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

Question

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.

lacktutor · Answer

Let’s say that the rate per minute is x cents 
2x + (x—10)*y = 360

(Statement1): x= 30
—> 60 + 20*y = 360
20y = 300
y= 15 
y+2 = 17 
Sufficient

(Statement2): 2x+(x—10)(y+8) =520
2x +( x—10)y +8(x—10) = 520
360 + 8(x—10) = 520
8(x—10)= 160
—> x = 30 
we can find that y+2 = 17 
Sufficient 
The answer is D

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GMATinsight · Answer

Let, Total Call time = t mins

Rate = x*2 + (x-10)*(t-2) = 360 cents

SO we need only x to calculate the value of t here

Question : t = ?

Statement 1 : The rate for the first two minutes is 30 cents per minute

i.e. x = 30 cents

SUFFICIENT

Statement 2 : If Sarah's call had been 8 minutes longer, it would have cost $5.20

Rate = x*2 + (x-10)*(t+8) = 520 cents

We also have x*2 + (x-10)*(t-2) = 360 cents

SOlving them gives us the value of x hence

SUFFICIENT

Answer: Option D

GMATWhizTeam · Answer

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 .

sambitspm · Answer

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

bumpbot · Answer

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