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# What is the distance between City A and City C ?

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Re: What is the distance between City A and City C ? [#permalink]
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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.
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Re: What is the distance between City A and City C ? [#permalink]
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Bunuel
What is the distance between City A and City C ?

(1) The distance between City A and City B is 75 kilometers.
(2) The distance between City B and City C is 135 kilometers.

(1) We need information for A to C. Insufficient.

(2) We need information for A to C. Insufficient.

Considering Both:

The orientation of C from B or A is not given. It can in between A to B, right to B, if in the right to B then the distance will be 75+135=205 km but it can be downward B then we can't determine the distance. Insufficient.

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Re: What is the distance between City A and City C ? [#permalink]
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Re: What is the distance between City A and City C ? [#permalink]
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