VERITAS PREP OFFICIAL SOLUTION:

Type of Question: Yes/No. This question asks whether the value of b (symbol) c is greater than 10.

Given information from the question stem: This question asks you to determine “yes” or “no” is b symbol C is greater than 10. Now you are told that the symbol is an “operation” and you might think that this means addition, subtraction, multiplication, and division only. But it does not. The symbol can really require you to take any mathematical action. It could have you add a million and then subtract 2 million. So do not make any assumptions here.

Statement 1: This statement tells you what the symbol represents. It says that for any two numbers “x symbol y” you square each of the numbers and then add them. This tells you what action the symbol requires. However, unless you know what the numbers are that you are squaring, you cannot get a definite answer. For example, if x and y each equal 1, then answer will be “no” because 1^2 + 1^2 = 2. But if x and y are each large numbers like 10, then the answer will be “yes” because 102 + 102 =200. Because you don’t know the value of b and c, this statement is not sufficient.

Statement 2: This statement gives you values for b and c. It may seem that this statement is sufficient because each standard operation—multiplication, division, addition, subtraction—will yield a result of less than 10. However, as mentioned above, the symbol does not necessarily represent one of these four operations and Statement 1 makes this possibility very clear. Since you do not know what to do with the values for b and c, you cannot determine what b symbol c will equal. This statement is not sufficient.

Together: Taken together the two statements provide you with the values for b and c as well as the action that you should perform with these numbers. You take 2^2 + 1^2 which equals 3, so the answer to the question is “no” b symbol c is not larger than 10. Together the statements are sufficient. The answer is C.
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