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rango
Joined: 28 Apr 2013
Last visit: 19 Jul 2014
Posts: 97
Given Kudos: 84
Location: India
Schools: Kellogg 1YR '16 Tuck '16 HKU'16 HKUST '16 Tsinghua '16 IIMA Guanghua '16 Haas '16 Darden '16
GPA: 4
WE:Medicine and Health (Healthcare/Pharmaceuticals)
Schools: Kellogg 1YR '16 Tuck '16 HKU'16 HKUST '16 Tsinghua '16 IIMA Guanghua '16 Haas '16 Darden '16
Posts: 97
11 Jan 2014, 22:29
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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64% (02:17) correct
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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
(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
12 Jan 2014, 06:26
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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?
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.
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.
26 May 2016, 06:08
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Attachment:
Car Purchase.JPG [ 13.12 KiB | Viewed 5384 times ]
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)
[Now it is important to note that there is an inherent assumption that both John and Peter bought bike on same day.]
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.
