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# In a shipment of 120 machine parts, 5 percent were defective

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Math Expert
Joined: 02 Sep 2009
Posts: 46062
In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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13 Feb 2014, 02:29
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:43) correct 12% (00:47) wrong based on 677 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

Problem Solving
Question: 95
Category: Arithmetic Percents
Page: 74
Difficulty: 550

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Math Expert
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Posts: 46062
In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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13 Feb 2014, 02:30
SOLUTION

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

For the two shipments combined, the percent of defective parts = (total # of defective parts)/(total # of parts)*100 = $$\frac{120*0.05+80*0.1}{120+80}*100=7%$$.

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Current Student
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Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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13 Feb 2014, 02:53
5% of 120 is 6
10% of 80 is 8

As the question says two shipments combined, we have two add the defective as well as total shipments.

8+6/120+80 = 15/200 = 7.5%

There are many different ways to calculate percentages, I think the best way here can be like this
To find 10% of any no. just move one decimal point to left (10% of 120 = 12) and (10% of 80 = 8)
To find 5% of any no. just halve the above no. (5% of 120 = 12/2 = 6)
Intern
Joined: 15 Nov 2013
Posts: 3
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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13 Feb 2014, 04:23
1
b2bt

Good logic, but I think you made a little error in your calculations.

(8+6)/(120+80) = 14/200, which leads to 7%

Manager
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Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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13 Feb 2014, 22:12
1
In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

$$TotalDefectiveMachineParts = (\frac{5}{100})120 + (\frac{10}{100})80 = 6 + 8 =14$$

So, $$%$$ $$OfDefectiveMachineParts= = \frac{Total Defective Machine Parts}{Total Machine Parts}=\frac{14}{200} = \frac{7}{100}=7%$$

Manager
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Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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14 Feb 2014, 02:34
1
Defective 1= 5% of 120 = 6;
Defective 2= 10% of 80 = 8;

Total Defective = 6 + 8 = 14/(120 + 80) = 14/200 = 7/100 = 7%;

Ans is (B).
Current Student
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Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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15 Feb 2014, 05:04
b2bt

Good logic, but I think you made a little error in your calculations.

(8+6)/(120+80) = 14/200, which leads to 7%

Oops
I always tend to make calculation mistakes.
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Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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15 Feb 2014, 10:44
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

Out of 120 , 5% are defective.
10% of 120 is 12 (remove the last 0 from numerator).
Half of 12 = 6 should be 5%

and Out of 80, 10% is defective. so 8
so 8+6 = 14 out of 200 (120+80) so 14/2 should be the required answer = 7% - Option B)
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Senior Manager
Joined: 20 Dec 2013
Posts: 250
Location: India
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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16 Feb 2014, 02:56
1
Option B
Def in ship. 1: 120 *5%=6 +
Def. in ship. 2:80 * 10%=8
Total def=14
Total no.=120+80=200
%age def in total=14 *100/200=7%
Intern
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Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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16 Feb 2014, 06:07
1
Option B - 7%
5% of 120 - 6 pieces
10% of 80 - 8 pieces

If both are combined - total pieces - 200
Total defective pieces - 14
So % defective pieces - 14/200 = 7%
Math Expert
Joined: 02 Sep 2009
Posts: 46062
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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17 Feb 2014, 01:21
SOLUTION

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

For the two shipments combined, the percent of defective parts = (total # of defective parts)/(total # of parts)*100 = $$\frac{120*0.05+80*0.1}{120+80}*100=7%$$.

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Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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23 Apr 2014, 23:43
for 120 shipments , 5% i.e 6 were defective .
for 80 shipments, 10% i.e 8 were defective.

Total = 200 shipments (combined) and defective =14 (combined).
question asks us 14 is what % of 200.

14/200 = x/100;
x=7% ;

Press kudos if this helps
Intern
Joined: 26 Jul 2014
Posts: 13
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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05 Aug 2017, 07:57
Another solution:
Call x (%) is percent of the machine parts were defective for the two shipments combined.
120/80=(10-x)/(x-5)
=> 120 (x-5) = 80(10-x)
=> 20x = 140
=> x = 7 (%)
Manager
Joined: 21 Jun 2017
Posts: 78
Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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22 Aug 2017, 13:38
1. 120 x 5 = 600 = move decimal two digits left because percent = 6 parts defective from 120 shipment
2. 80 x 10 = 800 = 8 (move decimal again) parts defective
3. Find total parts = 120 + 80 = 200
4. Find total defective parts = 6 + 8 = 14
5. (14 / 200) x 100 = 7% parts defective

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Re: In a shipment of 120 machine parts, 5 percent were defective [#permalink]

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24 Aug 2017, 16:35
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

In the shipment of 120 machine parts, 120 x 0.05 = 6 were defective. In the shipment of 80 machine parts, 80 x 0.1 = 8 were defective. Thus, 14/200 = 7/100 = 7% were defective overall.

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Re: In a shipment of 120 machine parts, 5 percent were defective   [#permalink] 24 Aug 2017, 16:35
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