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

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

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New post Updated on: 05 Jan 2015, 03:42
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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.

Originally posted by marcodonzelli on 11 Mar 2008, 10:14.
Last edited by Bunuel on 05 Jan 2015, 03:42, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: Last Thursday, John assembled chairs at a rate of 3 chairs  [#permalink]

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New post 11 Mar 2008, 11:40
3
Suppose John worked J hours and Larry for L hours.
So from question we know that J + L = 7

Statement 1:
Tells that total chairs they collected is 25,
So we can write that 3J + 4L = 25
Now we have two equation and two unknowns so can be easily solved.

Statement 2:
Says Larry assembled more chairs than John. But does not tells how many chair in total they assembelled. So this alone is insufficient.

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

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New post 03 Jan 2015, 11:50
Hi All,

Since the numbers involved in this DS question are relatively small, we can "brute force" all of the possible options rather easily (if needed) to prove the correct answer.

We're given the rates of two people:
John assembles 3 chairs/hour
Larry assembles 4 chairs/hour
We're told that 7 hours of total work time was done, but that the two men did not work at the same time.

We're asked how many chairs JOHN assembled.

Assuming that we're not dealing with "fractional chairs", the number of possibilities is really limited - each man worked from 1 to 6 hours, so the possible outcomes are:

John/Larry/Total
3/24/27
6/20/26
9/16/25
12/12/24
15/8/23
18/4/22

Fact 1: A Total of 25 chairs were made.

There's just one option that fits this: John makes 9 and Larry makes 16 --> the answer to the question is 9
Fact 1 is SUFFICIENT

Fact 2: Larry assembled more chairs than John.

Here, we have 3 possibilities: John could have made 3, 6 or 9 chairs.
Fact 2 is INSUFFICIENT

Final Answer:

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

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New post 06 Jan 2015, 09:53
GIVEN
John's Rate = 3 chairs/hour
Larry's Rate = 4 chairs/hour

In total both of them worked for 7 hours

STATEMENT 1
Let the amount of time John take be J and Larry take be L
Now, we're given that both of them on 2 days created a total of 25 chairs
so using the formula \(r*t=w\)
we get the following equation
\(3J + 4L = 25\)
\(J = \frac{(25 - 4l)}{3}\)
Only 2 pair of values satisfy this equation
\(L=1 and J=7\)
and
\(L=4 and J=3\)
we'll not consider the first equation since the total time they were given was 7 hours, but adding the those two values give us a total of 8
so the only other pair gives us the time, from which we can take out the no of chairs for both of them

Statement 2
Doesn't give us anything to solve for

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

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New post 15 Dec 2019, 10:03
Top Contributor
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

Answer: A

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

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New post 15 Dec 2019, 10:16
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] 15 Dec 2019, 10:16
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