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

Question

If a certain vase contains only roses and tulips, how many tulips are there in the vase?

(1) The number of roses in the vase is 4 times the number of tulips in the vase.

(2) There is a total of 20 flowers in the vase.

(DS10471)

Iakovos1995 · Answer

We need to find the number of tulips in the vase.

Statement 1  gives us that the number of roses is 4 times the number of tulips. This alone is  insufficient  without the overall number of flowers in the vase.
 Statement 2  gives us the total numbers of flowers in the vase. This alone is  insufficient  without any relationship between the number of roses and the number of tulips.

The  two statements together  are  sufficient  to answer the question. Since we know that the vase contains only roses and tulips, the total number of flowers in the vase and the relationship between the number of roses and the number of tulips, we can find how many tulips are there in the vase.

The correct answer is C.

EgmatQuantExpert · Answer

Solution

Given:  
 • A certain vase contains only roses and tulips

To find:  
 • The number of tulips present in the vase

Analysing Statement 1  
 • As per the information given in statement 1, the number of roses in the vase is 4 times the number of tulips in the vase
 o From this statement, we can only conclude that roses are more than tulips, but we can’t find their exact number

Hence, statement 1 is not sufficient to answer

Analysing Statement 2  
 • As per the information given in statement 2, there is a total of 20 flowers in the vase
 o From this statement, we can’t figure out the exact number of roses and tulips, out of those 20 flowers

Hence, statement 2 is not sufficient to answer

Combining Both Statements  
If we combine the data given in both the statements, we can say
 • Roses are 4 times of tulips and together there are 20 flowers
 o If we assume that there are f tulips, then there are 4f roses
o Together 4f + f = 20 
• Therefore, we can find out the number of tulips

Hence, the correct answer is option C.

Answer: C

BrentGMATPrepNow · Answer

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

gatz · Answer

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.

CareerGeek · Answer

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

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=n0G2lqxpU8s

ScottTargetTestPrep · Answer

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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=_jNsNfzpHOI

vikg007 · Answer

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.

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

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