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In a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets are birds. How many of the pets are dogs?
1) There are 30 birds at the pet shop.
2) There are 20 more dogs than birds at the pet shop.
OA D
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In a certain pet shop, 1/3 of the pets are dogs and 1/5 of
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Brent@GMATPrepNow
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Target question: How many of the pets are dogs?AAPL wrote:GMAT Prep
In a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets are birds. How many of the pets are dogs?
1) There are 30 birds at the pet shop.
2) There are 20 more dogs than birds at the pet shop.
OA D
Given: 1/3 of pets are dogs & 1/5 of pets are birds
Let T = TOTAL number of pets.
So, T/3 = number of dogs
And T/5 = number of birds
Statement 1: There are 30 birds at the pet shop
So, T/5 = 30
This means that T = 150, which means T/3 = 50 (i.e., there are 50 dogs)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: There are 20 more dogs than birds at the pet shop.
In other words, (# of birds) + 20 = # of dogs
We can now write: T/5 + 20 = T/3
IMPORTANT: We could solve this equation for T, but we're not going to waste time doing so. We need only recognize that we could solve the equation for T, which means we can definitely find the value of T/3 (the number of dogs)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
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Brent
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Alternate approach:AAPL wrote:GMAT Prep
In a certain pet shop, 1/3 of the pets are dogs and 1/5 of the pets are birds. How many of the pets are dogs?
1) There are 30 birds at the pet shop.
2) There are 20 more dogs than birds at the pet shop.
To determine the ratio of birds to dogs, plug in a TEST VALUE for the total number of pets.
Let b = the number of birds and d = the number of dogs.
Let the test value for the total number of pets = the LCM of 3 and 5 = 15.
Since 1/5 are birds, b = 1/5 * 15 = 3.
Since 1/3 are dogs, d = 1/3 * 15 = 5.
Thus:
b/d = 3/5.
Statement 1: There are 30 birds at the pet shop
Since b/d = 3/5 = 30/50, b=30 and d=50.
SUFFICIENT.
Statement 2: There are 20 more dogs than birds at the pet shop
The values yielded by statement 1 -- b=30 and d=50 -- are the only values for b and d such that b/d = 3/5 and d=b+20.
SUFFICIENT.
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].
Student Review #1
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