GATE CS 2015 Set 2 Q.5 (GA Q.5): Analytical and Logical Reasoning

Based on the given statements, select the most appropriate option to solve the given question.

What will be the total weight of 10 poles each of same weight?

Statements:
I. One fourth of the weight of a pole is 5 kg.
II. The total weight of three poles is 160 kg more than the total weight of two poles.

Statement I alone is not sufficient.

Statement II alone is not sufficient.

Either I or II alone is sufficient.

Both statements I and II together are not sufficient.

Official answer and solution

Official answer: C
From: Official GATE 2015 answer key

Solution

Determine whether each statement independently provides sufficient information to calculate the weight of 10 identical poles.

Let $w$ denote the weight of one pole in kilograms. The total weight of 10 poles is $10w$ .

Analyze Statement I:
'One fourth of the weight of a pole is 5 kg.'

\frac{1}{4} w = 5 \implies w = 20\text{ kg}.

Then the total weight of 10 poles is $10 \times 20 = 200\text{ kg}$ .
Hence, Statement I alone is sufficient.

Analyze Statement II:
'The total weight of these poles is 160 kg more than the total weight of two poles.'
Here, 'these poles' refers to the 10 poles mentioned in the question:

10w = 2w + 160 \implies 8w = 160 \implies w = 20\text{ kg}.

Then the total weight of 10 poles is $10 \times 20 = 200\text{ kg}$ .
Hence, Statement II alone is also sufficient.

Since either statement alone provides a unique solution, the correct choice is 'Either I or II alone is sufficient'.

Final answer

Common trap

Assuming both statements are needed together when each one independently determines $w$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 2
Question: 5 of 65, printed as GA Q.5
Section: General Aptitude

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