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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
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Official solution

Let x be the charge, in dollars, of each additional service. Determine the value of (60)(0.5) + 3x, or equivalently, determine the value of x.

The table below shows the value of x for each of the three possible massages that Jordan had.
Massage Total charge x
30-minute 15 + 3x = 37.50 7.50
60-minute 30 + 3x = 37.50 2.50
90-minute 45 + 3x = 37.50 −2.50

From the table it follows that there are two possible values of x, namely x = 7.5 and x = 2.5; NOT sufficient.
The table below shows the value of x for each of the three possible massages that Ryan had.
Massage Total charge x
30-minute 15 + 2x = 60 22.50
60-minute 30 + 2x = 60 15.00
90-minute 45 + 2x = 60 7.50
From the table it follows that there are three possible values of x, namely x = 22.5, x = 15, and x = 7.5; NOT sufficient.

Given (1) and (2), it follows that x = 7.5.

Both statements together are sufficient.
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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
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Each Statement is clearly insufficient alone. We know that adding 30 minutes of massage adds $15 to the price. So there's no way S1 and S2 describe massages that differ by only 30 minutes, because if we add $15 to $37.50, we don't get something as large as $60, and we're subtracting one service in S2 on top of that. The only possibility is that S1 describes a 30 minute massage, and S2 a 90 minute massage. Then the longer massage would add $30 to the price in S1, leading to a cost of $67.50, and now we can see that by subtracting a service, the cost drops by $7.50, so that's the price of one service. The answer is C.
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At a certain university recreation center, a member can receive a 30-m [#permalink]
gmatt1476 wrote:
At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0.50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?

(1) At this recreation center, Jordan, a member, had a massage and 3 additional services for a total charge of $37.50.
(2) At this recreation center, Ryan, a member, had a massage and 2 additional services for a total charge of $60.00.



DS48391.01


Can some expert please explain a simpler way
Bunuel
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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
Genoa2000 wrote:
hemantbafna wrote:
gmatt1476 wrote:
At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0.50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?

(1) At this recreation center, Jordan, a member, had a massage and 3 additional services for a total charge of $37.50.
(2) At this recreation center, Ryan, a member, had a massage and 2 additional services for a total charge of $60.00.



DS48391.01


Can some expert please explain a simpler way
Bunuel


I am definitely not an expert but I want to help you.

You know that a member pays for a 60-minute massage:

y= total charge

x = additional service

y = 60 * (0.5) + 3x --> y = 30 + 3x

Now we want to know what is the value of x so that we can complete our expression.

We try to understand it from the statements provided.

1) We don't know what massage he received (if 30/60/90) but we know the total charge and the number of additional services:

If it was 30 --> 37.50 = 15 + 3x --> x = 7.50

If it was 60 --> 37.50 = 30 + 3x --> x = 2.50

We are not sure what is x since we have two possibilities. INSUFFICIENT

REMEMBER: we are told that x is always the same. So if we find x in any service we do not have to think about a possible change of it and we have what we need.


2) Same situation as before but different values:

We don't know what massage he received (if 30/60/90) but we know the total charge and the number of additional services:

If it was 30 --> 60 = 15 + 2x --> x = 22.50

If it was 60 --> 60 = 30 + 2x --> x = 15.00

If it was 90 --> 60 = 45 + 2x--> x = 7.50

We are not sure what is x since we have three possibilities. INSUFFICIENT

(1) + (2):

Now we see that 7.50 is a possibility for both the message we were given information about --> x must be 7.50 SUFFICIENT



This makes a lot more sense, thank you!
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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
Bunuel can you please guide on this solution? Dont get why its C
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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
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hemantbafna wrote:
Genoa2000 wrote:
hemantbafna wrote:
gmatt1476 wrote:
At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0.50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?

(1) At this recreation center, Jordan, a member, had a massage and 3 additional services for a total charge of $37.50.
(2) At this recreation center, Ryan, a member, had a massage and 2 additional services for a total charge of $60.00.



DS48391.01


Can some expert please explain a simpler way
Bunuel


I am definitely not an expert but I want to help you.

You know that a member pays for a 60-minute massage:

y= total charge

x = additional service

y = 60 * (0.5) + 3x --> y = 30 + 3x

Now we want to know what is the value of x so that we can complete our expression.

We try to understand it from the statements provided.

1) We don't know what massage he received (if 30/60/90) but we know the total charge and the number of additional services:

If it was 30 --> 37.50 = 15 + 3x --> x = 7.50

If it was 60 --> 37.50 = 30 + 3x --> x = 2.50

We are not sure what is x since we have two possibilities. INSUFFICIENT

REMEMBER: we are told that x is always the same. So if we find x in any service we do not have to think about a possible change of it and we have what we need.


2) Same situation as before but different values:

We don't know what massage he received (if 30/60/90) but we know the total charge and the number of additional services:

If it was 30 --> 60 = 15 + 2x --> x = 22.50

If it was 60 --> 60 = 30 + 2x --> x = 15.00

If it was 90 --> 60 = 45 + 2x--> x = 7.50

We are not sure what is x since we have three possibilities. INSUFFICIENT

(1) + (2):

Now we see that 7.50 is a possibility for both the message we were given information about --> x must be 7.50 SUFFICIENT



This makes a lot more sense, thank you!




At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0.50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?

(1) At this recreation center, Jordan, a member, had a massage and 3 additional services for a total charge of $37.50.
(2) At this recreation center, Ryan, a member, had a massage and 2 additional services for a total charge of $60.00.


Let M are the minutes of massage and F is the fixed cost for additional service.

From Statement 1, 0.5M+3F=37.50. NS as we do not know M
From Statement 2, 0.5M+2F=60.00. NS as we do not know M

combine the two statements, we can get the unique value for M And F. hence sufficient.
solveing the above two
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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
A member can receive a 30, 60, or 90 minute massage, costing $15, $30, or $45 respectively. There is a fixed charge for each additional service.

What was the total charge for a 60 minute massage and 3 additional services?

We know a 60 minute massage is $30. We need to determine how much the 3 additional services are.

(1) Jordan paid a total of $37.50 for a massage and 3 additional services. We don't know if she received the 30 minute massage or the $60 minute massage, however, so we're not able to determine how much she spent on the 3 additional services.

(2) Ryan paid $60 for a massage and 2 additional services. Again, we don't know if Ryan received the 30, 60, or 90 minute massage. Insufficient.

(1&2) We're told that each additional service is the same fixed amount.

We know Jordan had 3 additional services and Ryan had 2 additional services. Notice Jordan's total of $37.50 is $7.50 more than a massage. The cheapest massage is $15, so she must have spent $22.50 on 3 additional services.

We can conclude that Ryan spent $15 on two additional services and received the 90 minute passage.

We can also answer the question: A 90 minute massage and 3 additional services costs: $45 + 22.50 = $67.50. SUFFICIENT.

Answer is C.
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Re: At a certain university recreation center, a member can receive a 30-m [#permalink]
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