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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Wed Sep 23, 2020 5:34 am

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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

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Source: Beat The GMAT — Data Sufficiency | Wed Sep 23, 2020 5:34 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

by deloitte247 » Sun Sep 27, 2020 1:47 am

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.

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