Data Sufficiency

NandishSS wrote: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.

OA:A

Source: GMATPrep EP1

Hi NandishSS,

We have a total of 89 boxes, thus the median weight would the weight of the 45th box if, according to weight, the boxes are arranged in an ascending or in descending order.

Since each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K, the median box lies in shelf J.

If we get the weight of the 45th box (the heaviest of them) in shelf J, we have the median.

Statement 1: The heaviest box on shelf J weighs 15 pounds.

This is what we are looking for. Median weight of 89 box = 15 lbs. Sufficient.

Statement 2: The lightest box on shelf K weighs 20 pounds.

We are not interested in self K. 20 lbs is the weight of the 46th box--not of any help! Insufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on the shelf K. What is the median weight of 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.

Target question: What is the median weight of 89 boxes on these shelves?

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

Cheers,
Brent

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

NandishSS wrote: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.

We are given that each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K and need to determine the median weight of the 89 boxes.

We may recall that when the boxes are ordered from least weight to greatest, the box with the median weight is in the (89 + 1)/2 = 90/2 = 45th position. Thus, the box with the median weight is on shelf J and it is the heaviest box on shelf J.

Statement One Alone:

The heaviest box on shelf J weighs 15 pounds.

Since the heaviest box on shelf J weighs 15 pounds, the 45th box weighs 15 pounds. Since the 45th box is the median of the boxes, the median weight is 15. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The lightest box on shelf K weighs 20 pounds.

Since the lightest box on shelf K weighs 20 pounds, when the boxes on both shelves are ordered from least to greatest, the 46th box weighs 20 pounds. However, we do not have enough information to determine the weight of the 45th box, i.e., the median weight.

Answer: A