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Math Expert V
Joined: 02 Sep 2009
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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ssriva2 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.

Hi Bunuel,
I am also getting A as suff.

M-J=2(M-K)
Thus,K=2J
Now M-J-2(M-K)
Substitute K=2J
WE GET 3J=M
So M+J+K/3=3J+J+2J/3
2J=This is average,and we are given J,so suff

How do you get K=2J from M-J=2(M-K)?
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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1
1
draw a number line to solve this question within 30 seconds
Intern  Joined: 30 Jun 2015
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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1
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!
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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Hchan145 wrote:
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!

Hello Hchan145
Looks like you are right: this is unneeded piece of information.
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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3
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

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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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My Approach:

|M-J| = 2|(M-K)| as given in the question. I took modulus because it was not specified which one would be greater.
Then they say M is greater.

so M-J = 2M-2K
2K= M+J or K = (M+K)/2;
As K is the average of the two numbers, M and J,
the average of M, K and J is K

so Stmnt 2 gives directly the value of K
Stmnt 1 doesnot. So answer is B
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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as given;
M-J = 2(M-K)
M-J-2M+2K=0
(add m+j+k on both sides)
M-J-2M+2K+M+J+K=M+J+K
3K=M+J+K
OR (M+J+K)/3 = K
HENCE B IS SUFFICIENT.
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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1
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.
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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1
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.

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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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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.
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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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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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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Let the difference of Salary between Mary-Karen=X

Than as per question stem
Difference of salary between
Mary-Jim=2x

This means that the differen has doubled.

When can this happen?

If salary of Jim is less than Karen's

Let us see this with an example.

Let's say the difference between Salary

Mary-Karen=10

Then difference between salary of Mary-Jim=20

Let's see how can above happen

Simple plugging another set of no's

Mary-Karen=50-40=10
Mary-Jim=50-30=20
Or
Mary-Karen=60-50=10
Mary-Jim=60-40=20

So now the salary looks like this

Mary>Karen>Jim and since Karen is the middle no of the set it is also the average of the set.

Hence statement 2 is sufficient.

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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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Hi Brent - with given info how could we conculde that salaries are evenly spaced. I am not able figure out. Please help.
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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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Re: In a certain year, the difference between Mary's and Jim's annual sala  [#permalink]

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_________________ Re: In a certain year, the difference between Mary's and Jim's annual sala   [#permalink] 15 Jul 2019, 04:49

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