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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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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 = \(\frac{120*0.05+80*0.1}{120+80}*100=7%\).

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% Answer C

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)

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

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13 Feb 2014, 22:12

1

This post received KUDOS

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?

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. Lets try to calculate without putting pen (read marker) to paper (read scratch pad). 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)
_________________

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 = \(\frac{120*0.05+80*0.1}{120+80}*100=7%\).

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 (%)

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

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.

Answer: B
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Scott Woodbury-Stewart Founder and CEO

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