A certain company produces only two products, P and Q. Last week the n

Question

A certain company produces only two products, P and Q. Last week the number of units of P produced by the company was 10 percent of the total number of units produced that week. This week the number of units of Q produced by the company was the same as last week, but the number of units of P produced increased so that the number of units of P produced during the two weeks was 20 percent of the total number of units produced during the two weeks. If a total of 9,000 units was produced during the two weeks, how many more units of product P were produced this week than last week?

A. 800
B. 900
C. 1000
D. 1600
E. 1800

A. 800
B. 900
C. 1000
D. 1600
E. 1800

chetan2u · Accepted Answer

Another way to look at is to concentrate on the amount of Q, which is the same for each of the two weeks.

At the end of two weeks, P is 20%, so Q is 80%.
Thus Q for both the weeks = 80% of 9000 or 7200. Since Q is same for both weeks, 7200/2 or 3600 is the number of Q produced each week. 
Last week 3600 was 90% or total was  3600*\frac{100}{90}  or 4000.

Thus the production this week is 9000-4000 or 5000.
Extra produced = 5000-4000 = 1000

C

chetan2u · Answer

Last week  
Let total produced be x. 
So P=0.1*x and Q=0.9*x

Present week  
Let total produced be a more = x+a
So P=0.1*x +a and Q=0.9*x

Total of two weeks = x+x+a=2x+a=9000….(i)
Also, Total of P is 20% of the total two weeks production. => 0.1x+0.1x+a=0.2*9000 
O.2x+a=1800….(ii)
Subtract ii from i => 2x-0.2x=9000-1800=7200 or x=4000

Now 2x+a=9000 or 2*4000+a=9000 or a=1000

C

gmatophobia · Answer

A certain company produces only two products, P and Q. Last week the number of units of P produced by the company was 10 percent of the total number of units produced that week.  
 
  Last Week  This Week  
  P  Q  P  Q  
  p  q        
 
 p = \frac{10}{100}(p+q)

q = 9p 
 
  Last Week  This Week  
  P  Q  P  Q  
  p  9p        
 
  This week the number of units of Q produced by the company was the same as last week, but the number of units of P produced increased so that the number of units of P produced during the two weeks was 20 percent of the total number of units produced during the two weeks.  
 
  Last Week  This Week  
  P  Q  P  Q  
  p  9p  x  9p  
 
 x + p = \frac{20}{100}(p+9p+9p+x)

x = \frac{14}{4}p 
 
  Last Week  This Week  
  P  Q  P  Q  
  p  9p   \frac{14}{4}p   9p

p + 9p + \frac{14}{4}p + 9p = 9000

p = 400 
 
  Last Week  This Week  
  P  Q  P  Q  
  400  9p   \frac{14}{4}*400 = 1400   9p  
 
Difference = 1400 - 400 = 1000

Option C

houston1980 · Answer

In these type of questions, I try to reduce the number of variables whenever possible. variables
Fist week, P and Q. However P is 10% of total of 1st week, Therefore Q is 90% of week or Q=9P

First week = P+9P

Second week, Q or 9P is unchanged. Represents the "new P" in second week by "K"

second week = 9P+K
Therefore total for two weeks is Fist week+second week= P+9P+9P+K =9000

However, P total for two weeks is 20% of 9000 = 1800
Q total for two weeks is therefore 80% of 9000 = 7200
Therefore total Q = 9P+9P = 18P = 7200. Therefore P = 7200/18 = 400
Solve for K (or 'P' in the second week) = 1400
Second week of P -first week of P = 1400-400 =1000

Therefore option  C  is the answer.

KarishmaB · Answer

Method 1: Here is a reasoning based video solution to this problem: https://youtu.be/k6Mfxr5PnI8 Method 2: If 'A' total units were produced last week, units of Q were 90% of A. The number of units produced of Q are the same this week too i.e. 90% of A. 2 * \frac{90}{100} * A = \frac{80}{100} * 9000 A = 4000 Also, 9000 = A + A + Extra P So Extra P = 1000 Answer (C)

pnwhikingfan · Answer

The total was 9000 units across the two weeks

1) Total P across the two weeks was 20% of the total units
0.2 * 9000 = 1800 units of P

2) Total Q across the two weeks was 80% of the total units
0.8 * 9000 = 7200 units of Q

3) Units of Q for each of the two weeks was the same. So each week there were 7200 / 2 = 3600 Units of Q

4) In week 1, we are told that units of P is 10% of total units that week. We know Q for the first week is 3600 units. 
P = 0.1 (3600+P)
P = 360 + 0.1P
0.9P = 360
P = 400

5) In the first week, we know there are 400 units of P. The total units of P across 2 weeks is 1800. Therefore the number of P units in week 2 is 1400.
1400 - 400 = 1000 more units of P were produced in week 2 versus week 1

GMATinsight · Answer

Please check the video solution here.   It's simply screen recording while explaining the solution to this question to one of my students.

For more professionally made videos, you can refer to the modular courses on our website.

https://www.youtube.com/watch?v=X0uHDuEMhhk

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