marcodonzelli wrote:
Last Thursday, John assembled chairs at a rate of 3 chairs per hour for part of the day and Larry assembled no chairs. Last Friday, Larry assembled chairs at a rate of 4 chairs per hour for part of the day and John assembled no chairs. If John and Larry assembled chairs for a total of 7 hours during these two days, how many chairs did John assemble last Thursday?
(1) During these two days, John and Larry assembled a total of 25 chairs.
(2) During these two days, Larry assembled more chairs than John did.
Given: Last Thursday, John assembled chairs at a rate of 3 chairs per hour for part of the day and Larry assembled no chairs. Last Friday, Larry assembled chairs at a rate of 4 chairs per hour for part of the day and John assembled no chairs. John and Larry assembled chairs for a total of 7 hours during these two days Let H = the number of hours that John spent assembling chairs on Thursday
So, 7 - H = the number of hours that Larry been assembling chairs on Friday (since they spent a total of 7 hours assembling chairs)
Target question: How many chairs did John assemble last Thursday? Statement 1: During these two days, John and Larry assembled a total of 25 chairs. Since John assembles 3 chairs per hour, and since Larry assembles for chairs per hour we can write: 3H + 4(7 - H) = total number of chairs assembled
This means: 3H + 4(7 - H) = 25
Expand: 3H + 28 - 4H = 25
Simplify: -H + 28 = 25
Solve to get: H = 3
This means that John spent 3 hours assembling chairs last Thursday.
At a rate of 3 chairs per hour, we know that
John assembled 9 chairs last ThursdaySince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: During these two days, Larry assembled more chairs than John didThis is not enough information to answer to part a question. Consider these two possible cases:
Case a: John spent 1 hour assembling chairs, and Larry spent 6 hours assembling chairs. At a rate of 3 chairs per hour,
John assembled 3 chairs last ThursdayCase b: John spent 2 hours assembling chairs, and Larry spent 5 hours assembling chairs. At a rate of 3 chairs per hour,
John assembled 6 chairs last ThursdaySince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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