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14 Apr 2024, 01:46
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E
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Difficulty:
35%
(medium)
Question Stats:
71% (01:42) correct
29%
(01:43)
wrong
based on 469
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Both restaurants in downtown Rosemond—Sam's Diner and the Main Street Café—offer a lunch special consisting of a sandwich, a dessert, and a drink for a set price. Which restaurant offers customers more choices for the lunch special?
(1) The Main Street Café offers twice as many sandwich choices as Sam's Diner.
(2) Sam's Diner has 2 more drink choices and 2 more dessert choices than the Main Street Café.
(1) The Main Street Café offers twice as many sandwich choices as Sam's Diner.
(2) Sam's Diner has 2 more drink choices and 2 more dessert choices than the Main Street Café.
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14 Apr 2024, 04:25
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Let the sandwiches = \(x\), drinks = \(y\) and desserts = \(z\)
To solve for the number of lunch special choices for either establishment we will multipy the number of sandwich choices by the number of drinks choices by the number of dessert options.
(1) The Main Street Café offers twice as many sandwich choices as Sam's Diner.
From this we have that Main Street Cafe has \(2x\) sandwich options while Sam's Diner has \(x\) sandwich choices. No info is provided pertaining to the number of drinks or desserts for either restaurant.
INSUFFICIENT
(2) Sam's Diner has 2 more drink choices and 2 more dessert choices than the Main Street Café.
Here we are told that Main Street Cafe has \(y\) drink choices and \(z\) dessert choices, while Sam's Diner has \(y+2\) drink choices and \(z+2\) dessert choices. No info is provided about the number of sandwich choices for either establishment.
INSUFFICIENT
(1+2)
Putting the info together we can conclude the following:
Main Street Cafe: Sandwich choices: \(2x\); Drink choices: \(y\) & Dessert choices: \(z\)
Total lunch special choices: \(2x*y*z\)
Sam's Diner: Sandwich choices: \(x\); Drink choices: \(y+2\) & Dessert choices: \(z+z\)
Total lunch special choices: \(x*(y+2)*(z+2)\)
Instead of plugging numbers, which can lead one astray, I want to set up two inequalities to check if it is possible that either could be bigger than the other.
Main Street Cafe has more options:
\(2x*y*z > x*(y+2)*(z+2)\)
\(2yz > (y+2)*(z+2)\)
Here if I let y = 10 and z = 10 the inequality holds. On the lefthand side I will get 200 and on the righthand side I will get 144.
Sam's Diner has more options:
\(2x*y*z < x*(y+2)*(z+2)\)
\(2yz < (y+2)*(z+2)\)
Here if I let y = 1 and z = 1 the inequality will hold. On the left I will have 2, and on the right I will have 9.
As both outcomes are possible, and no other parameters are provided, it is impossible to deduce which of the establishments has more choices for the lunch special.
INSUFFICIENT
ANSWER E
To solve for the number of lunch special choices for either establishment we will multipy the number of sandwich choices by the number of drinks choices by the number of dessert options.
(1) The Main Street Café offers twice as many sandwich choices as Sam's Diner.
From this we have that Main Street Cafe has \(2x\) sandwich options while Sam's Diner has \(x\) sandwich choices. No info is provided pertaining to the number of drinks or desserts for either restaurant.
INSUFFICIENT
(2) Sam's Diner has 2 more drink choices and 2 more dessert choices than the Main Street Café.
Here we are told that Main Street Cafe has \(y\) drink choices and \(z\) dessert choices, while Sam's Diner has \(y+2\) drink choices and \(z+2\) dessert choices. No info is provided about the number of sandwich choices for either establishment.
INSUFFICIENT
(1+2)
Putting the info together we can conclude the following:
Main Street Cafe: Sandwich choices: \(2x\); Drink choices: \(y\) & Dessert choices: \(z\)
Total lunch special choices: \(2x*y*z\)
Sam's Diner: Sandwich choices: \(x\); Drink choices: \(y+2\) & Dessert choices: \(z+z\)
Total lunch special choices: \(x*(y+2)*(z+2)\)
Instead of plugging numbers, which can lead one astray, I want to set up two inequalities to check if it is possible that either could be bigger than the other.
Main Street Cafe has more options:
\(2x*y*z > x*(y+2)*(z+2)\)
\(2yz > (y+2)*(z+2)\)
Here if I let y = 10 and z = 10 the inequality holds. On the lefthand side I will get 200 and on the righthand side I will get 144.
Sam's Diner has more options:
\(2x*y*z < x*(y+2)*(z+2)\)
\(2yz < (y+2)*(z+2)\)
Here if I let y = 1 and z = 1 the inequality will hold. On the left I will have 2, and on the right I will have 9.
As both outcomes are possible, and no other parameters are provided, it is impossible to deduce which of the establishments has more choices for the lunch special.
INSUFFICIENT
ANSWER E
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