Data Sufficiency

[GMAT math practice question]

If operation # represents one of addition, subtraction, multiplication, and division, what is the value of 0 # 1?

1) 2 # 1 = 2
2) 4 # 2 = 2

Max@Math Revolution wrote:[GMAT math practice question]

If operation # represents one of addition, subtraction, multiplication, OR division, what is the value of 0 # 1?

1) 2 # 1 = 2
2) 4 # 2 = 2

$$?\,\, = \,\,0\# 1\,\,\,\,\,\,\left( {\# \in \left\{ { + , - , \times , \div } \right\}} \right)$$

$$\left( 1 \right)\,\,2\# 1 = 2\,\,\,\, \Rightarrow \left\{ \matrix{
\,\,\# = \times \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr
\,\,{\rm{OR}} \hfill \cr
\,\,\# = \div \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( 2 \right)\,\,\,\,4\# 2 = 2\,\,\,\, \Rightarrow \left\{ \matrix{
\,\,\# = - \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = - 1 \hfill \cr
\,\,{\rm{OR}} \hfill \cr
\,\,\# = \div \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The operation is considered as a variable. Since we have 1 variable and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since 2#1 = 2, # is one of the operations, multiplication and division.
If # is the multiplication operation, then 0#1 = 0.
If # is the division operation, then 0#1 = 0.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since 4#2 = 2, # is one of the operations, subtraction and division.
If # is the subtraction operation, then 0#1 = -1.
If # is the division operation, then 0#1 = 0.
Since condition 2) doesn't yield a unique solution, it is not sufficient.

Therefore, A is the answer.
Answer: A