LalaB wrote:

Bunuel wrote:

Algebraic way:

what about a non-algebraic way? )

There are almost always lots of non-algebraic ways to solve a GMAT question. Though in this question, algebraic way in quite straight forward so you may want to stick to it. If you can clearly see an equation in a single variable, it may be wise to use it. Usually, questions involving addition/subtraction of constants (add 15 cows, subtract 15 horses) are best done using algebra.

Anyway, other methods are easy too.

On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?

A. 30

B. 60

C. 75

D. 90

E. 105

We want the difference between number of horses and cows after the transaction. We know that the ratio of horses:cows = 13:7. The difference between the numbers will be a multiple of 6 (= 13 - 7).

Since options (C) and (E) are not divisible by 6, ignore them.

Try option (B). If diff is 60, number of horses and cows is 130 and 70. Initial number must have been 145 and 55 which is not in the ratio 7:3.

Similarly, try other options.

Another method using integral solutions to equations involving two variables:

Consider horses:

You know that 7a - 15 = 13b

7a - 13b = 15

First solution a = 4, b = 1 (by hit and trial). This doesn't work since if initial no. of horses is 7*4 = 28 and cows is 3*4 = 12, when you take away 15 horses, you get 13 horses and when you add 15 cows, you get 27 cows. The new ratio is not 13:7.

Next solution will be a = 4+13 = 17, (and b = 1+7 = 8)

If you are wondering how, check this post:

http://www.veritasprep.com/blog/2011/06 ... -of-thumb/If initial number of horses = 7*17 = 119 and initial number of cows is 3*17 = 51, new no of horses = 104 and new number of cows = 66. The ratio is again not 13:7

Next solution will be a = 4+13+13 = 30

If initial number of horses = 7*30 = 210 and initial number of cows is 3*30 = 90, new no of horses = 195 and new number of cows = 105. The ratio is 13:7. So these must be the right numbers. The diff between number of horses and cows = 195 - 105 = 90

Alternatively, notice that you can make the other equation (using cows) as 3a + 15 = 7b.

You will solve the two simultaneously to get the answer but this is just your algebra approach!

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Karishma

Veritas Prep | GMAT Instructor

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