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Re: In a certain year, the difference between Mary's and Jim's
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09 Aug 2015, 13:10

What is the purpose of the question stating that "Mary's annual salary was the highest of the 3 people"? I was able to solve the problem without using this piece of information so am wondering if I am missing something since GMAT questions usually only give you information that you need to use. Thanks!

In a certain year, the difference between Mary's and Jim's
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15 Sep 2015, 18:27

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A more simpler solution is given below

Given is \(M - J = 2 (M - K)\)

\(M - J = 2M - 2K\)

Bringing everything to one side, \(0 = 2M - 2K - M + J\)

\(0 = M + J - 2K\)

so, \(M + J = 2K\)

Now, adding \(K\) to both the sides, \(M + J + K = 3K\)

and finally dividing by 3 gives \(\frac{(M + J + K)}{3} = K\),

So in short, knowing Kate's salary should be sufficient to find the mean of the three salaries

Statement 1. it gives us Jim's salary, but both M & K are unknown - Insufficient Statement 2. It gives us Kate's salary, and so from above - Sufficient

Re: In a certain year, the difference between Mary's and Jim's
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14 Feb 2016, 20:57

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Solution : By question, we got M-J=2(M-K) since M is the greatest of them all, which yields M=2K-J now AM is (M+K+J)/3 => (2K-J+K+J)/3 =>K We require K's value to get the AM A: insuff B: suff Hope it helps.

Re: In a certain year, the difference between Mary's and Jim's
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30 Aug 2016, 07:52

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Top Contributor

4

alimad wrote:

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Let's first deal with the given information. Let J = Jim's salary Let M = Mary's salary Let K = Kate's salary

Notice that the salaries (in ascending order) must be J, K, M Also, if the difference between Mary's and Jim's annual salaries equals twice the difference between Mary's and Kate's annual salaries, then we can conclude that the 3 salaries are equally spaced.

Target question: What was the average annual salary of the 3 people that year?

Statement 1: Jim's annual salary was $30,000 that year. In other words, J = 30,000 So, the three salaries, arranged in ascending order are: 30,000, K, M Plus we know that the 3 salaries are equally spaced. Do we now have enough information to answer the target question? No.

For proof that that we don't have enough information, consider these 2 cases: Case a: J=30,000, K=30,001, M=30,002, in which case the average salary is $30,001 Case b: J=30,000, K=30,002, M=30,004, in which case the average salary is $30,002 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Kate's annual salary was $40,000 that year. In other words, K = 40,000 Perfect! Since the 3 salaries are equally spaced, we can use a nice rule that says, "If the numbers in a set are equally spaced, then the mean and median of that set are equal" Since Kate's salary must be the median salary, we now know that the average salary must be $40,000 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Concentration: Entrepreneurship, General Management

WE: Engineering (Energy and Utilities)

Re: In a certain year, the difference between Mary's and Jim's
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09 Jul 2017, 04:54

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Somehow I solved this in very easy manner. From the question, we can write equation as below. M-J = 2(M-K) , So obviously J earns least . M=2K-J To find average salary, we need first total salary i.e. M+K+J Substitute M =2K-J in above equation, we get Total salary = K Now see at options .. First one doesn't give info about k salary , whereas second one gives.. So answer is B.

Re: In a certain year, the difference between Mary's and Jim's
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10 Jul 2017, 11:32

alimad wrote:

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Let \(M\), \(J\) and \(K\) be the salaries of Mary, Jim and Kate, respectively. We have \(| M - J | = 2| M - K |\), \(M > J\) and \(M > K\) from the conditions of the original questions. And the question asks what is the value of \(\frac{M + J + K}{3}\).

Then we have 3 variables and 1 equation. Thus C is the answer most likely.

This question is a key question by VA method, since it is related to Statistics. By CMT(Common Mistake Type) 4A, we should check the answer A or B too.

Since \(M > J\) and \(M > K\), we have \(M - J = 2(M-K)\) or \(M - J = 2M - 2K\), which is equivalent to \(M + J = 2K\). Thus the question asks what is the value of \(\frac{M + J + K}{3} = \frac{3K}{3} = K\).

Condition 1) From \(J = 30,000\), we can derive the values of \(M\) or \(K\). Thus this is not sufficient.

Condition 2) \(K = 40,000\). This is just the average of \(M\), \(J\) and \(K\) described. Thus this is sufficient.

Therefore, B is the Answer

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

Re: In a certain year, the difference between Mary's and Jim's
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10 Jul 2017, 11:49

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

(1) Jim's annual salary was $30,000 that year. (2) Kate's annual salary was $40,000 that year.

Let's Say Mary's, Jim's and Kate's annual salaries be $X, $Y and $z

given =>> x - y = 2( x - z) so x + y = 2z --- equation (1)

Thing to find out = average of x, y and z = \(\frac{x + y + z}{3}\) -- equation (2)

now substitute equation (1) in the (2) : we get Average = \(\frac{2z + z}{3}\) = z = which is kate's annual salary.

so we just need to find Kate's annual salary which is directly given in statement 2 _________________

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