GMAT Math : Arithmetic
Study concepts, example questions & explanations for GMAT Math
All GMAT Math Resources
Example Questions
Example Question #4 : Counting Methods
A Lunch Deal Meal at the Chinese restaurant where Mickey likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Meal Deals can Mickey choose from?
Statement 1: The number of appetizers and the number of beverages from which Mickey may choose are both equal to the number of entrees that do not have shrimp.
Statement 2: Mickey may choose any of ten entrees, but if he chooses any of the three entrees with shrimp, he must pay an upcharge of $1.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
By the multiplication principle, the number of possible Lunch Deal Meals is the product of the number of appetizers, the number of entrees, and the number of beverages. Neither statement alone gives all three numbers.
Assume both statements are true. From Statement 2, there are ten entrees on the menu, seven of which do not have shrimp (note that the upcharge is irrelevant). From Statement 1, the number of appetizers and the number of beverages are both equal to the number of entrees that do not have shrimp, which is seven. Therefore, the number of possible Lunch Deal Meals is 
Example Question #8 : Dsq: Understanding Counting Methods
A Veggie Platter at the restaurant where Steve likes to eat comprises four different vegetables. How many possible Veggie Platters can Steve choose from?
Statement 1: The menu from which Steve may choose his vegetables is below:
Statement 2: If Steve orders corn on the cob or broccoli, he will pay an upcharge; if he chooses only from the remaining eight vegetables, he will pay the regular price.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
From either statement alone, it can be determined that there are ten choices; Statement 1 lists them, and Statement 2, while giving some irrelevant information, still gives this number, albeit a bit obliquely ("corn on the cob or broccoli", "the other eight choices"). Therefore, the number of ways Steve can order a Veggie Platter can be determined to be 
Example Question #4 : Dsq: Understanding Counting Methods
A Lunch Deal Meal at the restaurant where Allen likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Meal Deals can Allen choose from?
Statement 1: Allen can choose iced tea, cola, milk, or any of nine other beverages.
Statement 2: Allen can choose General Tso's chicken, Mu Shu pork, egg foo young, or any of seven other entrees.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
By the multiplication principle, the number of possible Lunch Deal Meals is the product of the number of appetizers, the number of entrees, and the number of beverages. The two statements together give us the number of entrees and the number of beverages, but not the number of appetizers.
Example Question #5 : Counting Methods
A Veggie Platter at the restaurant where Maggie likes to eat comprises four different vegetables. How many possible Veggie Platters can Maggie choose from?
Statement 1: The Veggie Platter costs $6.19 plus tax if Maggie selects a baked potato as one of her choices, and $5.79 plus tax if Maggie chooses only from the remaining eleven choices.
Statement 2: Maggie has ordered corn on the cob every time she has ordered a Veggie Platter.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 1 gives the number of vegetables from which Maggie may choose, albeit somewhat obliquely ("baked potato", "the remaining eleven choices") and along with other, irrelevant information. Therefore, the number of ways Maggie can order a Veggie Platter can be determined to be 
Statement 2 alone is irrelevant, since the question asks for the total number of possible meals. What Maggie has actually ordered in the past has no bearing on the answer.
Example Question #11 : Dsq: Understanding Counting Methods
A Lunch Deal Meal at the Chinese restaurant where Phyllis likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Deal Meals can Phyllis choose from?
Statement 1: If Phyllis orders either shrimp-based appetizer or one of the three shrimp-based entrees, she will pay extra.
Statement 2: If Phyllis doesn't want shrimp, she has five appetizers and seven entrees to choose from.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
By the multiplication principle, the number of possible Lunch Deal Meals is the product of the number of appetizers, the number of entrees, and the number of beverages. The two statements together give the number of appetizers - two with shrimp and five without for a total of seven - and the number of entrees - three with shrimp and seven without - but not the number of beverages.
Example Question #11 : Counting Methods
A Lunch Deal Meal at the Japanese restaurant where Mary likes to eat comprises two different entrees and one beverage. How many possible Lunch Deal Meals can Mary choose from?
Statement 1: Mary can choose any of eight different entrees.
Statement 2: Mary can choose as many beverages as entrees.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
If there are 
Therefore, the number of entrees and the number of beverages need to be known. Neither statement alone gives both values, but from both statements together, we know that 
Example Question #141 : Arithmetic
A Lunch Deal Meal at the Korean restaurant where Vanessa likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Deal Meals can Vanessa choose from?
Statement 1: Vanessa can choose from twice as many entrees as appetizers.
Statement 2: Vanessa can choose from twice as many appetizers as beverages.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
By the multiplication principle, the number of possible Lunch Deal Meals is the product of the number of appetizers, the number of entrees, and the number of beverages. The two statements together only give a relationship among the three, but they do not give any clues as to the actual numbers. Therefore, they give insufficient information.
Example Question #144 : Arithmetic
A Lunch Deal Meal at the Chinese restaurant where Jing likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Deal Meals can Jing choose from?
Statement 1: The choices include six appetizers, six entrees, and seven beverages.
Statement 2: The Lunch Deal Meal menu is the one shown below:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
By the multiplication principle, the number of possible Lunch Deal Meals is the product of the number of appetizers, the number of entrees, and the number of beverages. Each statement alone gives all three numbers - Statement 1 states them explicitly, and Statement 2 gives the actual menu, allowing the number of meals to be calculated as 
Example Question #12 : Dsq: Understanding Counting Methods
A Lunch Deal Meal at the Korean restaurant where Mickey likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Deal Meals can Mickey choose from?
Statement 1: The number of appetizers, the number of entrees, and the number of beverages are the same.
Statement 2: If Mickey orders one of the shrimp dishes, there is a $1 upcharge; if he orders one of the other six entrees, there is no upcharge.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
By the multiplication principle, the number of possible Lunch Deal Meals is the product of the number of appetizers, the number of entrees, and the number of beverages.
Assume both statements are true. From Statement 1 it can be determined that there are an equal number of choices from each column, but the actual number of choices still needs to be determined. From Statement 2, it can be determined only that there are at least eight entrees - it is given that there are six dishes without shirimp, but the number of dishes with shrimp is not given (only that there must be more than two, since a plural is given). The statements together give insufficient information.
Example Question #1 : Sets
How many subsets does set 
Statement 1: 
Statement 2: 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
The number of subsets of any set can be calculated by raising 2 to the power of the number of elements in the set. The first statement gives you that information immediately. The second gives you enough information to find the number of elements, as there are eight primes between 1 and 20: 2, 3, 5, 7, 11, 13, 17, and 19. From either statement alone, you can deduce the answer to be 
All GMAT Math Resources
