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14 Aug 2024, 08:55
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E
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A person bought x number of apples, y number of oranges, and z number of mangoes from a shop. What is the total price of this transaction if each apple costs $2, each orange costs $2.50, and each mango costs $3 ?
(1) The number of apples bought is 12 more than the number of oranges bought. The number of mangoes bought is half the number of apples bought.
(2) The average number of fruits purchased from the three varieties is greater than 29 and less than 33.
ID: 700343
(1) The number of apples bought is 12 more than the number of oranges bought. The number of mangoes bought is half the number of apples bought.
(2) The average number of fruits purchased from the three varieties is greater than 29 and less than 33.
ID: 700343
14 Aug 2024, 09:13
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A person bought x number of apples, y number of oranges, and z number of mangoes from a shop. What is the total price of this transaction if each apple costs $2, each orange costs $2.50, and each mango costs $3 ?
We need to find the value of 2x + 2.5y + 3z.
(1) The number of apples bought is 12 more than the number of oranges bought. The number of mangoes bought is half the number of apples bought.
This implies x = y + 12 and x = 2z. However, without the actual values of x, y, or z, this information alone is not sufficient.
(2) The average number of fruits purchased from the three varieties is greater than 29 and less than 33.
This implies that 29 < (x + y + z)/3 < 33. This alone does not provide enough information to determine the total price. Not sufficient.
(1)+(2) Substituting y = x - 12 and z = x/2 into the inequality 29 < (x + y + z)/3 < 33, we get 198/5 < x < 222/5, which simplifies to 39.something < x < 44.something. Since x must be even (because x = 2z), x could be 40 or 42. Each of these values leads to different values for y and z, resulting in different total prices. Therefore, this combined information is still not sufficient.
Answer: E.
We need to find the value of 2x + 2.5y + 3z.
(1) The number of apples bought is 12 more than the number of oranges bought. The number of mangoes bought is half the number of apples bought.
This implies x = y + 12 and x = 2z. However, without the actual values of x, y, or z, this information alone is not sufficient.
(2) The average number of fruits purchased from the three varieties is greater than 29 and less than 33.
This implies that 29 < (x + y + z)/3 < 33. This alone does not provide enough information to determine the total price. Not sufficient.
(1)+(2) Substituting y = x - 12 and z = x/2 into the inequality 29 < (x + y + z)/3 < 33, we get 198/5 < x < 222/5, which simplifies to 39.something < x < 44.something. Since x must be even (because x = 2z), x could be 40 or 42. Each of these values leads to different values for y and z, resulting in different total prices. Therefore, this combined information is still not sufficient.
Answer: E.
General Discussion
17 Aug 2024, 07:44
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Question: 2x + 2.5y + 3z = ?
(1) The number of apples bought is 12 more than the number of oranges bought. The number of mangoes bought is half the number of apples bought.
\(x = y + 12\)
\(z = \frac{x}{2} = \frac{y}{2} + 6\)
=> Insufficient
(2) The average number of fruits purchased from the three varieties is greater than 29 and less than 33.
29 < \frac{x + y + z}{3} < 33
=> 87 < x + y + z < 99
=> Insufficient
(1) + (2) Combined
\(x + y + z = (y + 12) + y + (\frac{y}{2} + 6) = \frac{5y}{2} + 18 \)
87 < x + y + z < 99
=> 69 < \(\frac{5y}{2}\) < 81
=> 27 < y < 33
=> Insufficient
(1) The number of apples bought is 12 more than the number of oranges bought. The number of mangoes bought is half the number of apples bought.
\(x = y + 12\)
\(z = \frac{x}{2} = \frac{y}{2} + 6\)
=> Insufficient
(2) The average number of fruits purchased from the three varieties is greater than 29 and less than 33.
29 < \frac{x + y + z}{3} < 33
=> 87 < x + y + z < 99
=> Insufficient
(1) + (2) Combined
\(x + y + z = (y + 12) + y + (\frac{y}{2} + 6) = \frac{5y}{2} + 18 \)
87 < x + y + z < 99
=> 69 < \(\frac{5y}{2}\) < 81
=> 27 < y < 33
=> Insufficient
