GMAT Club Olympics 2024 (Day 2): Of the 100 flowers in a garden, 3/4

Question

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?
 
(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.

(2) 13/20 of the flowers in the garden are either roses or lilies.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Bunuel · Accepted Answer

GMAT Club Official Explanation:

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?

3/4 are either roses or tulips, which implies R + T = 75.
3/25 are either lilies or tulips, which implies L + T = 12.

Observe that the above indicates that there must be some other kinds of flowers in the garden, for example, orchids.

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.

This implies that R/T < 13/2, which gives 2R < 13T.

Substituting R = 75 - T, we get:

2(75 - T) < 13T
150 - 2T < 13T
150 < 15T
T > 10

Since there is at least one lily, from L + T = 12 we get T = 11. This is sufficient.

(2) 13/20 of the flowers in the garden are either roses or lilies.

This implies that R + L = 65. Subtracting this from R + T = 75, we get T - L = 10. Adding this to L + T = 12, we get 2T = 22, which gives T = 11. This is sufficient too.

Answer: D.

Kinshook · Answer

Given: Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips.
Asked: If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?
 
3/4 * 100 = 75 flowers are either roses or tulips; Roses + Tulips = 75
3/25 *100 = 12 flowers are either lilies or tulips; Lilies + Tulips = 12

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.
Roses / Tulips = 13/2 = 6.5; Roses = 6.5* Tulips
Roses + Tulips = 75
6.5*Tulips + Tulips = 75
7.5*Tulips = 75
Tulips = 10
SUFFICIENT

(2) 13/20 of the flowers in the garden are either roses or lilies.
Roses + Lilies = 13/20 *100 = 65
Roses + Tulips = 75
Lilies + Tulips = 12
Addiing all above equations together
2(Roses + Tulips + Lilies) = 65 + 75 + 12 = 152
Roses + Tulips + Lilies = 76
Tulips = (Roses + Tulips + Lilies) - (Roses +  Lilies) = 76 - 65 = 11
SUFFICIENT

IMO D

Evronredor · Answer

Information from the stem

1) Total number of flowers=100
2) R+T = 3/4 of 100 = 75
3) L+T = 3/25 OF 100 = 12
from the above two equations we can deduce,
R-L=63
4) We have at least 1 of each flower

Solving for statement 1

R/T < 13/2

we have, R= 75-T, substituting

75-T/T <13/2
150-2T<13T
150<15T
10<T, so we get that T is greater than 10

considering the below equation and the condition that we have at least 1 of each, we get T=11
L+T = 12

Solving for statement 2

R+L= 13/20 of 100 = 65

combing the two statements below,

R+L=65
R-L=63

we get R= 64, Substituting the value in the below equation,

R+T = 75 => T= 75-64 = 11

Hence, each statement alone is sufficient to answer the question.

Answer: D

busygmatbee1290 · Answer

Tricky question: The statement 1 is also sufficient and the answer is D. Here's how:

We have 
 R+T=75 
 L+T=12 
(1) This gives us number of Roses to be less than 6.5 times the number of tulips. Let's calculate what 6.5 gives us: 
 R=6.5T 
 6.5T + T = 75 
 T = 10 
We can see that  T+L=12  needs to be satisfied and hence the border case given in statement 1 seems to be a trick. We can see if the ratio was lesser, the number of tulips would increase to 11, 12, so on. But, the number of lilies has to be 1 and hence only 11 is a possible solution. Sufficient.

(2) This is straightforward. You have equation  R+L=65 . 
Add the 2 equations given in qs, we'll get  R+L+2T=87 .
Hence, T=11. 
Sufficient.

arraj · Answer

This was a challenging question

given 3/4 are rose or tulips. 3/4*100 = 75 = r+t
3/25 are lilies or tulips. 12 = l + t
we have to find t
1) r to t ratio is less than 13:2, given r+t = 75 if the ratio was 13:2  r= (75/15)*13 =65 and t = 10
if the ratio is less than this means the number of t must be higher r =64, t=11 or r =63, t=12
but given that there is atleast one of each kind and l+ t =12, l must atleast be 1 and t<12
so only option is r=64 and t=11
suff

2)13/20 are r or l,  r+l =65 
adding r+t, l+t, r+l 
2(l+r+t) = 65+75+12
2(l+r+t) = 152
l+r+t = 76
l+r =65
65+t =76
t = 11
suff

captain0612 · Answer

Choice D

total flowers = 100
Roses or Tulips = (3/4)*100 = 75
Lillies or Tulips = (3/25)*100 = 12

None of the flowers in the garden are 0.

Number Tulips in the garden =?

Statement 1:

Roses : Tulips < 13 : 2
Roses/ tulips < 13/2 ------(1)

We know that : Roses + Tulips = 75
=> Roses = 75 - Tulips ---(2)

Substitute (2) in (1) to get

=> 75 - Tulips < (13/2)*Tulips
=> 75 < (15/2)*Tulips
=> 10 < Tulips
Here, Tulips can 11, 12, 13. any number > 10
We also know that Lillies + Tulips = 12, and Least number of Lillies in the garden is 1
Therefore, From above we can arrive at Tulips = 11, as Tulips cannot be greater than 11

Sufficient.

Statement 2:

Roses + Lillies = (13/20)*100 = 65 ---(3)

We know that:
Roses + Tulips = 75 -------(4)
Lillies + Tulips = 12 -------(5)

(4) - (3) gives us
Tulips - Lillies = 10 -------(6)

(5) + (6) gives us

2Tulips = 22
Tulips = 11

Sufficient
Choice D

AthulSasi · Answer

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?
 
(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.

(2) 13/20 of the flowers in the garden are either roses or lilies.
-------------------------------------------------------------------
From the paragraph, 
Total 100 flowers out of whihc 3/4 are R or T and 3/25 are L or T

From this we get
R+T = 100*3/4 = 75
L+T = 100*3/25 = 12
.
 Since atleast one L is there the max value which T can take is 11 and the smallest value it can take is 1.
. 
Notice that the total R+L+2T is 87 only meaning there are other flowers in the garden other than these three (not relevant information, but still :p)
.
From the above two we get : R-L = 63
--------------------------
Statement 1 : Does give sufficient information. 
 \frac{R}{T} < \frac{13}{2} 
2R<13T

If we assume R as 64, then T will be 11 and 2R<13T and L wil be 1
IF we assume R as 65 then T will be 10 but 2R will not be less than 13T
Now as the value of T keekp going below 10 the value of 13T reduces and value of 2R keeps increasing. Hence only possible value for T is 11.
Hence statement 1 is sufficient. 
-------------------------------
Statement 2 : 13/20 of the flowers in the garden are either roses or lilies.
Given : R+L = 100*13/20 = 65
We have also deduced earlier that R+L+2T is 87, subtituting R+L as 65 we get
65+2T=87
2T=22
T=11
Hence statement 2 is sufficient. 
--------------------------------
Correct answer D

Jolex · Answer

To solve the problem, let's start by summarizing the given information and the requirements.

Given:
1. There are 100 flowers in a garden.
2. $\frac{3}{4}$ of the flowers are either roses or tulips, which translates to:
\ 
3. $\frac{3}{25}$ of the flowers are either lilies or tulips, which translates to:
\ 
4. There is at least one rose, at least one tulip, and at least one lily in the garden.

To Find:
The number of tulips ($ T $).

Analysis of Statements:

Statement 1: The ratio of the number of roses to the number of tulips is less than 13 to 2.

This can be expressed as:
\ 
\

From the given information:
\ 
\

Substituting $ R = 75 - T $ into the inequality:
\ 
\ 
\ 
\

So, the number of tulips $ T $ must be greater than 10. This gives us a range but not an exact number, so it might seem insufficient at first glance. However, let's proceed to see if we can find a conclusive number with this alone or if we need more information.

Statement 2: $\frac{13}{20}$ of the flowers in the garden are either roses or lilies.

This can be expressed as:
\

We already have:
\ 
\

Adding these two equations:
\ 
\

Using $ R + L = 65 $ from statement 2:
\ 
\ 
\

This statement alone gives us a definite number for $ T $.

Conclusion:
Both statements individually provide sufficient information to determine $ T $:

- From Statement 1, we deduce $ T > 10 $. While this is not a specific number, it sets a range.
- From Statement 2, we calculate that $ T = 11 $.

Therefore, each statement alone is sufficient to determine the number of tulips in the garden. The correct answer is:

D. EACH statement ALONE is sufficient to answer the question asked.

HarshaBujji · Answer

Let the number of flowers is represented by r,t,l; Given r + t = 75 , As both are mutually exclusive sets. Means plants cannot be both roses and tullips. In similar lines l+t = 12; We are looking for t?? From both equations r - l = 63; Statement 1 : The ratio of the number of roses to the number of tulips is less than 13 to 2. r/t < 13/2; r <13/2t; So r + t <13/2t +t =>15t/2> 75 So t>10; We also know that l+t=12; So if t = 11, l=1; If t=12.l cannot be 0 as per given conditions. So we will be able to find the t value with stmt 1; Statement 2 : 13/20 of the flowers in the garden are either roses or lilies. r + l = 65; r - l =63; l = 1; So t=12. Hence IMO D

prashantthawrani · Answer

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.

(2) 13/20 of the flowers in the garden are either roses or lilies.

Ans.

Roses+Tulips=3/4th of 100 flowers
 R+T=75 ..........(i)

Lillies+Tulips=2/25th of 100 flowers
 L+T=12 .........(ii)

(1)  R/T < 13/ 2
R<13T/2...........(iii)

substituting R=75-T from (ii) into (iii)
75-T<13T/2
150-2T<13T
150<15T
 T>10

From (ii)  L+T=12  and there is at-least 1 lily flower , so  L=1 (minimum).
This gives  T=11 
Statement 1 is sufficient alone.

(2)  Roses+Lilies=13/20th of 100 flowers.
R+L=65..........(iv)

Adding and subtracting (i)+(ii)-(iii)

R+T+L+T-(R+L)=75+12-65
2T=22
T=11

Statement 2 is sufficient alone.

Answer D

sayan640 · Answer

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?
 
(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.

(2) 13/20 of the flowers in the garden are either roses or lilies.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

From the passage, 75 = rose + tulips ;  lilly + tulip = 12  ( 3/25 * 100)

From the statement 1 , 
rose / tulip < 13/2
r / t < 13/2

2r < 13t
2 * ( 75 - t ) < 13t
t>10

Now t + l = 12
t must be 11 because there is at least one rose, at least one tulip, and at least one lily in the garden.
Statement 1 is sufficient

Statement 2 says ,
r + l = 65
75 = rose + tulips ;  lilly + tulip = 12

Addling , 
2 ( r + l + t ) = 152  ( r stands of rose and t stands for tulip )

r + l + t = 76 
l+ t = 12

r=64
t= 75 - 64 = 11

Statement 2 is also sufficient

D is the answer.

jairovx · Answer

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?

Given
L, T, R > 0
R + T = 75 (i)
R + L = 12 (ii)
T = ?

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.
R/T < 13/2
R/T < 6.5

Let's try numbers for L (plug-in eq. ii)
If L = 1, then T = 11.
Plug-in in eq. i.
T = 11, then R = 64
Meet the condition R/T < 6.5

Let's try numbers for L (plug-in eq. ii)
If L = 2, then T = 10.
Plug-in in eq. i.
T = 10, then R = 65
Doesn't meet the condition R/T < 6.5

For the next values L = 3,4... we can say that the condition R/T < 6.5 is not meet.
This condition is enough.
Delete answers B, C, E.

(2) 13/20 of the flowers in the garden are either roses or lilies.
R + L = 65, from the stem we can get R - L = 63
So we can solve the eq.
This condition is enough.
Delete answer A.

D. EACH statement ALONE is sufficient to answer the question asked.

xhym · Answer

We know from the statement that 3/4 flowers are either roses or tulips so: \frac{75}{100} are roses or tulips: R+T=75 and we know that 3/25 are either lilies or tulips so: \frac{12}{100} are lilies or tulips: L+T=12 Statement 1 \frac{R}{T} < \frac{13}{2} 2R<13T We know from the problem that R=75-T so we can say that: 2(75-T)<13T 150-2T<13T 150<15T 10 Statement 1 alone is sufficient. Statement 2 Since 13/20 flowers are either roses or lilies, R+L=65 Now with 3 equations and 3 unknowns, we can solve for the variables: R+T=75 T=75-R L+T=12 T=12-L So, 75-R=12-L With R+L=65 , we know that: 75-R=12-L 75-(65-L)=12-L 10+L=12-L 2L=2 L=1 Since L+T=12 , we know that T=11 -> Statement 2 alone is sufficient. Answer is D

Catman · Answer

Let Roses be "R", Lillies be "L" and Tulips be "T"

3/4 are either roses or tulips.
R+T =$ (\frac{3}{4})*100=75$

3/25 are either lilies or tulips.
L+T= $(\frac{3}{25})*100 = 12$

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.
$\frac{R}{T}<\frac{13}{2}$
$\frac{(R+T)}{T}<\frac{15}{2}$ R+T=75
$\frac{75}{T} < \frac{15}{2} $
$T>10$
L+T=12 ( Since R,L,T,>=1)
T=11, L=1
Sufficient.

(2) 13/20 of the flowers in the garden are either roses or lilies.
$R+L=(\frac{13}{20})*100 = 65$
R+T = 75
L+T=12
R-L=63
L=1, R=64, T=11
Sufficient.

IMO D.

smile2 · Answer

From given information, we can infer R + T = \frac{3}{4} * 100 L + T = \frac{3}{25} * 100 R + T = 75 L + T = 12 We need to find what T is. Statement 1 says \frac{R}{T }< \frac{13}{2} from this, we can write T > \frac{2R}{13} Substitute R + T = 75 in T > \frac{2R}{13} Then we get, R < 65 meaning T > 10. And we are given that there is at least one 🌹 (rose), one lily and one tulip, meaning R >= 1 and T >=1 , Then, we know T = 11, and L = 1 from L + T = 12. Therefore, A alone is sufficient. Statement 2 says R + L = 65 R + T = 75 R + L = 65 T - L = 10 T + L = 12 T = 11, L = 1 Therefore, B alone is sufficient. In total, D is the right answer choice as each is sufficient.

Dheeraj_079 · Answer

From the question, we can calculate the following:
Let the number of tulips be t, roses r and lilies l.
r+t= 3/4*100 = 75
l + t = 3/25*100 = 12

Statement 1: The ratio of the number of roses to the number of tulips is less than 13 to 2.

From the statement r:t = 13:2
So, we can calculate the value of l,r and t .
Statement 1 alone is sufficient

Statement 2: 13/20 of the flowers in the garden are either roses or lilies.
From the above equations, r + l = 65
We have three equations and three variables. Hence, statement two alone is sufficient.

Thus, the answer is D, Each statement alone is sufficient.

pranjalshah · Answer

I think it's D

Given, R+T = 75 and L+T=12. Also, R,T,L>0

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.

Given, R/T<13/2

This implies, R<13T/2

R = 75 - T

so, 75 - T < 13T/2
or, T > 10

as L+T=12 and L cannot be 0, so T can take only 1 value = 11.

Therefore (I) is sufficient.

(2) 13/20 of the flowers in the garden are either roses or lilies.

Given, R+L=65. Solving these 3 equations (other two being R+T = 75 and L+T=12), we get

R=64, T=11 and L=1.

Therefore (II) is sufficient.

Also the total is coming out to be 76. So there must be 24 flowers that are not R,T or L.

OmerKor · Answer

Hello, everyone. This is the second day of the competition. I truly like the concept of competitiveness. Every day is new. Everything can change. To win, you must maintain a consistent pace. https://cdn.gmatclub.com/cdn/files/forum/images/smilies/1f607.gif Get ready. Here we GO. Let's get started with our explanation for this topic on day two: Analyze the Question: Question : First, let's look at the question. We are dealing with kind of Fraction/Ratio problem. Reading and Understanding the question: Given : 100 flowers in overall 3/4 (75) 3/25 (12) Overall: 87 (with overlapp) Roses / Tulips Tulips / Lilies * at least 1 of each flower. Understanding : lets take some scenerios to understand: Roses(Max): 74 Tulips (Min): 1 Lilies (Max): 11 Overall: 86 flowers. Roses(Min): 64 Tulips (Max): 11 Lilies (Min): 1 Overall: 76 flowers. Roses(Middle): 70 Tulips (Middle): 5 Lilies (Middle): 7 Overall: 82 flowers. We can see that we have Max of 86 flowers and Min of 76 Flowers. I got it. Now i know for sure. this is a mix question of: Min/Max and Overlapp. I know that min max problems can be very confusing. so I will be more focus now. NOW, After Reading and Understanding we can move to the Statements

Solving: (1) the ratios of is less than meaning it can be or .. let's start with : multiply it by 5 we get: 65 and 10 = out given number of tulips and roses. so we know that we have 75 so. it must be less that the ratio of , in other words: less than . let's try some cases: = Work. we know that we can have 1 more Lilie. = Doesn't work. Now we don't have any Lilies and we know we have at least one

. SUFFICIENT (2) is either Roses or Lilies now we given more info that we hadn't about roses and lilies. = => we have 65 Lillies and Roses. what can we infer from that? let's understand: Roses(middle): 64 Tulips (Max): 11 Lilies (Min): 1 Overall: 76 flowers. = Min of flowers Roses(Max): 74 Tulips (Min): 1 Lilies (Max): 11 Overall: 76 flowers. but we know now that the max of Roses is 65 => can't be. Roses(Middle): 65 Tulips (Middle): 10 Lilies (Middle): 2 Overall: 82 flowers. but we know now that the max of Roses is 65 => can't be. So we have only one option here. SUFFICIENT Our Answer is D

THE END I hope you liked the explanation, I have tried my best here. Let me know if you have any questions about this question or my explanation.

DG1989 · Answer

Of the 100 flowers in a garden, 3/4 are either roses or tulips and 3/25 are either lilies or tulips. If there is at least one rose, at least one tulip, and at least one lily in the garden, how many of the flowers are tulips?

(1) The ratio of the number of roses to the number of tulips is less than 13 to 2.
(2) 13/20 of the flowers in the garden are either roses or lilies.

Solution:
Let's denote:
R is the number of roses
T is the number of tulips
L is the number of lilies

Given that
R + T = 75 ---------------- (1)
L + T = 12 ---------------- (2)
and there is at least 1 R, T, and L each
We need to find the value of T

Statement 1: The ratio of the number of roses to the number of tulips is less than 13 to 2.
This means, $\frac{R}{T}$ < $\frac{13}{2}$
From (1)

$\frac{(75 - T)}{T}$ < $\frac{13}{2}$
$\frac{(75 - T)}{T}$ < 6.5
75 - T < 6.5T
7.5T > 75
T > 10
From (2)
L + T = 12
Since L cannot be 0, T = 11
SUFFICIENT

Statement 2: 13/20 of the flowers in the garden are either roses or lilies.
This means R + L = 65
From (1) and (2)
75 - T + 12 - T = 65
87 - 2T = 65
2T = 22
T = 11
SUFFICIENT

The correct answer is D

GMAT Club Olympics 2024 (Day 2): Of the 100 flowers in a garden, 3/4

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GMAT Club Olympics 2024 (Day 2): Of the 100 flowers in a garden, 3/4

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards