Counting Methods - GMAT Quantitative
Card 1 of 120
Oteri can choose to wear jeans, sweat pants, or shorts, a button down or a tee shirt, and a hat or no hat. How many different outfit combinations does he have in his wardrobe?
Oteri can choose to wear jeans, sweat pants, or shorts, a button down or a tee shirt, and a hat or no hat. How many different outfit combinations does he have in his wardrobe?
Tap to reveal answer
He has 3 pants, 2 shirts, 2 hat choices (hat or no hat).
He has 3 pants, 2 shirts, 2 hat choices (hat or no hat).
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Olivia picks 
balls, each one after the other, from a basket containing 
balls.
How many possible combinations of balls can she end up with?
(1) 
(2) 
Olivia picks
How many possible combinations of balls can she end up with?
(1)
(2)
Tap to reveal answer
Each statement on its own gives us one equation with 2 unknowns, which is unsolvable. Therefore each statement alone is not sufficient.
The two equations are equivalent: x + y = 13 and 2.(x+y) = 2 x 13 = 26
Therefore we cannot sole for x and y either with both equations.
Each statement on its own gives us one equation with 2 unknowns, which is unsolvable. Therefore each statement alone is not sufficient.
The two equations are equivalent: x + y = 13 and 2.(x+y) = 2 x 13 = 26
Therefore we cannot sole for x and y either with both equations.
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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.
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.
Tap to reveal answer
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.
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.
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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.
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.
Tap to reveal answer
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 
.
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
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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:
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:
Tap to reveal answer
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 
.
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
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A Veggie Platter at the restaurant where George likes to eat comprises four different vegetables. How many possible Veggie Platters can George choose from?
Statement 1: George can choose from ten vegetables.
Statement 2: The choices are black-eyed peas, corn on the cob, and mashed potatoes, among seven others.
A Veggie Platter at the restaurant where George likes to eat comprises four different vegetables. How many possible Veggie Platters can George choose from?
Statement 1: George can choose from ten vegetables.
Statement 2: The choices are black-eyed peas, corn on the cob, and mashed potatoes, among seven others.
Tap to reveal answer
Each statement alone says that George can choose from ten vegetables - Statement 2 is different only in that it names three of them. George can choose any one of 
different Veggie Platters.
Each statement alone says that George can choose from ten vegetables - Statement 2 is different only in that it names three of them. George can choose any one of
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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.
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.
Tap to reveal answer
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.
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.
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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.
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.
Tap to reveal answer
If there are 
entrees and 
beverages, Mary can select two entrees from the 
entrees in 
ways; by the multiplication principle, she can choose a Lunch Meal Deal 
ways.
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 
and 
, and the number of possible meals can be calculated.
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
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A Lunch Deal Meal at the Chinese restaurant where Jack likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Meal Deals can Jack choose from?
Statement 1: Jack can choose from seven appetizers and ten entrees.
Statement 2: Jack can choose from as many beverages as appetizers.
A Lunch Deal Meal at the Chinese restaurant where Jack likes to eat comprises one appetizer, one entree, and one beverage. How many possible Lunch Meal Deals can Jack choose from?
Statement 1: Jack can choose from seven appetizers and ten entrees.
Statement 2: Jack can choose from as many beverages as appetizers.
Tap to reveal answer
By the multiplication principle, the number of meals Jack can make is the product of the number of appetizers, the number of entrees, and the number of beverages. Statement 1 tells only the first two; Statement 2 does not give any of these quantities. From the two statements together, we know that there are seven appetizers, ten entrees, and seven beverages, so there are 
possible Lunch Deal Meals.
By the multiplication principle, the number of meals Jack can make is the product of the number of appetizers, the number of entrees, and the number of beverages. Statement 1 tells only the first two; Statement 2 does not give any of these quantities. From the two statements together, we know that there are seven appetizers, ten entrees, and seven beverages, so there are
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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.
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.
Tap to reveal answer
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.
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.
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A Veggie Platter at the restaurant where Lucy likes to eat comprises four different vegetables. How many possible Veggie Platters can Lucy choose from?
Statement 1: The Veggie Platter costs $5.29 plus tax.
Statement 2: The menu from which Lucy may choose her vegetables is below:
A Veggie Platter at the restaurant where Lucy likes to eat comprises four different vegetables. How many possible Veggie Platters can Lucy choose from?
Statement 1: The Veggie Platter costs $5.29 plus tax.
Statement 2: The menu from which Lucy may choose her vegetables is below:
Tap to reveal answer
Statement 1 alone gives irrelevant information; the cost of the Veggie Platter has no bearing on the number of possible combinations.
From Statement 2 alone, it can be determined that there are ten choices; therefore, the number of ways Lucy can order a Veggie Platter can be determined to be 
.
Statement 1 alone gives irrelevant information; the cost of the Veggie Platter has no bearing on the number of possible combinations.
From Statement 2 alone, it can be determined that there are ten choices; therefore, the number of ways Lucy can order a Veggie Platter can be determined to be
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A Veggie Platter at the restaurant where Georgia likes to eat comprises four different vegetables. How many possible Veggie Platters can Georgia choose from?
Statement 1: Half the choices are listed as being "hearth healthy".
Statement 2: Seven of the choices are not listed as being "hearth healthy".
A Veggie Platter at the restaurant where Georgia likes to eat comprises four different vegetables. How many possible Veggie Platters can Georgia choose from?
Statement 1: Half the choices are listed as being "hearth healthy".
Statement 2: Seven of the choices are not listed as being "hearth healthy".
Tap to reveal answer
The only thing needed in order to answer the question is the number of vegetables from which Georgia has to choose. Neither statement alone gives this information.
However, it is possible to deduce this information from both statements together. From Statement 1, half the choices are "hearth healthy"; therefore, half are not. From Statement 2, this amounts to seven choices, so the total number of vegetables on the menu is fourteen, and there are a total of 
possible Veggie Platters.
The only thing needed in order to answer the question is the number of vegetables from which Georgia has to choose. Neither statement alone gives this information.
However, it is possible to deduce this information from both statements together. From Statement 1, half the choices are "hearth healthy"; therefore, half are not. From Statement 2, this amounts to seven choices, so the total number of vegetables on the menu is fourteen, and there are a total of
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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.
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.
Tap to reveal answer
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.
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.
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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.
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.
Tap to reveal answer
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 
.
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
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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.
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.
Tap to reveal answer
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.
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.
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Oteri can choose to wear jeans, sweat pants, or shorts, a button down or a tee shirt, and a hat or no hat. How many different outfit combinations does he have in his wardrobe?
Oteri can choose to wear jeans, sweat pants, or shorts, a button down or a tee shirt, and a hat or no hat. How many different outfit combinations does he have in his wardrobe?
Tap to reveal answer
He has 3 pants, 2 shirts, 2 hat choices (hat or no hat).
He has 3 pants, 2 shirts, 2 hat choices (hat or no hat).
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Olivia picks balls, each one after the other, from a basket containing balls.
How many possible combinations of balls can she end up with?
(1)
(2)
Olivia picks
How many possible combinations of balls can she end up with?
(1)
(2)
Tap to reveal answer
Each statement on its own gives us one equation with 2 unknowns, which is unsolvable. Therefore each statement alone is not sufficient.
The two equations are equivalent: x + y = 13 and 2.(x+y) = 2 x 13 = 26
Therefore we cannot sole for x and y either with both equations.
Each statement on its own gives us one equation with 2 unknowns, which is unsolvable. Therefore each statement alone is not sufficient.
The two equations are equivalent: x + y = 13 and 2.(x+y) = 2 x 13 = 26
Therefore we cannot sole for x and y either with both equations.
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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.
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.
Tap to reveal answer
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.
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.
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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.
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.
Tap to reveal answer
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 .
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
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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:
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:
Tap to reveal answer
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 .
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
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