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DS - Word trans.

by karthikpandian19 » Mon Jul 02, 2012 11:59 pm
At a certain restaurant, burgers, fries, and soft drinks are sold individually but can also be combined in a value meal consisting of a burger, an order of fries, and a soft drink. The cost of the value meal is less than the costs of the three items combined. If Hubert bought 3 value meals, 2 individual burgers, and an individual soft drink for a total of $24, and if all individual items and value meals cost whole dollar amounts, what is the price of one value meal?

The total cost for an individual burger and an individual soft drink is $5.
An order of fries is more expensive than a soft drink and less expensive than a burger.
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by Anurag@Gurome » Tue Jul 03, 2012 12:39 am
karthikpandian19 wrote:At a certain restaurant, burgers, fries, and soft drinks are sold individually but can also be combined in a value meal consisting of a burger, an order of fries, and a soft drink. The cost of the value meal is less than the costs of the three items combined. If Hubert bought 3 value meals, 2 individual burgers, and an individual soft drink for a total of $24, and if all individual items and value meals cost whole dollar amounts, what is the price of one value meal?

The total cost for an individual burger and an individual soft drink is $5.
An order of fries is more expensive than a soft drink and less expensive than a burger.
Let us assume,
  • Cost of a burger = $B
    Cost of an order of fries = $F
    Cost of a soft drinks = $S
    Cost of a value meal = $M

    B, F, S, and M are all positive integers and (B + F + S) > M
We need to find M

Now, 3M + 2B + S = 24
---> M = (24 - 2B - S)/3 = 8 - (2B + S)/3

As M should be a positive integer, (2B + S) must be a multiple of 3.

Statement 1: (B + S) = 5
Possible values of B and S are (1 and 4), (2 and 3), (3 and 2), and (4 and 1)
If B = 2 and S = 3 OR B = 3 and S = 2, (2B + S) is not a multiple of 3.
But if B = 1 and S = 4 OR B = 4 and S = 1, (2B + S) is a multiple of 3.
Hence,
  • Either M = 8 - (2B + S)/3 = 8 - (2 + 4)/3 = 8 - 2 = 6
    Or M = 8 - (2B + S)/3 = 8 - (8 + 1)/3 = 8 - 3 = 5
Not sufficient

Statement 2: S < F < B
This is not enough to determine the value of M

Not sufficient

1 & 2 Together: Now we know that S < B
Hence, only possible value of M is 5

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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