For the median, we need to know the center most length when arranged in order.
given:
Of the 13 logs in shipment X arranged in order, 7th log length is 84 inches
x1, x2, x3, x4, x5, x6, 84, y1, y2, y3, y4, y5, y6
of the 21 logs in shipment Y arranged in order, 11th log length is 85 inches

consider option 1,

The two logs transferred had lengths of 91 and 92 inches, respectively.

for the median we need to know the order. We know these two will be right side of the 84 length log in shipment X.
x1, x2, x3, x4, x5, x6, 84, y1, y2, y3, y4, y5, y6
91 and 92 can come after 84. But we don`t know anything about y1....y6.
if y1...y6 are 84, the median will be 84.
if y1 is 95, then median will be 91.
so we can`t answer from this.

consider option 2,

The longest log that was in shipment x before the transfer had length 90 inches.

x1, x2, x3, x4, x5, x6, 84, y1, y2, y3, y4, y5, 90
we don`t know anything about the lengths of the logs added to the shipment X.
so we can`t answer from this.

consider 1 and 2,
x1, x2, x3, x4, x5, x6, 84, y1, y2, y3, y4, y5, 90, 91, 92
for the above arrangmnet, the median is y1.
But we don`t know the value of y1.
hence, it is E

neotinx wrote:The median length of the 13 logs in shipment x was 84 inches, and the median length of the 21 logs in shipment y was 85 inches. If the two longest logs in shipment Y were transferred to shipment X, what would be the median length, in inches, of the 15 logs in shipment X after the transfer?

1) The two logs transferred had lengths of 91 and 92 inches, respectively.

2) The longest log that was in shipment x before the transfer had length 90 inches.

Target question: What is the median length of the 15 logs in shipment X after the transfer?

Let's jump straight to statements 1 and 2 combined. Here's what we know:
Originally, shipment X contained 13 logs, and the longest log measured 90 inches.
The median of the 13 log lengths is 84 inches.
So, if we arrange the 13 log lengths in ascending order, we see that the middle length (the 7th value) is 84.
Visual: ?, ?, ?, ?, ?, ?, 84, ?, ?, ?, ?, ?, 90,

Then we added two logs with lengths of 91 and 92 inches.
Now that we have 15 lengths, the median will be the 8th value in the list of ascending values.
Visual: ?, ?, ?, ?, ?, ?, 84, ?, ?, ?, ?, ?, 90, 91, 92

As you can see, the 8th value can have any value from 84 to 90 inclusive.
As such, the combined statements are not sufficient to answer the target question.

Answer = E

Cheers,
Brent