A large flower arrangement contains 3 types of flowers: carnations, li

Question

A large flower arrangement contains 3 types of flowers: carnations, lilies, and roses. Of all the flowers in the arrangement, 1/2 are carnations, 1/3 are lilies, and 1/6 are roses. The total price of which of the 3 types of flowers in the arrangement is the greatest?

(1) The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively.
(2) The price of one rose is $0.75 more than the price of one carnation, and the price of one rose is $0.25 more than the price of one lily.

DS67410.01

shridhar786 · Accepted Answer

let the total number of flowers be = x
carnations =  \frac{x}{2}

Lillies =  \frac{x}{3}

Roses =  \frac{x}{6}

STATEMENT (1)--The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively.
let the price of one carnation = y
one Lilly = 3y
one rose = 4y

the total price of carnation =  \frac{xy}{2}  = 0.5xy
the total price of Lillies =  \frac{3xy}{3}  = xy
the total price of roses =  \frac{4xy}{6}  = 0.6xy

from here we can say the price of Lillies are the greatest that is --xy
SUFFICIENT

STATEMENT (2)--The price of one rose is $0.75 more than the price of one carnation, and the price of one rose is $0.25 more than the price of one lily.
let the price of one carnation = y
one Lilly = y+0.50
one rose = y+0.75

the total price of carnation =  \frac{xy}{2}  
the total price of Lillies =  \frac{x(y+0.5)}{3} 
the total price of roses =  \frac{x(y+0.75)}{6}  
sine we dont know the value of x and y we cant decide which value is the greatest
INSUFFICIENT

A is the answer

Cellchat · Answer

The ratio of price can be combined with the ratio of quantity to determine the ratio of total price.
We are given that L = 3C (because C:L is 1:3) and R = 4C (because C:R is 1:4).

Carnation = Price x Quantity = C x 1/2T = 1/2 CT

Lily = Price x Quantity = 3C x 1/3T = CT

Rose = 4C x 1/6T = 2/3 CT

Lily has the greatest total price.  SUFFICIENT

Two examples can be used to show insufficiency.

- If the flower prices are extremely high, the extra cents will not have a large impact on the total price and ans. will be the flower with the most quantity. (Carnation)
- If the flower prices are extremely low, the extra cents will have a large impact on the total price and ans. will be the most expensive flower. (Rose)

Since we can come up with two different flowers with the greatest total cost - INSUFFICIENT.

Ans: A

Hope it helps.

Basim2016 · Answer

Normally, it has been noticed that Ratios, Percentages provide more accurate comparisons among different entities as compared to some fixed values. 
SIMILARLY, in this question also, statement 1 proves to be SUFFICIENT as compared to statement 2 (INSUFFICIENT).
Regards

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vaibhav101 · Answer

An easy approach

assume that the no. of flowers is 60. Then according to given information, there are 30 carnations, 20 lilies, and 10 roses.

(1) The prices per flower for carnations, lilies, and roses are in the ratio 1:3:4, respectively.

Again, assume the prices to be $1, $3 & $4. Then the no. of Carnations is 30 * $1= $30, Lilies is 20 * $3=$60 & roses is 10 * $4=$40. So statement A is sufficient

(2) The price of one rose is $0.75 more than the price of one carnation, and the price of one rose is $0.25 more than the price of one lily. 
Since no information about the absolute values is given it is insufficient.

Answer is A

Franzhel · Answer

I will try to add my two cents on how to solve this problem quickly

Statement 1)
Since they give us the ratio of the prices, we can assume that the price is the ratio itself. Therefore the prices will be 1, 3 and 4 respectively. Its easy to see now that we can multiply the ratio with the prices to find how much money will they cost. The key thing to realize is that there is no real difference in working with ratios and with totals since we only want to know which one is the highest one.

Sufficient

Statement 2) The easiest way to figure it out is to realize that we have no idea of what the prices are. We just know that roses are more expensive by some number. Another way to see it is that we have 3 unknowns and 2 equations, therefore we cannot find a solution. Now you can imagine a situation in where the prices are extremely high (1 million, 1 million and 75 cents and 1 million and 30 cents) and another situation in which prices are extremely low (almost 0, a bit more than75 cents and a bit more than 30 cents). Clearly both of these situations will give us different solutions.

Insufficient

Hope it helps

Bambi2021 · Answer

So we get that the relative number of the total of one flower to another is in a fixed ratio:

C : L : R

\frac{3}{6}:\frac{2}{6}:\frac{1}{6}

(1) Gives us the ratio of prices per flower:

C : L : R

1x:3x:4x

The prices of the flowers in the arrangement will be:

1x*\frac{3}{6} : 3x*\frac{2}{6} : 4x*\frac{1}{6}

No matter the value of x, the ratio of the totals for the different flowers in the arrangement will be:

C : L : R

\frac{3}{6} : \frac{6}{6} : \frac{4}{6} = 3 : 6 : 4

(2) is easily ruled out. If the price of one rose is 0,76, the price of one carnation is 0,01, a ratio of 1:76. If the price of one rose is 100,76 and the price of one carnation is 100,01, then simply one more carnation (two in total) will cost almost the double than one rose.

qlJshin · Answer

As great as the "correct" solution is, on questions like this, Brute Force usually works better for most actual testtakers. After all, most test takers aren't aspiring to be GMAT teachers.

Easiest way to arrange the flowers is to assume that there are 6 flowers total (common denominator of all 3 ratios). So, that means 3 carnations, 2 lilies, and 1 rose OR 6,4,2 OR 9,6,3

(1) Prices are 1:3:4: Let's assume that means $1, $3, $4. So cost for flowers is 3*$1, 2*$3, and 1*$4 or $3, $6, and $4. Cost of lilies is greatest. But would that be true always? You can double the number of flowers and/or double the costs.
flowers : cost : total cost
 6,4,2 : $1,$3,$4 : $6, $12, $8 - lilies
 3:2:1 : $2,$6,$8 : $6, $12, $8 - lilies
 6,4,2 : $2,$6,$8 : $12, $24, $16 - lilies 
(note that the total costs ratio is constant)
SUFFICIENT

(2) Prices  r = c +0.75 and  r = l +0.25:  c =0.25,  l =0.75,  r =1.00 OR  c =100.25,  l =100.75,  r =101.00
If 0.25,0.75,1.00 : total costs@3,2,1 = 0.75,1.50,1.00 - lilies 
If 100.25,100.75,101.00 : total costs@3,2,1 = 300.75,201.50,101,00 - carnations
INSUFFICIENT

Basshead · Answer

Notice the question doesn't ask for an exact amount. Instead, the question simply asks which type of flower in the arrange is the greatest?

Statement 1 gives us a ratio for the prices of each flower. At first, this may not seem sufficient. How can we determine the total price of each flower from a ratio?

However, we're don't need the exact price -- we only need to determine which flower has the highest total price. With a ratio of the flowers and a ratio of the prices of each flower, we can determine this. Statement 1 is sufficient.

Statement 2 should trigger red flags immediately. Imagine each flower costs $1 million. The $0.75 and $0.25 difference between each flower is insignificant. Statement 2 is not sufficient.

Answer is A.

sayan640 · Answer

MartyMurray   KarishmaB  Would you like to discuss this question ? If you find any concept worth mentioning and noting here , kindly put it across.

bumpbot · Answer

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A large flower arrangement contains 3 types of flowers: carnations, li

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GMAT Data Sufficiency (DS) Questions

A large flower arrangement contains 3 types of flowers: carnations, li

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