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
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ratio problem 3
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TeddyBonham
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A fast approach is to ASSIGN values that match the given information.TeddyBonham wrote: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
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
Last edited by Brent@GMATPrepNow on Sat Jun 06, 2015 1:05 pm, edited 1 time in total.
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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
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
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eldergalvao
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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!
...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!
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Brent@GMATPrepNow
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Thanks for pointing that out.
I've changed "white tulips" to "white roses"
Cheers,
Brent
I've changed "white tulips" to "white roses"
Cheers,
Brent
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komati_anusha
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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
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
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GMATGuruNY
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Y/R = Y/W * W/P * P/R.TeddyBonham wrote: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
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.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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Matt@VeritasPrep
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This looks pretty good! If it helps you get the right answer, the little extra time is worth it.komati_anusha wrote: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
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
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A fast approach is to ASSIGN values that match the given information.TeddyBonham wrote: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
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
Brent Hanneson - Creator of GMATPrepNow.com
