Brand A bike costs twice as much as the Brand B bike

Question

Brand A bike costs twice as much as the Brand B bike. The monthly maintenance cost of the Brand B bike is twice the monthly maintenance cost of Brand A. John purchased a Brand A bike, and Peter purchased a Brand B bike. If at any time the total expenditure on a bike is calculated as the purchase cost plus the maintenance cost up to that time, then after how many months would John and Peter have spent equal amounts on their bikes?

(1) The monthly maintenance cost of the Brand A bike is 5% of the cost of the bike.

(2) John and Peter purchased their bikes on the same day.

Source- Nova

Show Answer

Official Answer

C

(1) The monthly maintenance cost of the Brand A bike is 5% of the cost of the bike.

(2) John and Peter purchased their bikes on the same day.

Source- Nova

Bunuel · Answer

Brand A bike costs twice as much as the Brand B bike. The monthly maintenance cost of the Brand B bike is twice the monthly maintenance cost of Brand A. John purchased a Brand A bike, and Peter purchased a Brand B bike. If at any time the total expenditure on a bike is calculated as the purchase cost plus the maintenance cost up to that time, then after how many months would John and Peter have spent equal amounts on their bikes?

(1) The monthly maintenance cost of the Brand A bike is 5% of the cost of the bike.

(2) John and Peter purchased their bikes on the same day.

Source- Nova

Show Answer

Official Answer

C

Say the price of A is 2x and the price of B is x.

(1) The monthly maintenance cost of the Brand A bike is 5% of the cost of the bike.

This implies that the maintenance cost of A is  \frac{1}{20}*2x=\frac{x}{10} . We are also given that the monthly maintenance cost of B is twice the monthly maintenance cost of A, thus the monthly maintenance cost of B is  2*\frac{x}{10}=\frac{x}{5} . Since we don't know when the bikes were purchased, we cannot compare the total costs. Not sufficient.

(2) John and Peter purchased their bikes on the same day. Clearly insufficient.

(1)+(2) From above we have that the the total expenditure on bike A =  2x + \frac{x}{10}*n  and the the total expenditure on bike B =  x + \frac{x}{5}*n , where n is the number of months after the purchase. We need to find the value of n, for which  2x + \frac{x}{10}*n=x + \frac{x}{5}*n  --> reduce by x and solve for n to get  n=10 . Sufficient.

Answer: C.

Hope it's clear.

adiagr · Answer

Car Purchase.JPG Refer above table. Suppose after K months, the total expenditure of John and Peter are same. John's expense after k months: 2x + k(y) Peter's expense after k months: x + k(2y) 2x+ky = x+2ky x = ky k= (x/y). If we know the ratios of two costs, we will know "k" Statement (1) gives us just that. We get a ratio of x and y. Statement (2) seems innocuous, but is our inherent assumption. So both (1) and (2) together are sufficient. Neither alone is sufficient.

guptarahul · Answer

Suppose the Brand B bike costs x dollars. Then the cost of the Brand A bike must be 2x dollars (as given).
Now, the total expenditure after time t is defined as the (Purchase Cost) + (Maintenance cost till the time t).
From Statement (1) alone, we have that the monthly maintenance cost of the Brand A bike is 5% of its purchase cost. 5% of 2x = (5/100)2x = x/10. Hence, monthly maintenance cost is x/10.
Since we are given that the monthly maintenance cost of Brand B bike equals two times the monthly maintenance cost of the Brand A bike, the former equals 2(x/10) = x/5.
Now, we are required to find the time when the total expenditure (includes purchase cost and maintenance cost) on bike A equals the expenditure on bike B. But, we still do not have the time difference between the two purchases. Hence, we cannot evaluate when the two brands would yield equal costs. Hence, Statement (1) alone is not sufficient.
From Statement (2) alone, we have the required time difference, but we do not have the relation between the maintenance costs of the two bikes. Hence, Statement (2) alone is not sufficient.
With the statements together, we have the required costs in terms of x and, say, the total expenditures equal after n months.
Then the total expenditure on bike A equals
(Purchase cost) + (Maintenance cost) =
2x + (x/10)n
And the total expenditure on the bike B equals
(Purchase cost) + (Maintenance cost) =
x + (x/5)n
The two are equal when 2x + xn/10 = x + xn/5. Dividing both sides by x yields 2 + n/10 = 1 + n/5. Solving the equation for n yields n = 10. Hence, the statements together answer the question. The answer is (C)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Brand A bike costs twice as much as the Brand B bike

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Brand A bike costs twice as much as the Brand B bike

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards