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# Last Thursday, John assembled chairs at a rate of 3 chairs

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Re: Last Thursday, John assembled chairs at a rate of 3 chairs [#permalink]
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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 Thursday
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: During these two days, Larry assembled more chairs than John did
This 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 Thursday
Case 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 Thursday
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: Last Thursday, John assembled chairs at a rate of 3 chairs [#permalink]
from given info
Days-- J--L
Thu--3 -- 0
Fri---0--4
and x+y = 7
#1
3x+4y = 25
solve for both ; sufficient
#2
4y>3x
x+y= 7
insufficient
IMO A

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.
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Re: Last Thursday, John assembled chairs at a rate of 3 chairs [#permalink]
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Re: Last Thursday, John assembled chairs at a rate of 3 chairs [#permalink]
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