Word Translation: Chocolates

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ikaplan: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Sep 04, 2009 12:06 pmFollowed by: 1 member; Thanked: 17 times

by ikaplan » Sat Jul 05, 2014 1:36 am

I am a real chocolate connoisseur but I do have problem with the word translation of statement 2 of the following DS problem:
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What is the maximum possible number of chocolate bars per hour produced by a machine?

(1) Currently, the machine produces 1,200 chocolate bars per hour
(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%
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Can someone guide me through the thinking process? If there is a way of solving this problem without equations, please feel free to comment on that option as well.

Thank you~

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 05, 2014 1:36 am

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by GMATGuruNY » Sat Jul 05, 2014 2:42 am

ikaplan wrote: What is the maximum possible number of chocolate bars per hour produced by a machine?
(1) Currently, the machine produces 1,200 chocolate bars per hour
(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.

Statement 1: Currently, the machine produces 1,200 chocolate bars per hour.
The current rate does help us determine the maximum possible rate.
INSUFFICIENT.

Statement 2: If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.
Let h = HALF the maximum rate.
Half the maximum rate increased by 300 bars per hour = h + 300.
Half the maximum rate increased by 25% = h + (25/100)(h) = (125/100)h = (5/4)h.
Since increasing half the maximum rate by 300 is the same as increasing it by 25%, we get:
h + 300 = (5/4)h.
Since we can solve for h -- HALF the maximum rate -- we can determine the FULL maximum rate.
SUFFICIENT.

The correct answer is B.

Maximum possible rate:
h + 300 = (5/4)h
4h + 1200 = 5h
1200 = h.
Since 1/2 the maximum rate = 1200, the maximum possible rate = 2400.

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by Brent@GMATPrepNow » Sat Jul 05, 2014 5:50 am

What is the MAXIMUM possible number of chocolate bars per hour produced by a machine?

(1) Currently, the machine produces 1,200 chocolate bars per hour.

(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.

Target question: What is the maximum possible number of chocolate bars per hour produced by a machine?

Statement 1: Currently, the machine produces 1,200 chocolate bars per hour.
No idea what the MAXIMUM rate is.
So, statement 1 is NOT SUFFICIENT

Statement 2: If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.
Let M = current maximum rate
So, we start with a rate of M/2
After we add 300, we get a new rate of M/2 + 300
This represents a 25% increase.

Percent increase = 100(new - old)/old
So, we can write: 100(M/2 + 300 - M/2)/(M/2) = 25
Note: At this point, we might recognize that we can solve this equation for M, in which case the statement is SUFFICIENT. However, if we're not convinced, we can continue solving...
Simplify: 100(300)/(M/2) = 25
Divide both side by 100: (300)/(M/2) = 1/4
Cross multiply: 4(300) = M/2
Simplify: 1200 = M/2
Solve: M = 2400
So, the maximum rate is 2400 chocolate bars per hour.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Brent[/quote]

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sat Jul 05, 2014 7:26 am

Statement 1) It doesn't give a clue about the maximum rate of the machine.

Statement 2) Running rate of machine = (1/2) maximum rate

To be increased by 300 chocolate bars per hour, the rate is increased by 25%

which means, (25/100)x [(1/2) maximum rate] = 300 chocolate bars per hour

which means (1/8) maximum rate] = 300 chocolate bars per hour

Therefore Maximum rate = 2400 chocolate bars per hour SUFFICIENT

[spoiler]Answer Option - B[/spoiler]

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