Claire has a total of 99 pets consisting of gerbils and hamsters only.

Question

Claire has a total of 99 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 28 males altogether, how many gerbils does Claire have?

(A) 39
(B) 50
(C) 54
(D) 57
(E) 60

Kudos for a correct solution.

(A) 39
(B) 50
(C) 54
(D) 57
(E) 60

Kudos for a correct  solution .

Hemavakade · Answer

Answer = E

anudeep133 · Answer

Solutions :  Thinking critically can save a lot of time in these kind of questions.
Question says One-quarter of the gerbils are male i.e 1/4 of gerbils. So, no. of gerbils is a multiple of 4. So only option is E ie 60.

G/4 + H/3 = 28-->(1) and 3G/4 + 2H/3 = 71-->(2)
(2)-2(1) ==> G/4 = 15 ==> G=60

Option E

nicwin4 · Answer

I used back-solving and got the answer as E.

G= 1/4M; H= 1/3M 
where they asked for the total number of G

The only number in the answer choices that 4 divides is 60

Therefore, 1/4*60= 15; 
 1/3*39= 13 (99-60= 39)
 15+13= 28

Bunuel · Answer

Gmatprepnow Official Solution:

The good news: the GMAT Quantitative section tests concepts that you already learned in school. The bad news: if you insist on always solving GMAT math questions using the same techniques you learned in school, you’ll likely score lower than you should score.
 
The problem is that achieving a high math score in school requires certain strategies that, if applied to the GMAT, can actually harm your score. To see what I mean, try answering this question:

When solving GMAT math question, it’s important to recognize (and embrace!) two major differences between school math and GMAT math:

1. School math questions are seldom multiple choice, and GMAT math questions are always multiple choice.
2. In school, your math teachers typically want you to show all of your work. So, even if you determine the correct answer, you won’t receive full credit unless you show all of your work. The GMAT has no such nonsense; a correct response is a correct response.
 
So, a student encountering the “Gerbils and Hamsters” question in school would be forced to assign variable expressions to unknown values, create one or more equations, and so on. Fortunately, on the GMAT, we can use the answer choices to our advantage and plug in each value to see which one satisfies the given conditions in the question.
 
Now, at this point, you may be thinking (sarcastically), “Gee, I’ve never heard of plugging in the answer choices. Thanks Brent!”
 
Fine, plugging in the answer choices isn’t some remarkable new strategy that I just invented, but this poor strategy is, all too often, treated like a second-class strategy. It’s considered Plan B at best and, for many, it seems like a copout. In fact, after using this strategy to solve questions in class, I’ve had students scrunch their noses in disgust and ask, “What’s the mathematical solution?” These same students often have a hard time accepting the fact that most GMAT math question can be solved using more than one approach, and the best approach is not always the one learned in school.  The best approach is the one that allows us to determine the answer as quickly as possible. 
 
The fact of the matter is that the original question can be solved in 10 seconds. We’re told that ¼ of the gerbils are male, and the question asks us to determine the number of gerbils. Answer choice A says there are 39 gerbils, but ¼ of 39 is 9¾, and it’s impossible to have 9¾ male gerbils. In order to get an integer value for the number of male gerbils, the total number of gerbils must be divisible by 4. Since only answer choice E is divisible by 4, it must be the correct answer.
 
Of course, I specifically created that question to illustrate the utility of plugging in the answer choices, so one might argue that it’s unrealistic to think that this strategy always yields 10-second solutions, and I agree. However, it’s equally unrealistic to think that this strategy never yields the fastest solution. What’s important here is that you keep this strategy handy at all times. 
 
So, whenever you encounter a GMAT math question, you should always consider plugging in the answer choices as an option before choosing an approach.

Heseraj · Answer

Let the number of G be X and the number of H be 99-X

x= \frac{1}{4} m + \frac{3}{4} f

and  99-x= \frac{1}{3} m + \frac{2}{3} f

Therefore, one has

\frac{1}{4}X + \frac{1}{3} (99-X) = 28 => \frac{1}{4} x + 33 -\frac{1}{3} X = 28 => \frac{3-4}{12} X = 28-33 => \frac{-1}{12} X = -5 => X= 12*5 = 60

Hit the Kudos if you liked the Solution.

shashankism · Answer

Solution 1(Takes 30 second) : There are total 99 pets, pets may be gebrils or hamsters.
Now 1/4th of gebrils are male.

If we check the answer.. we see only 60 is divisible by 4 and hence E is the answer..

Solution 2(Takes 2 minutes) : G + H = 99
1/4 G + 1/3 H = 28 
3G + 4H = 28* 12 = 336

H = 39
G = 99 - 39 = 60

Answer E

bumpbot · Answer

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Claire has a total of 99 pets consisting of gerbils and hamsters only.

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