Data Sufficiency

At a certain refreshment stand, all hot dogs have the same price and all sodas have the same price. What is the total price of 3 hot dogs and 2 sodas at the refreshment stand?
1. The total price of 5 sodas at the stand is less than the total price of 2 hot dogs.
2. The total price of 9 hot dogs and 6 sodas at the stand is $21.

Answer is b.

Could you please explain?

Statement 1 tells us nothing that we can use to determine the prices.

Insufficient.

Statement 2 does not allow us to determine the prices of the hot dogs and sodas, doing which is one's initial inclination.

Notice something though. If hot dogs are H and sodas are S, Statement 2 gives us the following.

9H + 6S = 21

We can divide both sides by 3 to get 3H + 2S = 7.

So, because we have the price of 3H + 2S, Statement 2 is sufficient and the answer is B

(Notice my use of the Spoiler function to cover the right answer in case someone wants to try the question before seeing the answer.)

Marty Murray wrote:Statement 1 tells us nothing that we can use to determine the prices.

Insufficient.

Statement 2 does not allow us to determine the prices of the hot dogs and sodas, doing which is one's initial inclination.

Notice something though. If hot dogs are H and sodas are S, Statement 2 gives us the following.

9H + 6S = 21

We can divide both sides by 3 to get 3H + 2S = 7.

So, because we have the price of 3H + 2S, Statement 2 is sufficient and the answer is B

(Notice my use of the Spoiler function to cover the right answer in case someone wants to try the question before seeing the answer.)

Thanks Murray,
How about this one?


At a refreshment stand, each can of soda sells for the same price and each sandwich sells for the same price. What is the total price for 2 sandwiches and 3 cans of soda at the stand?

(1) At the stand the total price for 1 sandwich and 1 can of soda if $3
(2) At the stand the total price for 3 sandwiches and 2 cans of soda is $8

didieravoaka wrote: At a refreshment stand, each can of soda sells for the same price and each sandwich sells for the same price. What is the total price for 2 sandwiches and 3 cans of soda at the stand?

(1) At the stand the total price for 1 sandwich and 1 can of soda if $3
(2) At the stand the total price for 3 sandwiches and 2 cans of soda is $8

Statement 1 does not provide a way to determine the price of each item or a way to get to the cost of 2 sandwiches and 3 cans of soda.

Statement 2 does not provide a way to determine the price of each item or a way to get to the cost of 2 sandwiches and 3 cans of soda.

Let's call sandwiches S and cans of soda C.

Statement 1: S + C = 3.

Statement 2: 3S + 2C = 8

Those equations are distinct and can be combined to determine the values of S and C and, therefore, the value of 2S + 3C.

So combined the statements are sufficient and the answer is C.

didieravoaka wrote: How about this one?


At a refreshment stand, each can of soda sells for the same price and each sandwich sells for the same price. What is the total price for 2 sandwiches and 3 cans of soda at the stand?

(1) At the stand the total price for 1 sandwich and 1 can of soda if $3
(2) At the stand the total price for 3 sandwiches and 2 cans of soda is $8

This one is much less likely to appear on the GMAT, though: the obvious answer (C) is correct, and unless you're on a very easy (for you) question, the obvious answer is seldom the right one on test day! I would guess about 80-90% of test takers would get this one right, while the other would be much harder.