 20. We don't know the value of K though...

IF....
K = 0
The answer to the question is (12+0)/(20+0) = 12/20 = 3/5

IF...
K = 1
The answer to the question is (12+1)/(20+1) = 13/21
Fact 1 is INSUFFICIENT

Fact 2: K = 7

We don't know the values of R and S, but we DO know that they fall into the ratio of 3:5......

IF...
R = 3
S = 5
The answer to the question is (3+7)/(5+7) = 10/12 = 5/6

IF...
R = 6
S = 10
The answer to the question is (6+7)/(10+7) = 13/17
Fact 2 is INSUFFICIENT

Combined, we know....
R = 12 (so S = 20)
K = 7

The answer to the question MUST be (12+7)/(20+7) = 19/27
Combined, SUFFICIENT

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

CrackverbalGMAT · Answer

Hi All,
This is a tricky question. Here students may do careless error by chosing D or B.
But the answer is together sufficient:
Ratio of R to S is 3 to 5.
Then value of R to S is 3x to 5x.
Now the question asks for value of the ratio R+k to S+k.
So that’s 3x+k to 5x+k.
We need x and k values.
Statement 1 : Not sufficient:
From statement 2 we only get x value because R= 3x and 3x=12 so x = 4.
But no info about K.
So not sufficient.
Statement 2 : Not sufficient:
Gives the K value and no info about x.
So not sufficient.
Together it is sufficient.
Because we get both x and K values. 
So answer is C.

Reaper · Answer

Yes Harsh, it makes sense. x=K is not definitive.

-Thanks

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 3 variables and 1 Equation: Let the original condition in a DS question contain 3 variables and 1 Equation. In other words, there are two fewer equations than variables. Now, we know that each condition (1) and (2) would usually give us an equation, however, since we need 2 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find value of the ratio \(\frac{(R + K)}{ (S + K)}\).

=> Given that: x, y, and z are three positive consecutive odd integers.

Second and the third step of Variable Approach: From the original condition, we have 3 variables (R, S, and K). and 1 Equation (R:S = 3:5)To match the number of variables with the number of equations, we need 3 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Let’s take a look at both conditions together .

Condition(1) tells us that R = 12.

Condition(2) tells us that k = 7.

=> Since R =12 and ratio of R : S is 3 : 5 then S = 4 and as K = 7

=> R + K = 12 + 7 = 19 and S + K = 20 + 7 = 27

=> By substituting values for each variable, we can find value of \(\frac{(R + K) }{ (S + K)}\)

Since the answer is unique, both conditions together are sufficient by CMT 2.

So, C is the correct answer.

Answer: C

Basshead · Answer

\frac{R}{S} = \frac{3}{5}

\frac{R + K }{ S + K} ?

(1) If  R = 12 ,  S = 18 .

However, depending on the value of K, we can get different ratios. INSUFFICIENT.

(2)  K = 7

Depending on the value of R and S, we can get different ratios. INSUFFICIENT.

(1&2) Together, we can determine the ratio. SUFFICIENT.

Answer is C.

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