Data Sufficiency

[GMAT math practice question]

Five data values are 11, 14, 16, 18 and x. What is the value of x?

1) The mode of the 5 data values is 11
2) The average (arithmetic mean) of the 5 data values is 14

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

Five data values are 11, 14, 16, 18 and x. What is the value of x?

1) The mode of the 5 data values is 11
2) The average (arithmetic mean) of the 5 data values is 14

$$L = \left\{ {11,14,16,18,x} \right\}$$
$$? = x$$

$$\left( 1 \right)\,\,{\rm{Mo}}\left( L \right) = 11\,\,\,\, \Rightarrow \,\,\,\,? = 11\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\,\,\left( {{\rm{Mo}}\,\,{\rm{ = }}\,\,{\rm{Mode}}\,\,{\rm{ = }}\,\,{\rm{most}}\,\,{\rm{frequent}}} \right)$$
$$\left( 2 \right)\,\,\mu \left( L \right) = {{x + \left( {11 + 14 + 16 + 18} \right)} \over 5} = 14\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$

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

Regards,
Fabio.

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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.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
The data values include four different values and x.
Since the mode of the five data values is 11, x must equal 11.
Condition 1) is sufficient.

Condition 2)
Calculating the mean of the five data values yields
( 11 + 14 + 16 + 18 + x ) / 5 = 14.
Solving for x gives
11 + 14 + 16 + 18 + x = 70
59 + x = 70
x = 11
Condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D