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Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.

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(1) The sum of Joe's age (in year's) and Jan's age (in years) is 39 x+y = 39(we can have many ways in which we can fill x and y) eg 19+20,15+24 Hence, we cannot arrive at an unique age of Joe. Insufficient

(2) The product of Joe's age (in year's) and Jan's age (in years) is 380 x*y = 380(again we have several ways of giving a value of x and y) eg 19*20,38*10 Hence, we cannot arrive at an unique age of Joe. Insufficient

On combining the two equations, We prime factorize \(380 = 19*2^2*5\) Now we have an option 19,20 which will give a sum of 39 and a product of 380 But we cannot be sure which of the ages is Joe's. It could be either of the ages. Hence since we cannot arrive at an unique solution for the age of Joe, insufficient(Option E)
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You've got what it takes, but it will take everything you've got

(1) The sum of Joe's age (in year's) and Jan's age (in years) is 39

Clearly Insufficient

(2) The product of Joe's age (in year's) and Jan's age (in years) is 380

Clearly Insufficient

Combining 1 & 2:

Without rushing to solve, I know that I can setup equation and solve but there is one problem remains: who is older than the other? There is no statement, for example, that Joe is 3 years more than Jan. Hence, we can't know for sure.

(1) The sum of Joe's age (in years) and Jan's age (in years) is 39 (2) The product of Joe's age (in years) and Jan's age (in years) is 380

ASIDE: I created this question to illustrate a common myth that suggests that 2 equations with 2 variables are always solvable.

Target question:What is Joe's age?

Statement 1: The sum of Joe's age (in years) and Jan's age (in years) is 39 There are several scenarios that satisfy statement 1. Here are two: Case a: Joe is 38 and Jan is 1. In this case, Joe is 38 Case b: Joe is 37 and Jan is 2. In this case, Joe is 37 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The product of Joe's age (in years) and Jan's age (in years) is 380 There are several scenarios that satisfy statement 2. Here are two: Case a: Joe is 38 and Jan is 10. In this case, Joe is 38 Case b: Joe is 380 and Jan is 1. In this case, Joe is 380 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Let x = Joe's age Let y = Jan's age

Statement 1 tells us that x + y = 39, which we can rewrite as y = 39 - x Statement 2 tells us that xy = 380

Replace y in second equation with 39 - x to get: x(39 - x) = 380 Expand: 39x - x² = 380 Rearrange: x² - 39x + 380 = 0 Factor: (x - 20)(x - 19) = 0 So, x = 20 or x = 19 So, Joe is EITHER 20 years old OR 19 years old Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

So, what happened here? We had two equations with 2 variables (y = 39 - x and xy = 380) yet we were unable to determine the value of x. The reason is that one of our equations (xy = 380) is a QUADRATIC equation. The rule that says "we can solve a system of 2 equations with 2 variables" applies only to situations in which the 2 equations are both LINEAR equations. That is, the variables are not raised to any powers greater than 1. Now one might say "But wait, x and y are not raised to powers greater than 1 in the equation xy = 380." This is true, however, we have a product of 2 variables in xy, so we can think of it as variable², which makes is a QUADRATIC.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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