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07 May 2025, 00:30
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
79% (02:07) correct
21%
(01:51)
wrong
based on 53
sessions
History
Date
Time
Result
Not Attempted Yet
A man travelled from one city to another. What is the distance between the two cities?
(1) He travelled the first 1/4 of his distance at a uniform speed of 15 miles per hour. Thereafter, he increased his speed to 20 miles per hour.
(2) The time for which he travelled at 20 miles per hour was 5 hours greater than the time for which he travelled at 15 miles per hour.
(1) He travelled the first 1/4 of his distance at a uniform speed of 15 miles per hour. Thereafter, he increased his speed to 20 miles per hour.
(2) The time for which he travelled at 20 miles per hour was 5 hours greater than the time for which he travelled at 15 miles per hour.
07 May 2025, 00:46
Kudos
Bookmarks
Bunuel
Question: Distance = ?
Statement 1: He travelled the first 1/4 of his distance at a uniform speed of 15 miles per hour. Thereafter, he increased his speed to 20 miles per hour.
This information can tell us the average speed but not the distance in total hence
NOT SUFFICIENT
Statement 2: The time for which he travelled at 20 miles per hour was 5 hours greater than the time for which he travelled at 15 miles per hour.
if Time of travel 15 mph = T
then, Time of travel 20 mph = T+5
Distance = 15T + 20*(T+5)
NOT SUFFICIENT
COmbning the statements
DIstance ratio 15 and 20 = (1/4) : (3/4) = 1/3
Therefore, 15T = (1/3)*(T+5)
SUFFICIENT
Answer: Option C
07 May 2025, 02:17
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❓Question:
A man travelled from one city to another.
What is the distance between the two cities?
🔹 Statement (1):
He travelled the first 1/4 of his distance at 15 mph, and the remaining 3/4 at 20 mph.
🧠 Let's define total distance = D
Then:
We only have proportions and speeds, no actual time or distance value. 😐
👉 Statement (1) is NOT sufficient ❌
🔹 Statement (2):
The time at 20 mph was 5 hours more than the time at 15 mph.
Let’s assign variables again:
We don’t know the proportion of the journey at each speed (that was in Statement 1!).
So with just this, too many unknowns.
👉 Statement (2) is NOT sufficient ❌
🔹 Combine (1) and (2):
From (1):
Time at 20 mph is 5 hours more than at 15 mph:
So:
(3D)/80 = D/60 + 5
Now we solve:
Multiply all terms by 240 to eliminate denominators:
(3D/80) * 240 = (D/60) * 240 + 5 * 240
→ 9D = 4D + 1200
→ 5D = 1200
→ D = 240 miles
🎉 BOOM! We got the distance! ✅
👉 Statements (1) and (2) TOGETHER are sufficient
✅ Final Answer:
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 🎯💯
📌 Summary:
In rate/time/distance problems, always define variables and remember:
Distance = Speed × Time
Watch out for proportions, time differences, and units! 🕒📏
A man travelled from one city to another.
What is the distance between the two cities?
🔹 Statement (1):
He travelled the first 1/4 of his distance at 15 mph, and the remaining 3/4 at 20 mph.
🧠 Let's define total distance = D
Then:
- Time at 15 mph = (1/4)D ÷ 15 = D/60
- Time at 20 mph = (3/4)D ÷ 20 = (3D)/(80)
We only have proportions and speeds, no actual time or distance value. 😐
👉 Statement (1) is NOT sufficient ❌
🔹 Statement (2):
The time at 20 mph was 5 hours more than the time at 15 mph.
Let’s assign variables again:
- Let time at 15 mph = t
- Then time at 20 mph = t + 5
We don’t know the proportion of the journey at each speed (that was in Statement 1!).
So with just this, too many unknowns.
👉 Statement (2) is NOT sufficient ❌
🔹 Combine (1) and (2):
From (1):
- First 1/4 of D at 15 mph → time = D/60
- Remaining 3/4 of D at 20 mph → time = (3D)/80
Time at 20 mph is 5 hours more than at 15 mph:
So:
(3D)/80 = D/60 + 5
Now we solve:
Multiply all terms by 240 to eliminate denominators:
(3D/80) * 240 = (D/60) * 240 + 5 * 240
→ 9D = 4D + 1200
→ 5D = 1200
→ D = 240 miles
🎉 BOOM! We got the distance! ✅
👉 Statements (1) and (2) TOGETHER are sufficient
✅ Final Answer:
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 🎯💯
📌 Summary:
- Statement 1 ❌: Gives speeds and distance ratios, but no time.
- Statement 2 ❌: Gives time difference, but no segment breakdown.
- Combined ✅: Allows us to form and solve an equation!
In rate/time/distance problems, always define variables and remember:
Distance = Speed × Time
Watch out for proportions, time differences, and units! 🕒📏
Bunuel
