A farmer has a total of 60 pigs, cows, and horses on his farm. How

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This question asks for the number of pigs on the farm.

Given information in the question stem or diagram: Pigs (P) + Cows (C) + Horses (H) = 60. P + C + H = 60.

Statement 1: H:C = 2:9. This statement is not sufficient because it does not give an exact number of cows and horses, so it is not possible for you to determine the number of pigs. However, you should check to make sure that multiple cases are possible given a total of 60 animals. For instance, you could have 2 horses, 9 cows, and 49 pigs; or it could be 4 horses, 18 cows, and 38 pigs. Not sufficient, so you can eliminate answers A and D. Note: if the total was, for instance, 20 animals, then this statement would be sufficient because it would be impossible for there to be more than 2 horses and 9 cows (or total would be over 20); this would leave 9 pigs and a definite answer to the question.

Statement 2: C > 36. This statement also does not give you specific numbers for any of the animals, so it is clearly insufficient and the answer is C or E. However, you should already be considering the “Why Are You Here?” strategy and wondering how this information might matter when combined with the first statement.

Together: Taken together you know that C > 36 and H:C = 2:9. The hidden fact on many ratio questions is that the number of animals (or children or photocopiers) must be an integer. There is no such thing as 1/3 of a horse. This means that you have more information here than you might think. From the two statements together, you know that C must be a multiple of 9 and must be greater than 36. The next multiple of 9 is 45. If there are then 45 cows there are 10 horses because of the ratio in Statement 1. That leaves a total 5 pigs since P + C + H = 60. What about 54 cows? That is a multiple of 9. This is not possible, because 54 cows would mean 12 horses, and that is over 60 animals. Together the two statements are sufficient and there are 5 pigs on the farm. The correct answer is C. Note: People miss this because they under-leverage the information given in these statements and do not take the hint given in the second statement.

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