GMAT Math : GMAT Quantitative Reasoning
Study concepts, example questions & explanations for GMAT Math
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Example Questions
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 
Example Question #1 : Dsq: Understanding Arithmetic Sets
Let 
The multiples of 3 between 29 and 50 are 30, 33, 36, 39, 42, 45, and 48 - therefore, 
The number of subsets in a set can be calculated by raising 2 to the power of the number of elements. Therefore, the answer to our question is 
Example Question #2 : Dsq: Understanding Arithmetic Sets
The senior class of Watson High School has 613 students. An election was held for Senior Class President between three candidates, Martindale, Nance, and Osgood.
If every student voted for one of these three, and the student with the most votes was declared the winner, who won the election?
Statement 1: Martindale got 240 votes.
Statement 2: Nance got 244 votes.
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 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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
If we only know Martindale got 240 votes, since 240 is not a majority, we cannot determine the winner with certainty. For example, the following two results are possible:
Martindale: 240, Nance: 0, Osgood 373 - Osgood wins
Martindale 240, Nance 373, Osgood 0 - Nance wins.
A similar argument shows the second statement insufficient as well, since 244 is not a majority.
But the two statements together allow us a complete picture;
Martindale 240, Nance 244, Osgood 129 - Nance wins
Example Question #1 : Sets
The senior class has 457 students. An election was held for Senior Class President between three candidates, Anderson, Benson, and Carter.
If every student voted for one of these three, and the student with the most votes was declared the winner, who won the election?
Statement 1: Benson got 251 votes.
Statement 2: Carter got 101 votes.
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 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT 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.
From Statement 1 alone, it can be immediately deduced that Benson won, since 251 of the 457 votes consititute a majority:
Benson got 54.9% of the vote, so there is no way that Anderson or Carter could have bested Benson.
Statement 2 tells only that Carter did not win, since either Anderson or Benson had to have won at least half, or 
Example Question #3 : Sets
Let 
Infinitely many
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