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.
Please explain how you solved. OA to follow. Thanks much.
GMATPrep: Mary Jim Kate average annual salary
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M - J = 2 * (M - K)California4jx 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.
Please explain how you solved. OA to follow. Thanks much.
You need at least two variables to determine the third and thus find out the average annual salary.
C.
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I answered C as well. But its B. Can't understand how ?
Also, abhinav85 - pls provide ur solutions, which are more valuable than just the answers, which a poster already know in most of the cases.
Thanks.
Also, abhinav85 - pls provide ur solutions, which are more valuable than just the answers, which a poster already know in most of the cases.
Thanks.
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I wasn't sure,thats why i was first checking the answer and if i would have been right i will post the sol later.Also, abhinav85 - pls provide ur solutions, which are more valuable than just the answers, which a poster already know in most of the cases.
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M-j = 2(M-K)
M-J = 2m -2K
2k = M+j
k = M+J/2
1 not sufficient
2.M+j+k/3
now from equation1 we have M+J = 2K
therefore M+J+K/3 = 2K+k/3
=k
hence sufficient ..
hope u got it ..
M-J = 2m -2K
2k = M+j
k = M+J/2
1 not sufficient
2.M+j+k/3
now from equation1 we have M+J = 2K
therefore M+J+K/3 = 2K+k/3
=k
hence sufficient ..
hope u got it ..
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From the question stem:
M-J = 2(M-K)
Simplifying this:
M + J - 2K = 0
M+J = 2K
What we need to find is : (M+J+K)/3
Substituting (M+J) in the average above we get:
(2K + K)/3 = K
So if we know K we can say what is the average of the salaries.
1. Insufficient
2. Sufficient, since we are given kate's salary Hence the answer: B
On first look it definitely looks like C would be the answer, but this is exactly the kind of pitfall we should be careful against in GMAT.
M-J = 2(M-K)
Simplifying this:
M + J - 2K = 0
M+J = 2K
What we need to find is : (M+J+K)/3
Substituting (M+J) in the average above we get:
(2K + K)/3 = K
So if we know K we can say what is the average of the salaries.
1. Insufficient
2. Sufficient, since we are given kate's salary Hence the answer: B
On first look it definitely looks like C would be the answer, but this is exactly the kind of pitfall we should be careful against in GMAT.
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thanks !kaulnikhil wrote:M-j = 2(M-K)
M-J = 2m -2K
2k = M+j
k = M+J/2
1 not sufficient
2.M+j+k/3
now from equation1 we have M+J = 2K
therefore M+J+K/3 = 2K+k/3
=k
hence sufficient ..
hope u got it ..
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thanks.atulkumar79 wrote:From the question stem:
M-J = 2(M-K)
Simplifying this:
M + J - 2K = 0
M+J = 2K
What we need to find is : (M+J+K)/3
Substituting (M+J) in the average above we get:
(2K + K)/3 = K
So if we know K we can say what is the average of the salaries.
1. Insufficient
2. Sufficient, since we are given kate's salary Hence the answer: B
On first look it definitely looks like C would be the answer, but this is exactly the kind of pitfall we should be careful against in GMAT.
I am going to try my hand at explaining how I would approach this problem.
We know that Mary makes the most, Kate makes the second most, and Jim makes the least simply by interpreting that if the difference is greater between Jim and Mary than it is between Kate and Mary. So, plot down for order of salary ..... M K J
I would normally approach this using algebray but the "twice as much statement" jumped out at me. Just by looking at the order and being asked for an average, I can determine that K = the average amount because if if M-K is half as large as M-J we know that K-J equals M-K hence K is exactly in the middle of M and J and is thus the average of M and J. Hence all we need to know is K's salary. Option 1 can be tested using any number you choose to prove insufficient info which leaves us with option B.
We know that Mary makes the most, Kate makes the second most, and Jim makes the least simply by interpreting that if the difference is greater between Jim and Mary than it is between Kate and Mary. So, plot down for order of salary ..... M K J
I would normally approach this using algebray but the "twice as much statement" jumped out at me. Just by looking at the order and being asked for an average, I can determine that K = the average amount because if if M-K is half as large as M-J we know that K-J equals M-K hence K is exactly in the middle of M and J and is thus the average of M and J. Hence all we need to know is K's salary. Option 1 can be tested using any number you choose to prove insufficient info which leaves us with option B.
I am going to try my hand at explaining how I would approach this problem.
We know that Mary makes the most, Kate makes the second most, and Jim makes the least simply by interpreting that if the difference is greater between Jim and Mary than it is between Kate and Mary. So, plot down for order of salary ..... M K J
I would normally approach this using algebray but the "twice as much statement" jumped out at me. Just by looking at the order and being asked for an average, I can determine that K = the average amount because if if M-K is half as large as M-J we know that K-J equals M-K hence K is exactly in the middle of M and J and is thus the average of M and J. Hence all we need to know is K's salary. Option 1 can be tested using any number you choose to prove insufficient info which leaves us with option B.
We know that Mary makes the most, Kate makes the second most, and Jim makes the least simply by interpreting that if the difference is greater between Jim and Mary than it is between Kate and Mary. So, plot down for order of salary ..... M K J
I would normally approach this using algebray but the "twice as much statement" jumped out at me. Just by looking at the order and being asked for an average, I can determine that K = the average amount because if if M-K is half as large as M-J we know that K-J equals M-K hence K is exactly in the middle of M and J and is thus the average of M and J. Hence all we need to know is K's salary. Option 1 can be tested using any number you choose to prove insufficient info which leaves us with option B.
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This question is a great illustration of how logic and common sense can be a more powerful tool than algebra on the GMAT.California4jx 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.
Please explain how you solved. OA to follow. Thanks much.
Let's start as we always do, by focusing on the question stem:
Q: what's the average of the three salaries?
What do we know? M is biggest and, since the gap between M and J is bigger than the gap between M and K, the order is M > K > J.
Further, M-J is twice as much as M-K. So, if the gap between M and K is x, the gap between M and J is 2x. Let's plot on a number line (smallest on the left, as always):
J ------ 2x ------- M
K ----x---M
Looking at the relationships, we can see that the distance from J to K is also x; in other words, K is right in the middle of J and M, making it the average of the 3 salaries.
So, we can rephase the question: what's the value of K?
(1) gives us the value of J. No way to deduce K from that info, since we don't know x.
(2) gives us the value of K - exactly what we needed, sufficient.
(2) is suff, (1) isn't: choose B.
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Nice question!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 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 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
Answer = B
Cheers,
Brent
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I'd use BTG's tagging feature to look for questions tagged as DS questions AND as statistics questions.paml wrote:Can anyone recommend similar problems (preferably from one of the Official Guides) to this one that I can practice with?
Here are all of the questions tagged as statistics questions: https://www.beatthegmat.com/forums/tags/ ... statistics
Search the list and check those tagged as DS questions too. That might lead you to some similar questions.
Cheers,
Brent