TANCET 2014 DS Question 71: Cubes
Directions for Data Sufficiency Questions
The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:
 Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
 Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
 Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
 Choice 4 if each statement ALONE is sufficient.
 Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.
Question
Is rectangular block B a cube?
 Statement 1: At least two faces of the rectangular block B are squares.
 Statement 2: The volume of the rectangular block B is 64.
Correct Answer Choice (5). Statements (1) and (2) TOGETHER are not sufficient.
Explanatory Answer  step by step

What do we know from the Question Stem?
Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.
What kind of an answer will the question fetch?
The question is "Is the rectangular block B a cube?"
The answer to an “is” question should be “yes” or “no”.
When is the data sufficient?
If we are able to come up with a CONCLUSIVE answer – a DEFINITE YES or a DEFINITE NO, the data is sufficient.
If we are not able to come up with a DEFINITE answer – if we find that the block could be a cube and need not be a cube, the data is NOT sufficient.

Statement (1) ALONE
At least two faces of the rectangular block B are squares.
Example: Two faces could be squares and the remaining 4 could also be squares of the same dimension. Then the block will be a cube.
A rectangular block of dimension 4 * 4 * 4 will have at least two faces that are squares and the block will be a cube.Counter Example: Two faces could be squares – say measuring 4 * 4. The other 4 could measure 4 * 6. In that case the block will not be a cube. It will be cuboid
We are not able to answer the question with a definite yes or definite no.
Statement (1) ALONE is NOT sufficient.
If statement (1) ALONE is NOT sufficient, we can eliminate choices 1 and 4.
Choices narrow down to 2, 3, or 5.

Statement (2) ALONE
The volume of the rectangular block B is 64.
Example: The sides measure 4 * 4 * 4. The volume is 64 and the rectangular block is a cube.
Counter Example: The sides measure 2 * 2 * 16. The volume is 64 and the rectangular block is NOT a cube.
Using statement (2) we could NOT get a definite YES or a definite NO.
Statement (2) ALONE is NOT sufficient.
If statement (2) ALONE is NOT sufficient, we can eliminate choice 2 as well.
Choices narrow down to 3 or 5.

Statements Together
1. At least two faces of the rectangular block B are squares.
+
2. The volume of the rectangular block B is 64.
Let us look for a counter example that will satisfy both the statements
Example: The sides measure 4 * 4 * 4.
Satisfies both statements. At least two of the faces are squares and the volume is 64.The given block is a cube.
Counter Example: The sides measure 2 * 2 * 16.
This example also satisfies both possibilities. At least two of the faces are squares. Two faces will measure 2 * 2. The other 4 will measure 2 * 16 each. The volume is 64.
The given block is a cuboid. It is not a cube
Despite using statements (1) and (2) together we could NOT determine the answer to the question.
Hence, Choice (5) is the answer.
Video Explanation
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