The cost of a phone call is x cents/min for the first 5 minutes and

Question

The cost of a phone call is x cents/min for the first 5 minutes and x/2 cents for every additional minute.If Jack paid $1 for a phone call,for how long did he talk?

(1) If he had spoken for another minute,he would have paid 10 cents more
(2) If he had spoken for one minute fewer,he would have paid 20 cents fewer.

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rajatchopra1994 · Answer

Explanation: Statement 1: If he had spoken for another minute, he would have paid 10 cents more.
So, He total paid 1.1 Dollars, But we got X/2=10
X=20.
therefore he talked for 6 minutes.
Sufficient.

Statement 2: If he had spoken for one minute fewer, he would have paid 20 cents fewer.
As we cannot make any from this statement about total timings of talk.
Insufficient

Answer is A.

Please provide kudos, if you find my explanation good enough

sach24x7 · Answer

Hi Rajat,

How did you assume that total time for 1 $ is 5 min. 
It can be less than 5 min or more than 5 min also. 
Two diff values for x for this scenario.

I think answer would be C because we are getting shift in value with both statements from x to x/2

Posted from my mobile device

rajatchopra1994 · Answer

Dear Sach24×7,

As given in 1st statement, if he had talked for 1more minute, he paid 10 scents extra. So we know cost of extra minutes talking. So X/2 = 10 scents.
So X will be 20 scents.

Cost for first 5 minutes is 1 dollar. (Given initially)
So A is sufficient.

That is my understanding

Posted from my mobile device

JiddiHuMain · Answer

Explanation: Statement 1: If he had spoken for another minute, he would have paid 10 cents more.
So, He total paid 1.1 Dollars, But we got X/2=10
X=20.
therefore he talked for 6 minutes.
Sufficient.

Statement 2: If he had spoken for one minute fewer, he would have paid 20 cents fewer.
As we cannot make any from this statement about total timings of talk.
Insufficient

Answer is A.

sach24x7 · Answer

Rajat,

Got my mistake.

“ first statement clearly shows the time is greater than 5 min because if x=10 then 10 * 5 min. can not give 100 cents”

So x = 20 and x/2=10

Second statement shows that if x=20 then x/2 =10

And 
20* 5 min = 100 so time is 5 min. And also satisfies equation 2

And if x/2= 20 then. x =40
40* 2.5= 100 which is not possible because it will not full fill second statement

So answer is D

Posted from my mobile device

rajatchopra1994 · Answer

How ????

See, In statement 2, we cannot define Fewer, as X/2=20 or X=20.
as we don't know how many minutes he had talked. In statement, it clearly told 1 minute fewer.
Hope you understand my point.

Please give kudos, if you got it!!!

avirup2018 · Answer

Bunuel  @chetan4u In st 1 It is said 1 min more So, X/2=10 or X= 20 So he has spoken for 6 mins according to St 1.

But in St 2 it is said 1 Min fewer now this 1 minute few it can either be less than 5 min or additional 1 min less.
So it cannot be decided how many minutes he has talked over phn. So it is insufficient...

Let say extra min be y So equation is either 4X=80 So X= 20 
or
5X+(y-1)X/2= 80 
5X +(YX/2)-X/2=80 
100-(X/2)=80 (Intially given cost of call is 1 Dollar=100 cent)
X=40 
hence clearly indecisive.

Hence answer is A.

Please guide

GMATTER18 · Answer

@Bunuel- Please provide the solution

Masri · Answer

lets analyze it

A) If he had spoken for  another minute , he would have paid 10 cents more. 
- so if x equals to 10 cents, and we have a 1$ call, then he must have talked more than 5 minutes, and hence for the first 5 minutes he would have paid 50 cents ( 10 * 5 cents ), and then paid x/2 (10/2), 5 cents for another 10 minutes. so that the call lasted for 15 minutes to pay 1$  This  rate. So speaking for  another minute  he would have paid 5 cents more not 10 cents as the sentence suggests. T his means that x equals to 20 so that every additional minute would cost x/2 =10 cents.   This statement is sufficient.

(2) If he had spoken for one minute fewer,he would have paid 20 cents fewer.
- Again, if x equals to 20 cents, and we have a 1$ call, so the call must have lasted for exactly 5 minutes, so for a 4 minute call, he would have paid 20 cents fewer. This statement is also sufficient.

sanjitscorps18 · Answer

Let the number of minutes talked be N. As per the question stem
5X + (N - 5)X/2 = 100

(1) If he had spoken for another minute, he would have paid 10 cents more
Now consider the scenario that after another minute, either the call ended within or precisely at 5 minutes or it extended more than 5 minutes

1st scenario  - the call ended within 5 minutes. If we take a maximum of 5 minutes we get the call cost of 50 cents while the call cost is 100 cents.
 Not possible.

2nd scenario  - the call ended past 5 minutes. Then we have the differential of 1 minute as X/2 = 10 cents
=> X = 20 cents. If X = 20 then N = 5
 This confirms that the actual call went on for 5 minutes

(2) If he had spoken for one minute fewer, he would have paid 20 cents fewer.
Now we consider the scenario for one minute fewer, either the call ended within or precisely at 5 minutes or it extended more than 5 minutes

1st scenario  - the call ended within 5 minutes. If we take a maximum of 5 minutes we get the call cost as 100 cents (actual call cost). Hence talking 1 minute fewer would lead to a 20 cents reduction
5X + (N - 5)X/2 = 100
=> 5X = 100
=> X = 20 cents
Also if we reduce a minute 4X = 80 cents, hence for a minute it is 20 cents
 This confirms that the actual call went on for 5 minutes

2nd scenario  - the call ended past 5 minutes. Then we have the differential of 1 minute as X/2 = 20 cents
=> X = 40 cents. However, 40 cents cannot be the call rate for the first 5 minutes. 
 Not possible

Option D

Aary · Answer

Hi, is the answer A or D?? IMO should be A, as we don't know the number of mins in statement 2 could be more or less than 5?

sanjitscorps18 · Answer

The answer is D.

Please have a look at the explanations provided and share your concerns if you still have doubts.

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The cost of a phone call is x cents/min for the first 5 minutes and

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