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16 Sep 2014, 01:06
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A shop offers candy bars for sale either individually or in packs of 10. If buying a pack of 10 candy bars costs less than buying 10 individual candy bars, how much does the shop charge for a pack of 10 candy bars?
(1) Buying a pack of 10 candy bars costs $2 more than buying 8 individual candy bars.
(2) Buying a pack of 10 candy bars costs 10 percent less than buying 10 individual candy bars.
(1) Buying a pack of 10 candy bars costs $2 more than buying 8 individual candy bars.
(2) Buying a pack of 10 candy bars costs 10 percent less than buying 10 individual candy bars.
16 Sep 2014, 01:06
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Official Solution:
A shop offers candy bars for sale either individually or in packs of 10. If buying a pack of 10 candy bars costs less than buying 10 individual candy bars, how much does the shop charge for a pack of 10 candy bars?
Let's assume the cost of a pack of 10 candy bars is \(x\) and the cost of an individual candy bar is \(y\).
(1) Buying a pack of 10 candy bars costs $2 more than buying 8 individual candy bars.
From this, we have: \(x = 8y + 2\). With two unknowns and one equation, this is not sufficient to determine \(x\).
(2) Buying a pack of 10 candy bars costs 10 percent less than buying 10 individual candy bars.
From this, we have: \(x = 0.9 *10y\). Again, with two unknowns and one equation, we cannot determine \(x\).
(1)+(2) We have two distinct linear equations with two unknowns. Thus, we can solve for both \(x\) and \(y\). Sufficient.
Answer: C
A shop offers candy bars for sale either individually or in packs of 10. If buying a pack of 10 candy bars costs less than buying 10 individual candy bars, how much does the shop charge for a pack of 10 candy bars?
Let's assume the cost of a pack of 10 candy bars is \(x\) and the cost of an individual candy bar is \(y\).
(1) Buying a pack of 10 candy bars costs $2 more than buying 8 individual candy bars.
From this, we have: \(x = 8y + 2\). With two unknowns and one equation, this is not sufficient to determine \(x\).
(2) Buying a pack of 10 candy bars costs 10 percent less than buying 10 individual candy bars.
From this, we have: \(x = 0.9 *10y\). Again, with two unknowns and one equation, we cannot determine \(x\).
(1)+(2) We have two distinct linear equations with two unknowns. Thus, we can solve for both \(x\) and \(y\). Sufficient.
Answer: C
08 Oct 2023, 02:35
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
