Bunuel wrote:
Sarah made a phone call from New York to Memphis. After the first two minutes, the rate per minute dropped by 10 cents. If the call cost $3.60, how many minutes did the call last?
(1) The rate for the first two minutes is 30 cents per minute.
(2) If Sarah's call had been 8 minutes longer, it would have cost $5.20.
Solution
Step 1: Analyse Question Stem
• After the first 2 minutes, rate per minute dropped by 10 cents.
• Let us assume that the call lasts for t minutes.
• Total call cost for t minutes = $3.60 = 360 cents.
We need to find the value of t.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The rate for the first two minutes is 30 cents per minute.
• According to this statement: rate for first 2 minutes = 30 cents per minute
o So, rate after 2 minutes \(= 30- 10 = 20\) cents per minute
• Hence, we can write: \(2*30 + (t – 2)*20 = 360\)
• Since, we have one variable and one equation, we can easily solve the above equation to get the value of t.
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.
Statement 2: If Sarah's call had been 8 minutes longer, it would have cost $5.20.
• According to this statement, cost for (t+8) minutes = $5.20 \(= 520\) cents
• So, call rate (in cents per minute) after first 2 minutes \(= \frac{(520 – 360)}{8} \)
o Hence, rate for the first 2 minutes (in cents per minute) \(= \frac{(520 – 360)}{8} + 10\)
• Thus, \((\frac{(520 – 360)}{8} + 10)*2 + (\frac{(520 – 360)}{8})* (t-2) = 360\)
• Here also, we have one variable and one equation, we can solve it to get the value of t.
Hence, statement 2 is also sufficient.
Thus, the correct answer is Option D.
Alternate method:
Step 1: Analyse Question Stem
• Let us assume that the call rate for the first 2 minutes = x cents per minute.
o So, call rate after first 2 minutes( in cents per minute) \(= (x – 10) \)
• Let us assume that Sarah called for t minutes.
• Total call cost for t minutes = $3.60 = 360 cents
o \(x*2 +(x-10) *(t-2) = 360. ……..Eq.(i)\)
• We need to find the value of t.
o If we know the value of x we can substitute it in Eq.(i) and can easily solve to get the value of t.
Thus, we need to find the value of x.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The rate for the first two minutes is 30 cents per minute.
• According to this statement: \(x = 30\)
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.
Statement 2: If Sarah's call had been 8 minutes longer, it would have cost $5.20.
• According to this statement, cost for (t+8) minutes = $5.20 = 520 cents
• So, call rate (in cents per minutes) after first 2 minutes, or \(x - 10 = \frac{(520 – 360)}{8} \)
o Hence, \(x = (\frac{(520 – 360)}{8} + 10\)) cents per minute
Here also, we are able to find the value of x.
Hence, statement 2 is also sufficient.
Thus, the correct answer is
Option D.
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