Question: The average monthly expenditure of a family for the first four months is $2750, for the next three months is $2940, and for the last five months $3130. If the family saves $5330 throughout year, find the average monthly income of the family for that year.

(A) $4200
(B) $3800
(C) $3500
(D) $3400
(E) $3200

“The average monthly expenditure of a family for the first four months”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1
Income= Expenditure + Savings
Total expenditure = (4 x 2750) + (2940x3) x (3130x5) = (11000) + (8820) x (15650) = $35470.
Total Savings = $ 5330
Average Monthly Income = ( Total expenditure+Total Savings)/Months in a year = (35470 + 5330)/12 = $ 3400

Correct Answer: D

Approach Solution 2:
Average= Sum/Total
Sum = Average * Total
=> Sum (first 4 months) = 4 * 2750 = 11,000
=> Sum (next 3 months) = 3 * 2940 = 8,820
=> Sum (last 5 months) = 5 * 3130 = 15,650
Overall expense: 11,000 + 8,820 + 15,650 = 35,470
=> Monthly expense : 35,470/12= 2955.xxx
Monthly income = Monthly expense + Monthly savings
Savings: 5330 in a year => Monthly savings : 5330/12= 444.xxx
Monthly income : 2955 + 444 = 3,399

Correct Answer: D

Approach Solution 3:
Average monthly expenditure of 4 months = $2700
Total expenditure for 4 months = 2700×4= $11000
Average monthly expenditure of 3 months = $2940
Total expenditure for 3 months = $2940*5= $8820 ....(1)
Average monthly expenditure of 5 months = $3130
Total expenditure of 5 months = $31020
= $1560 ....(2)
Total expenditure in the whole year
= $11000 + 8820 +$15650
= $35470
Savings during the whole year = $5330
Total income of the family during the year
= $35470 + $5330 = $40800
∴ Average monthly income during the year 40800/12= $3400

Correct Answer: D

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