BTGModeratorVI wrote: ↑Fri Aug 14, 2020 1:03 pm
Ann and Bea leave X-ville at the same time and travel towards Y-ville, which is 70 kilometers away. Their individual speeds are constant, but Ann’s speed is greater than Bea’s speed. Upon reaching Y-ville, Ann immediately turns around and drives toward X-ville until she meets Bea. When they meet, how far has Bea traveled?
1) Ann’s speed is 30 kilometers per hour greater than Bea’s speed
2) Ann’s speed is twice Bea’s speed
Answer:
B
Source: GMAT Prep Now
Target question: When they meet, how far has Bea traveled?
Statement 1: Ann’s speed is 30 kilometers per hour greater than Bea’s speed
We can see that is not sufficient if we examine some EXTREME CASES:
Case a: Ann's speed = 30.00000001 kilometers per hour, and Bea's speed = 0.00000001 kilometers per hour. In this case,
Bea travels almost 0 kilometers
Case b: Ann's speed = 40 kilometers per hour, and Bea's speed = 10 kilometers per hour. In this case,
Bea travels more than 0 kilometers
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Ann’s speed is twice Bea’s speed
One option here is to test a bunch of cases to see what happens. If we do this, we'll find that we keep getting the same answer to the
target question
Alternatively, we can use some algebra:
Let B = the distance Bea traveled
Let R = Bea's speed.
NOTE: the total distance from Townville to Villageton and then BACK TO Townville = 140 kilometers.
So, 140 - B = the distance Ann traveled
And 2R = Ann's speed (since her speed is TWICE Bea's speed)
From here, let's create a WORD EQUATION that uses distance and speed.
How about:
Ann's travel time =
Bea's travel time
Time = distance/rate, so we get:
(140 - B)/2R =
B/R
Cross multiply to get: (B)(2R) = (R)(140 - B)
Expand: 2BR = 140R - BR
Add BR to both sides: 3BR = 140R
Divide both sides by R to get: 3B = 140
Divide both sides by 3 to get: B = 140/3
In other words,
Bea traveled 140/3 kilometers
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
