OG 2016 DATA Sufficiency #135
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Hi AshB,
When posting questions in the Forums, you should post the entire question.
For this particular prompt, you should also explain why you disagree with the solution.
GMAT assassins aren't born, they're made,
Rich
When posting questions in the Forums, you should post the entire question.
For this particular prompt, you should also explain why you disagree with the solution.
GMAT assassins aren't born, they're made,
Rich
A list contains 3 different numbers. Does the median of the 3 numbers equal the average(arithmetic mean) of the 3 numbers?
1) The range of 3 numbers is equal to twice the difference between the greatest number and the median
2) The sum of the 3 numbers is equal to 3 times one of the numbers
OG solves 2) by deriving that all the 3 numbers in the list are equal, which contradicts the question stem information: "different numbers"? Does this happen often on GMAT?
1) The range of 3 numbers is equal to twice the difference between the greatest number and the median
2) The sum of the 3 numbers is equal to 3 times one of the numbers
OG solves 2) by deriving that all the 3 numbers in the list are equal, which contradicts the question stem information: "different numbers"? Does this happen often on GMAT?
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When numbers are EVENLY SPACED, the median is equal to the average.AshB wrote:A list contains 3 different numbers. Does the median of the 3 numbers equal the average(arithmetic mean) of the 3 numbers?
1) The range of 3 numbers is equal to twice the difference between the greatest number and the median
2) The sum of the 3 numbers is equal to 3 times one of the numbers
Question stem, rephrased:
Are the 3 numbers evenly spaced?
Statement 1:
Let the 3 numbers, in ascending order, be a, b and c.
Range = biggest - smallest = c-a.
Difference between the greatest number and the median = c-b.
Since the range is equal to twice the difference between the greatest number and the median, we get:
c-a = 2(c-b)
c-a = 2c - 2b
2b = a + c
b = (a+c)/2.
Since b is equal to the average of a and c, b must be HALFWAY between a and c, implying that a, b and c are EVENLY SPACED.
SUFFICIENT.
Statement 2:
Case 1: One of the numbers is 1.
If the sum is equal to three times 1, then the sum is equal to 3.
Options for the 3 numbers:
0, 1, 2 --> 0+1+2 = 3.
-1, 1, 3 --> -1+1+3 = 3
-10, 1, 12 --> -10+1+12 = 3.
In every case, the 3 numbers are EVENLY SPACED.
Case 2: One of the numbers is 10.
If the sum is equal to three times 10, then the sum is equal to 30.
Options for the 3 numbers:
9, 10, 11 --> 9+10+11 = 30.
0, 10, 20 --> 0+10+20 = 30.
-10, 10, 30 --> -10+10+30 = 30.
In every case, the 3 numbers are EVENLY SPACED.
As Cases 1 and 2 illustrate, for the sum to be equal to three times one of the numbers, the 3 numbers must be EVENLY SPACED.
SUFFICIENT.
The correct answer is D.
Last edited by GMATGuruNY on Sun Dec 27, 2015 10:36 pm, edited 1 time in total.
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The OG's explanation for Statement 2 is faulty.AshB wrote:OG solves 2) by deriving that all the 3 numbers in the list are equal, which contradicts the question stem information: "different numbers"? Does this happen often on GMAT?
Since the prompt requires that the 3 numbers be DIFFERENT, the explanation for Statement 2 should not discuss cases in which the 3 numbers are EQUAL.
As my solution above shows, statement 2 can be satisfied by 3 different numbers.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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