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

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If a certain vase contains only roses and tulips, how many tulips are  [#permalink]

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21 Jun 2018, 08:00
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Question Stats:

96% (00:31) correct 4% (00:37) wrong based on 909 sessions

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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.

NEW question from GMAT® Official Guide 2019

(DS10471)

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Re: If a certain vase contains only roses and tulips, how many tulips are  [#permalink]

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27 Jun 2018, 05:18
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Bunuel wrote:
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.

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

Cheers,
Brent
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Re: If a certain vase contains only roses and tulips, how many tulips are  [#permalink]

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21 Jun 2018, 08:40
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.

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Re: If a certain vase contains only roses and tulips, how many tulips are  [#permalink]

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22 Jun 2018, 09:16

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.

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Re: If a certain vase contains only roses and tulips, how many tulips are  [#permalink]

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04 Aug 2018, 17:42
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

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Re: If a certain vase contains only roses and tulips, how many tulips are  [#permalink]

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24 May 2019, 19:16
Bunuel wrote:
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.

NEW question from GMAT® Official Guide 2019

(DS10471)

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
Re: If a certain vase contains only roses and tulips, how many tulips are   [#permalink] 24 May 2019, 19:16
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