ratio problem 3

[TeddyBonham]

In Erica's garden the ratio of purple tulips to red tulips is 3:5, and the ratio of white roses to yellow roses is 2:3. If the number of white roses in Erica's garden is twice the number of purple tulips, what is the ratio of yellow roses to red tulips?

(A) 5:1 (B) 10:1 (C) 2:7 (D) 9:5 (E) 4:9

[Brent@GMATPrepNow]

In Erica's garden the ratio of purple tulips to red tulips is 3:5, and the ratio of white roses to yellow roses is 2:3. If the number of white roses in Erica's garden is twice the number of purple tulips, what is the ratio of yellow roses to red tulips?

(A) 5:1 (B) 10:1 (C) 2:7 (D) 9:5 (E) 4:9

A fast approach is to ASSIGN values that match the given information.

The ratio of purple tulips to red tulips is 3:5
So, let there be 3 purple tulips and 5 red tulips.

...the number of white roses in Erica's garden is twice the number of purple tulips
Above, we said there are 3 purple tulips, so this means there must be 6 white roses

the ratio of white roses to yellow roses is 2:3
Above, we said there are 6 white roses .
If the ratio of white roses to yellow roses is to be 2:3, then there must be 9 yellow tulips

So, using our values, the ratio yellow : white : purple : red = 9 : 6 : 3 : 5

What is the ratio of yellow roses to red tulips?
Answer: 9:5

Answer: D

Cheers,
Brent

[[email protected]]

Hi TeddyBonham,

TESTing VALUES (the approach Brent used) is perfect for this type of question. You can also take an Algebraic approach to the prompt:

We're told that the ratio of purple tulips to red tulips is 3:5. This means that the number of purple tulips MUST be a multiple of 3 and the number of red tulips MUST be an equivalent multiple of 5. We can write this information in the following way:

P : R
3X:5X where 'X' is the unknown multiple.

We're also told that the ratio of white roses to yellow roses is 2:3. We can write that information in a similar way (but we need to use a DIFFERENT variable, since we don't know which 'multiple' we'll be using.

W : Y
2Y:3Y

Finally, we're told that the number of white roses is TWICE the number of purple tulips. Using the variables we've already created, we have...

2Y = 2(3X)

We're asked for the ratio of yellow roses to red tulips (so we want to figure out what 3Y:5X 'reduces' to).

Since 2Y = 2(3X) = 6X, we can substitute values into the given ratios....

W : Y
2Y:3Y becomes

W : Y
6X:9X

So now we can figure out the ratio of yellow roses to red tulips:

3Y:5X becomes

9X:5X

Remove the Xs and you have 9:5

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[eldergalvao]

I just noticed some wrong words in the explanation. Since there's no such thing as white tulips in the question, souldn't it be:

...the number of white roses in Erica's garden is twice the number of purple tulips
Above, we said there are 3 purple tulips, so this means there must be 6 white roses

the ratio of white roses to yellow roses is 2:3
Above, we said there are 6 white roses?

istead of 6 white tulips?

cheers!

[Brent@GMATPrepNow]

Thanks for pointing that out.
I've changed "white tulips" to "white roses"

Cheers,
Brent

[komati_anusha]

Solved as below.
Purple : Red = 3x:5x tulips
White : Yellow = 2y:3y Roses
White = 2times pruple
X = 2
Y = 6
12 White = 2 ( 6 ) Pruple
So, Red : Yellow = 5 : 9

Is my strategy right? But I feel it's a time consuming by plugging IN

[GMATGuruNY]

In Erica's garden the ratio of purple tulips to red tulips is 3:5, and the ratio of white roses to yellow roses is 2:3. If the number of white roses in Erica's garden is twice the number of purple tulips, what is the ratio of yellow roses to red tulips?

(A) 5:1 (B) 10:1 (C) 2:7 (D) 9:5 (E) 4:9

Y/R = Y/W * W/P * P/R.

On the right side of the equation above, the values in red CANCEL OUT, leaving Y/R.

Since Y/W = 3/2, W/P = 2/1, and P/R = 3/5, we get:
Y/R = 3/2 * 2/1 * 3/5 = 9/5.

The correct answer is D.

[Matt@VeritasPrep]

Solved as below.
Purple : Red = 3x:5x tulips
White : Yellow = 2y:3y Roses
White = 2times pruple
X = 2
Y = 6
12 White = 2 ( 6 ) Pruple
So, Red : Yellow = 5 : 9

Is my strategy right? But I feel it's a time consuming by plugging IN

This looks pretty good! If it helps you get the right answer, the little extra time is worth it.

[Brent@GMATPrepNow]

In Erica's garden the ratio of purple tulips to red tulips is 3:5, and the ratio of white roses to yellow roses is 2:3. If the number of white roses in Erica's garden is twice the number of purple tulips, what is the ratio of yellow roses to red tulips?

(A) 5:1 (B) 10:1 (C) 2:7 (D) 9:5 (E) 4:9

A fast approach is to ASSIGN values that match the given information.

The ratio of purple tulips to red tulips is 3:5
So, let there be 3 purple tulips and 5 red tulips.

...the number of white roses in Erica's garden is twice the number of purple tulips
Above, we said there are 3 purple tulips, so this means there must be 6 white roses

the ratio of white roses to yellow roses is 2:3
Above, we said there are 6 white roses .
If the ratio of white roses to yellow roses is to be 2:3, then there must be 9 yellow tulips

So, using our values, the ratio yellow : white : purple : red = 9 : 6 : 3 : 5

What is the ratio of yellow roses to red tulips?
Answer: 9:5

Answer: D

Cheers,
Brent