Carrie, Lisa, and Betty all make purchases at a music store that sells

Question

Carrie, Lisa, and Betty all make purchases at a music store that sells all records for a certain price and all CDs for a certain price. How much does Carrie pay for 1 record and 2 CDs?

(1) Lisa bought 3 records for $22.50.

(2) Betty bought 2 records and 4 CDs for $55.00.

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ManifestDreamMBA · Answer

Since store sells all records for a certain price and all CDs for a certain price, we need to know the price of these items (or required combinations) to know how many Carrie spent

Asked: R + 2C?

Statement 1
3R = 22.5
This only gives R, no information on C
Insufficient

Statement 2
2R + 4C = 55
1R + 2C = 27.5
Sufficient

Gmat750aspirant · Answer

Let r = price of 1 record 
Let c = price of 1 CD

Carrie's cost: r + 2c

Statement (1): 
Lisa bought 3 records for $22.50 
3r = 22.50 → r = 7.50 
This gives r but no info about c → Insufficient

Statement (2): 
Betty bought 2 records and 4 CDs for $55.00 
2r + 4c = 55.00 
This gives a relationship but not enough to find r and c → Insufficient

Combining Statements (1) and (2): 
From (1), r = 7.50 
From (2): 2(7.50) + 4c = 55.00 → 15.00 + 4c = 55.00 → 4c = 40.00 → c = 10.00

Carrie's cost: r + 2c = 7.50 + 2(10.00) = 27.50

Answer: (C) Both statements together are sufficient.

bhargavhhhhhhhh · Answer

Let:
R = Price of one record
C = Price of one CD

We need to find: 
Cost of 1 record + 2 CDs = R + 2C

Statement (1):
Lisa bought 3 records for $22.50.
Equation: 3R = 22.50
=> R = 22.50 / 3 = 7.50
This gives R but no info about C. INSUFFICIENT.

Statement (2):
Betty bought 2 records and 4 CDs for $55.00.
Equation: 2R + 4C = 55.00
This has two variables, so alone it's INSUFFICIENT.

Combining (1) & (2):
From (1): R = 7.50
Substituting in (2):

2(7.50) + 4C = 55
15 + 4C = 55
4C = 40
C = 10

Now, calculating R + 2C:
7.50 + 2(10) = 7.50 + 20 = 27.50

Final Answer: (C) Both statements together are sufficient, but neither alone.

NextstopISB · Answer

Let the price of one record be R dollars and the price of one CD be C dollars.

We need to determine the cost for Carrie, who buys 1 record and 2 CDs: 
Total cost = R + 2C

From Statement (1): 
Lisa bought 3 records for $22.50, which gives the equation:
3R = 22.50 
=> R = 22.50 / 3 
=> R = 7.50

From Statement (2): 
Betty bought 2 records and 4 CDs for $55.00, giving us the equation:
2R + 4C = 55

Substituting R = 7.50 into the second equation: 
2(7.50) + 4C = 55 
15 + 4C = 55 
4C = 40 
C = 10

Now, calculating the cost for Carrie: 
R + 2C = 7.50 + 2(10) 
= 7.50 + 20 
= 27.50

Thus, Carrie pays $27.50.

Since both statements together allow us to determine the cost, the answer is C (Both statements together are sufficient).

Bissap · Answer

Am I missing something but IMO it is B.

We are not asked to find r and c, we are asked to find r+2c.
Since all records are at the same price and all the CDs are at the same prices, knowing what is the cost of any multiple of r+2c would be sufficient.

Therefore, the statement 2 : 2r+4c = 55 <=> r+2c = 55/2 = 27,5
Ans B

Correct me if I am wrong.

icrilov · Answer

The answer is B and these explanations are wrong. Just divide the equation in the second statement by 2 and you have the answer.

Carrie, Lisa, and Betty all make purchases at a music store that sells

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GMAT Data Sufficiency (DS) Questions

Carrie, Lisa, and Betty all make purchases at a music store that sells

Prep Toolkit

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