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# At what speed was Erik running when he was at the halfway

tagged by: BTGmoderatorLU

00:00

A

B

C

D

E

## Global Stats

Difficult

Source: Veritas Prep

At what speed was Erik running when he was at the halfway point of his route?

(1) Erik's route was 10 miles long and took him 2 hours to complete.
(2) Erik ran at an average speed of 5 miles per hour on the route.

The OA is E.

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BTGmoderatorLU wrote:
Source: Veritas Prep

At what speed was Erik running when he was at the halfway point of his route?

(1) Erik's route was 10 miles long and took him 2 hours to complete.
(2) Erik ran at an average speed of 5 miles per hour on the route.
Statements combined:
Each statement conveys the same information: that the average speed for the whole trip was 5 miles per hour.
The AVERAGE speed for the whole trip does not constrain the speed AT THE HALWAY POINT.
At the halfway point, the speed could be ANY NONNEGATIVE VALUE.
Thus, the two statements combined are INSUFFICIENT.

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BTGmoderatorLU wrote:
Source: Veritas Prep

At what speed was Erik running when he was at the halfway point of his route?

(1) Erik's route was 10 miles long and took him 2 hours to complete.
(2) Erik ran at an average speed of 5 miles per hour on the route.
IMPORTANT: The two statements essentially provide the exact same information.
If it took Erik 2 hours to travel 10 miles, we can conclude that his average speed was 5 miles per hour.
When the two statements provide the same information in a Data Sufficiency question, the correct answer must be either D or E

Target question: At what speed was Erik running when he was at the halfway point of his route?

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: Erik traveled the first 1 mile at 1 mile per hour, and then traveled the last 9 miles at 9 miles per hour. So, at the halfway mark (upon completion of the 5th mile), Erik was running at a speed of 9 mph
Case b: Erik traveled the first 2 miles at 2 miles per hour, and then traveled the last 8 miles at 8 miles per hour. So, at the halfway mark (upon completion of the 5th mile), Erik was running at a speed of 8 mph
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent

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