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10 Jul 2024, 04:40
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Assuming
Number of Roses = r, Number of tulips = t and Number of lilies = l,
Question stem tells us that,
\(r + t = 100 * \frac{3}{4}\) = \(75\)
\(l + t = 100 * \frac{3}{25}\) = \(12\)
And \(r, l, t > 0\)
We need to find \(t\).
Statement-1
We are given that,
\(\frac{r}{t} < \frac{13}{2}\)
\(2r < 13t\)
But we know that \(r+t = 75\),
\(2(75-t) < 13t\)
\(150 < 15t \)
\(t > 10\)
Now coming to the equation \(l + t = 12\),
Value of l cannot be less than 1.
If we take \(l=1\) to get maximum value of t,
We get value of \(t=11\).
We cannot take \(t=12\) as value of \(l=0 \)then which is opposite of question stem provided information.
We got only 1 answer.
t=11.
Sufficient statement.
Statement-2
\( r + l = 100 * \frac{13}{20}\) = \(65\)
From \(l + t = 12\) and \(r + t = 75\),
\((75-t) + (12-t) = 65\)
\(87 - 65 = 2t\)
\(t = 11\)
Only 1 solution.
Sufficient statement.
Final answer - D. Both statements are sufficient alone.
Number of Roses = r, Number of tulips = t and Number of lilies = l,
Question stem tells us that,
\(r + t = 100 * \frac{3}{4}\) = \(75\)
\(l + t = 100 * \frac{3}{25}\) = \(12\)
And \(r, l, t > 0\)
We need to find \(t\).
Statement-1
We are given that,
\(\frac{r}{t} < \frac{13}{2}\)
\(2r < 13t\)
But we know that \(r+t = 75\),
\(2(75-t) < 13t\)
\(150 < 15t \)
\(t > 10\)
Now coming to the equation \(l + t = 12\),
Value of l cannot be less than 1.
If we take \(l=1\) to get maximum value of t,
We get value of \(t=11\).
We cannot take \(t=12\) as value of \(l=0 \)then which is opposite of question stem provided information.
We got only 1 answer.
t=11.
Sufficient statement.
Statement-2
\( r + l = 100 * \frac{13}{20}\) = \(65\)
From \(l + t = 12\) and \(r + t = 75\),
\((75-t) + (12-t) = 65\)
\(87 - 65 = 2t\)
\(t = 11\)
Only 1 solution.
Sufficient statement.
Final answer - D. Both statements are sufficient alone.
10 Jul 2024, 05:00
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3/4 are either Roses of Tulips
So Roses + Tulips = 75
3/25 are either Lilies or Tulips
So, Lilies + Tulips = 12
We need to find no. of Tulips
Statement 1:
Ratio of no. of Roses to no. of Tulips < 13:2
R / T < 13 / 2
R < 13T / 2
Now we know R + T = 75
13T/2 > R
So if we replace it with R in this equation, it would be greater than 75
13T/2 + T > 75
13T+2T > 150
15T>150
T > 10
We also know that L + T = 12 and we have atleast 1 Lily
So, only possible value for Tulips is 11
Statement 1 is sufficient
Statement 2:
13/20 of the flowers are Roses or Lilies
R + L = 65
Adding the first 2 equations we have in the questions
R + T + T + L = 75 + 12
(R+L) + 2T = 87
65 + 2T = 87
2T = 22
T = 11
Statement 2 is also sufficient
Answer is D
So Roses + Tulips = 75
3/25 are either Lilies or Tulips
So, Lilies + Tulips = 12
We need to find no. of Tulips
Statement 1:
Ratio of no. of Roses to no. of Tulips < 13:2
R / T < 13 / 2
R < 13T / 2
Now we know R + T = 75
13T/2 > R
So if we replace it with R in this equation, it would be greater than 75
13T/2 + T > 75
13T+2T > 150
15T>150
T > 10
We also know that L + T = 12 and we have atleast 1 Lily
So, only possible value for Tulips is 11
Statement 1 is sufficient
Statement 2:
13/20 of the flowers are Roses or Lilies
R + L = 65
Adding the first 2 equations we have in the questions
R + T + T + L = 75 + 12
(R+L) + 2T = 87
65 + 2T = 87
2T = 22
T = 11
Statement 2 is also sufficient
Answer is D
10 Jul 2024, 05:35
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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.
Let R be the numbers of Roses, T be the number of Tulips, L be the number of Lilies.
Of the 100 flowers, R + T = 75, L + T = 12. And there is at least one rose, at least one tulip, and at least one lily in the garden, so
Max of L = 11, max of T = 11, and max of R = 74, min of R=64
(1) R/T < 13/2. Together with R + T = 75, we can conclude that T > 10.
As T>10 and <=11, T can only be 11. Sufficient
(2) R + L = 65, together with R + T = 75, L + T = 12, we also can calculate T. Sufficient
I choose D. EACH statement ALONE is sufficient to answer the question asked
(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.
Let R be the numbers of Roses, T be the number of Tulips, L be the number of Lilies.
Of the 100 flowers, R + T = 75, L + T = 12. And there is at least one rose, at least one tulip, and at least one lily in the garden, so
Max of L = 11, max of T = 11, and max of R = 74, min of R=64
(1) R/T < 13/2. Together with R + T = 75, we can conclude that T > 10.
As T>10 and <=11, T can only be 11. Sufficient
(2) R + L = 65, together with R + T = 75, L + T = 12, we also can calculate T. Sufficient
I choose D. EACH statement ALONE is sufficient to answer the question asked
