Of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout, the number of males is 45 more than twice the number of females. If the ratio of female speckled trout to male rainbow trout is 4:3 and the ratio of male rainbow trout to all trout is 3:20, how many female rainbow trout are there?
A 192 B195 C 200 D205 E208
Rainbow trout VS speckled trout
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Whenever you have a problem that presents two either-or categories (male or female, rainbow or speckled), the best way to approach the problem is to set up a matrix as follows:
Use M and F to represent the total number of males and females, respectively. We know that together they add up to the total number, so:
M + F = 645
If the number of males is 45 more than twice the number of females, then:
M = 45 + 2F
Now we have a system of equations - 2 equations and 2 variables - so we can substitute for M:
(45 + 2F) + F = 645
3F = 600
F = 200
M = 445
If the ratio of female speckled to male rainbow is 4/3, we know that the number of female speckled is 200, so:
(200/x) = (4/3)
4x = 600
x = 150
There are 150 male rainbow trout, so put that in the the grid. If the ratio of male rainbow to all trout is 3/20, then:
(150/y) = (3/20)
3Y = 3000
Y = 1000
There are 1,000 total trout. Once we add this to our grid, we can easily solve for the number of female rainbow trout. There are 645 speckled trout and 1000 total trout, so:
1000 - 645 = 355 There are 355 total rainbow trout.
Total rainbow trout - male rainbow trout = female rainbow trout, so:
355 - 150 = 205
There are 205 female rainbow trout. The answer is D.
Use M and F to represent the total number of males and females, respectively. We know that together they add up to the total number, so:
M + F = 645
If the number of males is 45 more than twice the number of females, then:
M = 45 + 2F
Now we have a system of equations - 2 equations and 2 variables - so we can substitute for M:
(45 + 2F) + F = 645
3F = 600
F = 200
M = 445
If the ratio of female speckled to male rainbow is 4/3, we know that the number of female speckled is 200, so:
(200/x) = (4/3)
4x = 600
x = 150
There are 150 male rainbow trout, so put that in the the grid. If the ratio of male rainbow to all trout is 3/20, then:
(150/y) = (3/20)
3Y = 3000
Y = 1000
There are 1,000 total trout. Once we add this to our grid, we can easily solve for the number of female rainbow trout. There are 645 speckled trout and 1000 total trout, so:
1000 - 645 = 355 There are 355 total rainbow trout.
Total rainbow trout - male rainbow trout = female rainbow trout, so:
355 - 150 = 205
There are 205 female rainbow trout. The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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All trout = male rainbow + female rainbow + total speckled.AIM TO CRACK GMAT wrote:Of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout, the number of males is 45 more than twice the number of females. If the ratio of female speckled trout to male rainbow trout is 4:3 and the ratio of male rainbow trout to all trout is 3:20, how many female rainbow trout are there?
A 192 B195 C 200 D205 E208
Since male rainbow : all trout = 3:20 and total speckled = 645, we get:
20x = 3x + female rainbow + 645
17x = female rainbow + 645.
The answer choices represent the number of female rainbow trout.
The equation above implies that the sum of the correct answer choice and 645 must be a multiple of 17.
Only D works:
205+645 = 850 = 17*50.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
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.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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