Data Sufficiency

If each month, Gandalf spends \(\$1400\) of his earnings on food, how much does he save every month?

(1) Gandalf spends \(\dfrac14 th\) of his earnings on rent, \(\dfrac12\) of his earnings he saves, and the remaining amount he spends on food.
(2) He spends \(\dfrac14 th\) of his earnings on food.

Answer: A

Source: e-GMAT

Let total earnings = x
Target question: how much does he save every month?
Statement 1: Gandalf spends 1/4th of his earnings on rent, 1/2 of his earnings he saves, and the remaining amount he spends on food.
$$rent=\frac{1x}{4};\ savings\ =\ \frac{1x}{2}$$
$$Amount\ spent\ on\ food=x-\frac{x}{4}-\frac{x}{2}$$
$$Amount\ spent\ on\ food=\left(\frac{4-1-2}{4}\right)x$$
$$=\frac{x}{4}$$
From question stem; Gandalf spends $1400 on food.
Therefore, x/4 = 1400
x = 5600 and
Savings = 1/2 * 5600 = $2800
From the remaining 4200, the total amount of money he saves cannot be evaluated with the information provided in this statement. Hence, statement 2 is NOT SUFFICIENT.
Since only statement 1 is SUFFICIENT, Option A is the correct answer.