Sarah made a phone call from New York to Memphis. After the first two

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.

Say call is t minutes
For first 2 minutes rate is r cents
After than rate is (r-10) cents/minute
t = ?
Cost = 360 cents

2r+ (t-2) *(r-10) = 360

Statement 1 =>
2r+ (t-2) *(r-10) = 360
r =given
t can be calculated
GO AHEAD

Statement 2=>
8 minutes longer means t + 8
2r+ (t+6) *(r-10) = 520
By the equation given in question
t can be calculated
GO AHEAD

D

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