sgpk242 wrote:
A sandwich shop offers a sandwich menu, a soup menu, and a salad menu. The number of salads listed on the salad menu is twice the number of sandwiches listed on the sandwich menu and 1 more than the number of soups listed on the soup menu. How many soups are listed on the soup menu?
(1) The total number of choices a customer has when choosing 1 item from each of 2 of the menus is 63.
(2) The total number of choices a customer has when choosing 1 item from each of the 3 menus is 90.
Really struggling on the wording from Statement 1...
Bunuel can you please break down how you derived an equation from Statement 1?
(1) indicates that the total number of combinations available when a customer chooses one item from any two of the three menus is 63. Assuming x represents the number of sandwiches, salads are then 2x (twice the number of sandwiches) and soups are 2x - 1 (one fewer than the number of salads). This can be broken down into the following combinations:
1. Sandwich & Salad = x*2x = 2x^2
2. Sandwich & Soup = x(2x - 1) = 2x^2 - x
3. Salad & Soup = 2x(2x - 1) = 4x^2 - 2x
Adding these combinations gives:
2x^2 + (2x^2 - x) + (4x^2 - 2x) = 63
x(8x - 3) = 63
By plugging in factors of 63 for x, we find that only x = 3 works (testing is only necessary up to 7, since already if x = 7, the product exceeds 63). Hence, the first statement is sufficient.
Similarly, (2) indicates that the total number of combinations available when a customer chooses one item from each of the three menus is 90. This implies that:
x*2x(2x - 1) = 90
Again, by plugging in factors of 90 for x, we quickly find that x = 3 (similarly, testing only up to 5 is necessary, since already if x = 5, the product exceeds 90). Thus, the second statement is also sufficient.
Answer: D.
Hope it's clear.