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# A machine, working at a constant rate, manufactures 36 staplers in 28

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Posts: 52344
A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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12 Mar 2015, 05:50
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Difficulty:

5% (low)

Question Stats:

87% (01:22) correct 13% (02:03) wrong based on 145 sessions

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A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125
B. 128
C. 135
D. 144
E. 150

Kudos for a correct solution.

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Re: A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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12 Mar 2015, 06:34
the machine rate=R
R*28=36
R=36/28

staplers that can make in 1 hr 45 min (105 minutes)=36/28*105=135
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Re: A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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12 Mar 2015, 08:55
1
If the machine makes 36 staples in 28mins, then how many staples would it make in 105mins
36staples ---> 28mins
y staples ---> 105mins

y = 36 x 105 /28
y = 135
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A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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12 Mar 2015, 09:57
Bunuel wrote:
A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125
B. 128
C. 135
D. 144
E. 150

Kudos for a correct solution.

The rate of the machine is 540/7.
Multiplying that rate by the time, which is 7/4 gives us 135 staples produced.

Or

we can solve through ratios.
36/28 = X/105
X = 135

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Re: A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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13 Mar 2015, 01:56
1

Convert Hours in Minutes

Staplers $$= (60+45)* \frac{36}{28} = 135$$
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A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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13 Mar 2015, 03:16
1
A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125
B. 128
C. 135
D. 144
E. 150

Ans: C.
How?
Well the machine makes 36 staplers in 28 mins. That means every minute it makes 36/28 = 9/7 staplers. It essentially means that it makes more than ~1.2 staplers a min.
1hr 45min is 60mins + 45mins = 105mins

so to rephrase the question, how many staplers can the machine (which makes ~1.2 or 9/7 staplers a min) make in 105 mins?

=$$9/7$$ x 105
=9 x 15
=135 staplers.
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Posts: 52344
Re: A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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15 Mar 2015, 20:50
Bunuel wrote:
A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125
B. 128
C. 135
D. 144
E. 150

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Change 1 hr 45 min to 105 min. For this, we need to set up a simple proportion of staplers per time
36/28 = S/105

The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can and can’t cancel in a proportion, see this post. We can cancel the factor of 4 in the 36 and 38.
9/7 = S/105

We absolutely cannot cancel any factors between the 9 and 105. That kind of “cross-canceling” is 100% illegal in a proportion. We can cancel the common factor of 7 in the two denominators.
9/1 = S/15.

Now that the fraction is entirely simplified, we can cross-multiply.
S = 9*15 = 135

The machine would be 135 staples in 1 hr 45 min.

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Re: A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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16 Mar 2015, 22:06
1
Hi All,

This question is essentially about ratios, so the math can be done in a variety of ways (using fractions, decimals, percents, etc.). Here's a way to get to the correct answer with a little less "math work"

We're told that a machine manufactures 36 staplers in 28 minutes. We're asked how many staplers would be manufactured in 1 hour and 45 minutes.

1 hour and 45 minutes = 60+45 = 105 minutes

28 does NOT divide evenly into 105, but we can still use some estimation here...

(28 minutes)(4) = 112 minutes, so using this estimate, we'll end up with a total that is a little BIGGER than it should be.

(36 staplers)(4) = 144 staplers. Now, we know that this is TOO BIG, so we're looking for an answer that is a little below 144. With a ratio of 36 staplers per 28 minutes, we know that a little more than 1 stapler is made per minute. Since we're dealing with a calculation that is 7 minutes TOO BIG, the difference in staplers would have to be a little more than 7.

144 - (a little more than 7) = about 136

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A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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16 Mar 2015, 22:18
This is true. As test takers we must remember that answer choices on the GMAT are also resources that we must exploit.

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Re: A machine, working at a constant rate, manufactures 36 staplers in 28  [#permalink]

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11 Jan 2018, 07:12
Top Contributor
Bunuel wrote:
A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125
B. 128
C. 135
D. 144
E. 150

Kudos for a correct solution.

We can solve this using equivalent ratios

We're comparing machine output (measured in # of staplers) with time (in minutes)

1 hr 45 min = 105 minutes
Let x = # of staplers that can be made in 105 minutes

We get: 36/28 = x/105
Cross multiply to get: (28)(x) = (36)(105)
Divide both sides by 28 to get: x = (36)(105)/(28)
To calculate this, it's useful to recognize that 105 = (7)(15) and 36 = (4)(9) and 28 = (4)(7)
So, we get: x = (4)(9)(7)(15)/(4)(7)
Simplify to get: x = (9)(15)
= 135

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Re: A machine, working at a constant rate, manufactures 36 staplers in 28 &nbs [#permalink] 11 Jan 2018, 07:12
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