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03 Mar 2020, 02:54
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B
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Difficulty:
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57% (03:04) correct
43%
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The price of Darjeeling tea (in rupees per kilogram) is \(100 + 0.10n\), on the \(n_{th}\) day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is \(89 + 0.15n\), on the \(n_{th}\) day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal? (Note: 2007 was not a leap year)
A. May 21
B. May 20
C. April 20
D. April 11
E. April 10
Are You Up For the Challenge: 700 Level Questions
A. May 21
B. May 20
C. April 20
D. April 11
E. April 10
Are You Up For the Challenge: 700 Level Questions
03 Mar 2020, 11:16
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Bunuel
Since each formula tells us the price on Day n, we can set those two formulas equal to each other.
We get: \(100 + 0.10n=89 + 0.15n\)
Subtract \(89\) from both sides of the equation to get: \(11 + 0.10n=0.15n\)
Subtract \(0.10n\) from both sides of the equation: \(11=0.05n\)
Solve: \(n = \frac{11}{0.05} = 220\)
So, it SEEMS that the two prices will be equal on Day 220
HOWEVER, the formula for the price of Darjeeling tea only goes until Day 100, at which point its price remains the same forever afterwards.
On Day 100, the price of Darjeeling tea = \(100 + 0.10(100) = 100 + 10 = 110\)
So, AFTER Day 100, price of Darjeeling tea = 110 rupees
So let's now determine which day the price of Ooty tea is 110 rupees
We can write the equation: \(89 + 0.15n = 110\)
Subtract \(89\) from both sides to get: \(0.15n = 21\)
Solve: \(n = \frac{21}{0.15} = 140\)
So, on Day 140, the two teas will each sell for 140 rupees per kilogram.
Our job now is to determine what day of the year is Day 140
January has 31 days
February has 28 days (in a non leap year)
March has 31 days
April has 30 days
31 + 28 + 31 + 30 = 120 days.
In other words Day 120 is on April 30th
So, 20 days later (on May 20th) will be Day 140
Answer: B
Cheers,
Brent
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 820
03 Mar 2020, 03:38
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Bunuel
We will first evaluate this equation - If the value of n comes greater than 100 then this will not be valid
\(100 + 0.10n\) = \(89 + 0.15n\)
11 = .05*n => n = 220 which is greater than 100.
Therefore the value of Darjeeling tea will be at a price what it will be on 100th day as it will be constant thereafter
\(100 + 0.10n\) = \(100 + 0.10*100\) = 110
\(89 + 0.15n\) = 110 => 0.15n = 21 => n = 140
Jan - 31 days
Feb - 28 days
March - 31 days
April - 30 days
May - 20th day
All if this adds up to 140 days
Answer - B - 20th May
