Source: GMAT Prep
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf k. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf k weighs 20 pounds.
The OA is A.
44 lightest books in J( in any order), middle "HEAVIEST IN J", 44 heaviest boxes in k.
FROM ONE ... SUFFICIENT.
FROM TWO,
We can deduct that the median is lower than 20 but can't know exactly how much.
Hence, A is the correct answer.
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Each of the 45 boxes on shelf J weighs less than each of the
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Brent@GMATPrepNow
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Target question: What is the median weight of 89 boxes on these shelves?AAPL wrote:Source: GMAT Prep
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf k. What is the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf k weighs 20 pounds.
Given: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on the shelf K.
Let J1 be the weight of the lightest box on shelf J.
Let J2 be the weight of the 2nd lightest box on shelf J.
.
.
.
Let J45 be the weight of the heaviest box on shelf J.
Let K1 be the weight of the lightest box on shelf K.
Let K2 be the weight of the 2nd lightest box on shelf K.
etc.
So, the given information tells us that J1 < J2 < J3 < ... < J45 < K1 < K2 < ...< K44
Since the 89 boxes are now arranged in ascending order (according to weight), the median weight will be the weight of the middle box.
That is, the median weight, will be the weight of the 45th box.
So, we can REPHRASE the target question....
REPHRASED target question: What is the weight of box J45?
Statement 1: The heaviest box on shelf J weighs 15 pounds.
PERFECT! Box J45 is the heaviest box on shelf J
So, box J45 weighs 15 pounds.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: The lightest box on shelf K weighs 20 pounds.
This tells us that box K1 weighs 20 pounds.
This does not help us find the weight of box J45
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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Brent
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Hi NandishSS,
This is a great 'concept' question, meaning that you don't really have to do any math to answer it as long as you understand the concepts involved.
We're told that EACH of the 45 boxes on shelf J weighs LESS than EACH of the 44 boxes on shelf K. We're asked for the MEDIAN weight of the 89 boxes.
To start, the 'median box' will be the 45th box. Since each of the boxes on shelf J weigh LESS than each of the boxes on shelf K, the 'heaviest' box on shelf J will be the median. If we have that one value, then we can answer the question.
1) The heaviest box on shelf J weighs 15 pounds.
This Fact gives us exactly what we need to answer the question.
Fact 1 is SUFFICIENT
2) The lightest box on shelf K weighs 20 pounds.
Unfortunately, this Fact doesn't tell us anything about the weights of the boxes on shelf J. Maybe the median is 19 pounds, but it could just as easily be 18 pounds, 17 pounds, 16.5 pounds, etc.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This is a great 'concept' question, meaning that you don't really have to do any math to answer it as long as you understand the concepts involved.
We're told that EACH of the 45 boxes on shelf J weighs LESS than EACH of the 44 boxes on shelf K. We're asked for the MEDIAN weight of the 89 boxes.
To start, the 'median box' will be the 45th box. Since each of the boxes on shelf J weigh LESS than each of the boxes on shelf K, the 'heaviest' box on shelf J will be the median. If we have that one value, then we can answer the question.
1) The heaviest box on shelf J weighs 15 pounds.
This Fact gives us exactly what we need to answer the question.
Fact 1 is SUFFICIENT
2) The lightest box on shelf K weighs 20 pounds.
Unfortunately, this Fact doesn't tell us anything about the weights of the boxes on shelf J. Maybe the median is 19 pounds, but it could just as easily be 18 pounds, 17 pounds, 16.5 pounds, etc.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
