GMAT Challenge Series (700+): Q22

Dinner Party.png

Question:

At a restaurant, a group of friends ordered four main dishes and three side dishes at a total cost of $89. The prices of the seven items, in dollars, were all different integers, and every main dish cost more than every side dish. What was the price, in dollars, of the most expensive side dish?

(1) The most expensive main dish cost $16.
(2) The least expensive side dish cost $9.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

MBA Wisdom's Answer:

$$\text{Let the price of each main dish be: MD1, MD2, MD3 and MD4 (most expensive to least expesive)}$$ $$\text{Let the price of each side dish be: SD1, SD2, and SD3 (most expensive to least expesive)}$$ $$\text{Let the bill be: (MD1, MD2, MD3, MD4, SD1, SD2, SD3)}$$ $$$$ $$\text{Statement 1:}$$ $$\text{Most expensive bill: (16, 15, 14, 13, 12, 11, 10), Total cost: 91}$$ $$\text{We need to reduce the total cost by 2}$$ $$\text{Options:}$$ $$\text{Reduce SD3 by 2: (16, 15, 14, 13, 12, 11, 8), Total cost: 89}$$ $$\text{Reduce SD2 and SD3 by 1: (16, 15, 14, 13, 12, 10, 9), Total cost: 89}$$ $$\text{We cannot reduce SD1 as the total cost will be < 89}$$ $$\text{SD1 can only be 12}$$ $$\text{Statement 1 is SUFFICIENT}$$ $$$$ $$\text{Statement 2:}$$ $$\text{Least expensive bill: (15, 14, 13, 12, 11, 10, 9), Total cost: 84}$$ $$\text{We need to increase the total cost by 5}$$ $$\text{Options:}$$ $$\text{Increase MD1 by 5: (20, 14, 13, 12, 11, 10, 9), Total cost: 89}$$ $$\text{Increase MD1-4 and SD1 by 1: (16, 15, 14, 13, 12, 10, 9), Total cost: 89}$$ $$\text{SD1 can take on different values}$$ $$\text{Statement 2 is NOT SUFFICIENT}$$

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.