Which weighs more, a cubic unit of water or a cubic unit of liquid X ?

Question: Is wt of water > weight of X for smae volume?

Statement 1: A cubic unit of water weighs more than 1/3 cubic unit of liquid X.

If 1 cubic unit of water is heavier than 1/3 cubic unit of other then we can NOT be conclusive of comparison

NOT SUFFICIENT

Statement 2: A cubic unit of liquid X weighs less than 3 cubic units of water.
dividing both sides by 3
If 1 cubic unit of water is heavier than 1/3 cubic unit of other then we can NOT be conclusive of comparison

NOT SUFFICIENT


Combinig the statements

Both statements have same information hence

If 1 cubic unit of water is heavier than 1/3 cubic unit of other then we can NOT be conclusive of comparison

NOT SUFFICIENT


Answer: Option E

By statement 1, A cubic unit of water weighs > 1/3 cubic unit of liquid X

=> 3 cubic unit of water weighs > 1 cubic unit of liquid X

But we don't know whether a cubic unit of water is more or less than a cubic unit of liquid X.
Hence, statement 1 alone is insufficient.

By statement 2, 3 cubic unit of water weighs > 1 cubic unit of liquid X

This is same as we got in statement 1 , hence statement 2 alone is also insufficient.

Also, as both statements are same we can't answer by combining both.

Thus OA is E

Step 1: Analyse Question Stem

We have been told about one cubic unit of water and one cubic unit of a certain liquid X.
We have to find out which one of the two has more weight.

Cubic unit of a liquid sounds a little abstract, so, you could introduce your own unit to understand it better.
I would use ‘Cubic centimetres’. Therefore, we have to find out which one of the two has more weight – 1 CC of water OR 1 CC of liquid X.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: A cubic unit of water weighs more than \(\frac{1}{3}\) cubic unit of liquid X.

If 1 cc of liquid X weighs 27gms and 1 cc of water weighs 10gms, information given in statement 1 is satisfied.
In this case, 1 cc of liquid X weighs more.

If 1 cc of liquid X weighs 9gms and 1 cc of water weighs 10gms, information given in statement 1 is satisfied.
In this case, 1 cc of water weighs more.

The data in statement 1 is insufficient to find out which one of the two is heavier.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: A cubic unit of liquid X weighs less than 3 cubic units of water.

If 1 cc of liquid X weighs 27gms and 1 cc of water weighs 10gms, information given in statement 1 is satisfied.
In this case, 1 cc of liquid X weighs more.

If 1 cc of liquid X weighs 9gms and 1 cc of water weighs 10gms, information given in statement 1 is satisfied.
In this case, 1 cc of water weighs more.

The data in statement 2 is insufficient to find out which one of the two is heavier.
Statement 2 alone is insufficient. Answer option B can be eliminated.


Step 3: Analyse Statements by combining

From statement 1: A cubic unit of water weighs more than 1/3 cubic unit of liquid X.
From statement 2: A cubic unit of liquid X weighs less than 3 cubic units of water.

If 1 cc of liquid X weighs 27gms and 1 cc of water weighs 10gms, information given in statement 1 and 2 is satisfied.
In this case, 1 cc of liquid X weighs more.

If 1 cc of liquid X weighs 9gms and 1 cc of water weighs 10gms, information given in statement 1 and 2 is satisfied.
In this case, 1 cc of water weighs more.

The combination of statements is insufficient to find out which one of the two is heavier.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.

The correct answer option is E.
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