If a certain vase contains only roses and tulips, how many tulips are

We can also solve this question using 2 variables

Let R = number of roses in the vase
Let T = number of tulips in the vase

Target question: What is the value of T?

Statement 1: The number of roses in the vase is 4 times the number of tulips in the vase.
We can write: R = 4T
As we can see, there are infinitely many different values of R and T that satisfy this equation. For example...
Case a: T = 3 and R = 12. In this case, the answer to the target question is T = 3
Case b: T = 4 and R = 16. In this case, the answer to the target question is T = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: There is a total of 20 flowers in the vase.
We can write: R + T = 20
As we can see, there are many different values of R and T that satisfy this equation. For example...
Case a: T = 3 and R = 17. In this case, the answer to the target question is T = 3
Case b: T = 4 and R = 16. In this case, the answer to the target question is T = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that R = 4T
Statement 2 tells us that R + T = 20
At this point, we should recognize that we have a system of 2 linear equations with 2 variables. As such, we COULD solve this system for R and T, which means we COULD answer the target question.
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Q: t=?

(1) r=4t
Statement one is not sufficient because we do not know the total number of flowers in the vase.
Eliminate A and D

(2) r+t=20
Statement two is not sufficient because there are more than one combination that results 20.
Eliminate B

(1 and 2) From statement one and two we have an equation system with two unknowns, from which we can solve t.
4t+t=20
5t=20
t=4


Correct answer is C.

Statement 1:

Roses Tulips Total
4x x 5x

Nothing can be said about tulips.
Insufficient

Statement 2:

total = 20. There are many combinations possible (1,19), (2,18) . . . . .
Insufficient

Combining (1) & (2)

5x = 20
x = 4.
So, tulips = x = 4

Sufficient

Option C

Answer: Option C

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Solution:

Question Stem Analysis:

We need to determine the number of tulips in a certain vase that contains only roses and tulips.

Statement One Alone:

Since we don’t know the number of roses in the vase, knowing that the number of roses is 4 times the number of tulips does not allow us to determine the number of tulips in the vase. Statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know the number of roses in the vase, knowing there are 20 flowers in the vase does not allow us to determine the number of tulips in the vase. Statement two alone is not sufficient.

Statements One and Two Together:

Since we know that the number of roses is 4 times the number of tulips and the total number of flowers in the vase is 20, then we can create the equation (where t is the number of tulips):

t + 4t = 20

5t = 20

t = 4

Therefore, there are 4 tulips in the vase. Statements one and two together are sufficient.

Answer: C

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­Statement 1: This statement suggests the co-relation between the number of roses and number of tulips in the vase; however, we must know at least one of the variables - either number of roses or number of tulips to calculate correctly the other variable. 

In mathematical terms, Statement 1 helps in arriving at x (number of roses) = 4y (number of tulips) --------- (1)

Statement 2: This statement only helps in identifying the sum of number of roses and number of tulips 

In mathematical terms, Statement 2 helps in arriving at x + y = 20 ------------- (2)

Only when we combine (1) and (2), we get: 

20 - y = 4y (replacing x with 20 - y in 1)

20 = 5y

y = 4
x = 4y = 4(4) = 16

Hence, both statements TOGETHER are sufficient, but NEITHER ALONE is sufficient.