OGQR 2020: Question No. 216
What is the distance between City A and City C?
- The distance between City A and City B is 75 kilometres.
- The distance between City B and City C is 135 kilometres.
| Source | OGQR 2020 |
| Type | Data Sufficiency |
| Topic | Geometry |
| Sub-Topic | Coordinate Geometry |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
We are given that:
- Three cities – A, B, and C.
We need to find the:
- Distance between city A and C.
S we do not have much information to infer from, let us now analyse the individual statements.
Step 3: Analyse Statement 1
“The distance between City A and City B is 75 kilometres.”
- From this statement, we cannot find the distance between city A and C.
Thus, statement 1 is not sufficient to answer the question.
Step 4: Analyse Statement 2
“The distance between City B and City C is 135 kilometres.”
- From this statement, we cannot find the distance between city A and C.
Thus, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
From statement 1:
- Distance between city A and B = 75 kilometres.
From statement 2:
- Distance between city B and C = 135 kilometres.
Case-1: City A, B, and C are on a straight line and City A is between B and C.
In this case, distance between A and C = 135 – 75 = 60 km
Case-2: City A, B, and C are on a straight line and City A is not between B and C.
In this case, distance between A and C = 135 + 75 = 120 km.
Case- 3: City A, B and C are points of a triangle.
In this case, 135 – 75 < AC < 135 + 75.
Hence, it is not possible to determine the distance between city A and C.
Since we could not find the answer even after combining both the statements together, the correct answer is E.
