During the four years that Mrs. Lopez owned her car, she fou

Question

During the four years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the remainder. The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total. If the only other expenses were taxes and license fees, then the cost of financing was how much more or less than the cost of taxes and license fees?

(A) $1,500 more

(B) $1,200 more

(C) $100 less

(D) $300 less

(E) $1,500 less

(A) $1,500 more

(B) $1,200 more

(C) $100 less

(D) $300 less

(E) $1,500 less

EMPOWERgmatRichC · Accepted Answer

Hi AbdurRakib,

While this question IS wordy, the math behind it is just arithmetic. If you break the prompt into 'pieces', then the work shouldn't be too difficult.

The first two sentences tell us that the total car expenses were $18,000, fuel and maintenance costs accounted for 1/3 of THAT total and depreciation accounted for 3/5 of the REMAINDER.

TOTAL = $18,000
Fuel/Maint. = (1/3)($18,000) = $6,000
Remainder = $18,000 - $6,000 = $12,000

Depreciation = (3/5)($12,000) = $7,200

Next, we're told that 
Insurance = 3(Financing)
Insurance + Financing = (1/5)($18,000)

Here, we have a 'system' of equations (2 variables and 2 unique equations), so we can solve for both variables...

Insurance + Financing = $3,600
3(Financing + Financing = $3,600
4(Financing) = $3,600
Financing = $900

Insurance + $900 = $3,600
Insurance = $2,700

At this point, we have....
Total = $18,000
Fuel/Maint. = (1/3)($18,000) = $6,000
Depreciation = (3/5)($12,000) = $7,200
Financing = $900
Insurance = $2,700

$6,000 + $7,200 + $900 + $2,700 = $16,800

This leaves $1,200 for the remaining costs, which we're told are the Taxes and Licensing Fees

Taxes&Licensing = $1,200

The question asks how much more/less the Financing cost was compared to the Taxes&Licensing....

$900 - $1,200 = - $300 = $300 LESS

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

maaadhu · Answer

OA is D

Fuel & Maintenance = 1/3
depreciation = 3/5 of the rest = 3/5*2/3 = 2/5
Insurance = 3 * Financing
Insurance + Finance = 1/5

Let Taxes & License = x

so compute for x

1/3 + 2/5 + 1/5 + x = 1
x= 1/15

Amount of x = 1/15*18000 = 1200 -- (1)

Now I + F = 1/5*18000
but I = 3F
so 4F = 1/5*18000
F= 900 -- (2)

Ans is (2) - (1)...i.e. 300 less

SVaidyaraman · Answer

1. Assume total expenses to be $180 for simplicity and to avoid mistakes in calculation
2.Maintenance cost =$60, depreciation = 3/5(180-60) = $72
3. Insurance + financing cost= 1/5(180)
i.e., three times financing cost +financing cost =1/5(180) 
i.e., 4 * financing cost = 1/5(180) = $36 . 
Therefore financing cost =$9 and Insurance cost = 3*9 = $27
4. Taxes and License fee= 180 -(60+72+27+9)=$12
5, We find financing cost to be $3 less than the tax and license fee if the total expenses is $180.
6. But the actual total expenses is $18,000. so financing cost is less than tax and license fee by $300.

mathivanan · Answer

The best strategy is to assume a convenient number. 300 is a convenient number (avoiding fractions).
Out of 300, 100 is F and M costs.
Out of the remaining 200, 120 is depreciation.
Cost of insurance and financing together is 60 (insurance=45 and financing is 15)
Remaining 20 is taxes and licence fees.
The difference between financing and taxes is 5
If 300 is the total expenses then $5 less
If 18000 is the total expenses then $300 less

shyind · Answer

Total = 18000

Fuel and maintenance = 1/3 = 6000

Depreciation = (2/3)(3/5) = 12000 (3/5) = 7200

Insurance & Financing is 1/5 of total 
18000 (1/5) = 3600

Insurance and Financing are in 3:1 ratio. So, I = 2700 & F = 900

Therefore, total expenditure as of now,

6000 + 7200 + 3600 = 16800,

Taxes and License cost will be the remaining, 
So, 18000 - 16800 = 1200

then the cost of financing was how much more or less than the cost of taxes and license fees ?

Cost of finance = 900
Cost of Tax, License = 1200,

Therefore, the difference is 300 less.

KarishmaB · Answer

Analyse the question while reading each statement. Just manipulate the fractions.

During the four years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total  - Fuel & M cost is 1/3 of total. So 2/3 of total is left.

and depreciation accounted for 3/5 of the remainder . - Depr cost is (3/5) of remainder = (3/5) of (2/3) of total = (2/5) of Total
Leftover is (2/5) of (2/3) of total = (4/15) of Total

The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total . - Insur + Fin cost = 1/5 of Total = 3/15 of Total.
Leftover cost = 4/15 - 3/15 = 1/15 of Total
Cost of insurance = (3/4)*(1/5) = 3/20 of Total
Cost of Fin = 1/20 of Total

If the only other expenses were taxes and license fees,  - taxes are the leftover 1/15 of Total

then the cost of financing was how much more or less than the cost of taxes and license fees   - Compare cost of Fin with cost of taxes:
1/15 - 1/20 = 1/60 of Total

Financing cost is 1/60 * 18000 = $300 less than cost of taxes.

Answer (D)

Abhishek009 · Answer

Total Exp = 18000
Fuel and maintenance = 6000 ; remaining = 12000
Depreciation = 7200
Cost of Insurance + Cost of Financing = 3600
Financing + 3*Financing = 3600
So, Financing = 900
Cost of License Fee & Tax = 18000 - ( 6000 + 7200 + 3600 ) = 1200

So , Cost of financing was $300 less than the cost of taxes and license fees..
 
Answer will be (D) $ 300 Less

ScottTargetTestPrep · Answer

We are given that Mrs. Lopez’s total car expenses during the four years were $18,000.

Since fuel and maintenance (F&M) costs accounted for 1/3 of the total expenses:

F&M costs = 1/3(18,000) = $6,000.

Since depreciation accounted for 3/5 of the remainder:

depreciation = 3/5(18,000 - 6,000) = 3/5 (12,000) = $7,200.

Since we don’t know the actual cost of insurance or financing except that the cost of insurance was 3 times the cost of financing, and the two costs together accounted for 1/5 of the total expenses, we can let x = cost of financing and 3x = cost of insurance, and create the following equation:

x + 3x = 1/5(18,000)

4x = 3,600

x = 900

So the cost of financing was $900 and the cost of insurance was 3($900) = $2,700.

The last expense is taxes and license (T&L) fees, so T&L fees must be the difference between the total expenses and the sum of all the items (F&M, depreciation, insurance, and financing) mentioned above. Thus:

T&L fees = 18,000 - (6,000 + 7,200 + 900 + 2,700) = 18,000 - 16,800 = $1,200

Finally, we are asked: “the cost of financing was how much more or less than the cost of taxes and license fees?” Since the cost of financing was $900 and T&L fees were $1,200, the cost of financing is $300 less than that of T&L fees.

Answer: D

Mehemmed · Answer

People they there's no calculation intensive problems in GMAT quant.

This is nothing but mere calculation.

KarishmaB · Answer

If you deal with fractions for the most part, you need minimal calculations (shown here: https://gmatclub.com/forum/during-the-f ... l#p1568748)

epiphany1 · Answer

7.30min how to speed up. Speed up or ditch it all together??????????????????????????????????????

sameerm22 · Answer

Old post... by nice one  VeritasKarishma . Have seen quite a few official solutions for such kind of problems, but fractions technique is very awesome! Got down to 2 min, 25 sec from 3 mins in my first attempt.

ArnauG · Answer

Let's calculate the different expenses one by one.

Total car expenses = $18,000

Fuel and maintenance costs = 1/3 * $18,000 = $6,000

Remainder after fuel and maintenance costs = $18,000 - $6,000 = $12,000

Depreciation = 3/5 * $12,000 = $7,200

Remainder after depreciation = $12,000 - $7,200 = $4,800

Cost of insurance + Cost of financing = 1/5 * $18,000 = $3,600

Let's denote the cost of financing as x.

Cost of insurance = 3 * x

According to the given information, the cost of insurance plus the cost of financing is $3,600, so we can set up the equation:

3 * x + x = $3,600

4 * x = $3,600

x = $3,600 / 4 = $900

Therefore, the cost of financing is $900.

Now, we can calculate the cost of taxes and license fees:

Cost of taxes and license fees = Remainder after depreciation - Cost of financing = $4,800 - $900 = $3,900

The cost of financing is $900 less than the cost of taxes and license fees.

Therefore, the answer is (D) $300 less.

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