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B
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Difficulty:
95%
(hard)
Question Stats:
29% (02:58) correct
71%
(02:28)
wrong
based on 31
sessions
History
Date
Time
Result
Not Attempted Yet
At two shops, A and B, the prices per kilogram of three types of cheese—American, Provolone, and Swiss—were as follows:
• American: $15 at A and $16 at B
• Provolone: $17 at A and $18 at B
• Swiss: $19 at A and $20 at B
Nerea bought a total of 3 kilograms of cheese at A, whereas Octavio bought a total of 3 kilograms of cheese at B.
Did Octavio spend more than Nerea?
(1) Octavio bought American, Provolone, and Swiss cheese in the ratio 2 : 7 : 6.
(2) Nerea bought American, Provolone, and Swiss cheese in the ratio 6 : 2 : 1.
• American: $15 at A and $16 at B
• Provolone: $17 at A and $18 at B
• Swiss: $19 at A and $20 at B
Nerea bought a total of 3 kilograms of cheese at A, whereas Octavio bought a total of 3 kilograms of cheese at B.
Did Octavio spend more than Nerea?
(1) Octavio bought American, Provolone, and Swiss cheese in the ratio 2 : 7 : 6.
(2) Nerea bought American, Provolone, and Swiss cheese in the ratio 6 : 2 : 1.
26 Mar 2026, 15:18
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For Statement 1,
Octavio bought American, Provolone, and Swiss Cheese in the ratio of 2:7:6. Since we know he bought 3 kgs of cheese we can take:
2x + 7x + 6x = 3
15x = 3
x = 1/5 = 0.2
We can infer from this that he bought, 0.2 x 2 = 0.4 of American, 0.2 x 7 = 1.4 of Provolone, and 0.2 x 6 = 1.2 of Swiss Cheese.
Multiplying by the prices of deli B:
Octavio spent (16 x 0.4) + (18 x 1.4) + (20 x 1.2) = 55.6 $
Now, the minimum that Nerea could have spent is by buying 3 kgs of the cheapest cheese, and the max is 3 kgs of the most expensive cheese which gives us the potential value of Nerea's spend as:
Min = 3 x 15 = 45 $
Max = 3 x 19 = 57 $
Therefore, it cannot be exactly deduced if Octavio outspent Nerea or not
Statement 2
Nerea bought American, Provolone, and Swiss Cheese in the ratio of 6:2:1
which similar to the first case gives us: 6y + 2y + y = 3
9y = 3
y = 1/3
Nerea therefore bought 2 kg of American, 2/3 kg of Provolone, and 1/3 kg of Swiss cheese
Multiplying by prices we get
(15 x 2) + (17 x 2/3) + (19 x 1/3) = approx. 47.67$
Now the minimum Octavio could've spent is if he bought 3 kgs of the cheapest cheese (American cheese in this case)
Which gives us 3 x 16 = 48$
The minimum amount Octavio could have spent is greater than the amount Nerea could've spent so we statement 2 is sufficient.
The answer is B.
Octavio bought American, Provolone, and Swiss Cheese in the ratio of 2:7:6. Since we know he bought 3 kgs of cheese we can take:
2x + 7x + 6x = 3
15x = 3
x = 1/5 = 0.2
We can infer from this that he bought, 0.2 x 2 = 0.4 of American, 0.2 x 7 = 1.4 of Provolone, and 0.2 x 6 = 1.2 of Swiss Cheese.
Multiplying by the prices of deli B:
Octavio spent (16 x 0.4) + (18 x 1.4) + (20 x 1.2) = 55.6 $
Now, the minimum that Nerea could have spent is by buying 3 kgs of the cheapest cheese, and the max is 3 kgs of the most expensive cheese which gives us the potential value of Nerea's spend as:
Min = 3 x 15 = 45 $
Max = 3 x 19 = 57 $
Therefore, it cannot be exactly deduced if Octavio outspent Nerea or not
Statement 2
Nerea bought American, Provolone, and Swiss Cheese in the ratio of 6:2:1
which similar to the first case gives us: 6y + 2y + y = 3
9y = 3
y = 1/3
Nerea therefore bought 2 kg of American, 2/3 kg of Provolone, and 1/3 kg of Swiss cheese
Multiplying by prices we get
(15 x 2) + (17 x 2/3) + (19 x 1/3) = approx. 47.67$
Now the minimum Octavio could've spent is if he bought 3 kgs of the cheapest cheese (American cheese in this case)
Which gives us 3 x 16 = 48$
The minimum amount Octavio could have spent is greater than the amount Nerea could've spent so we statement 2 is sufficient.
The answer is B.
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