For a global sports event, Nike has to make 810 pair of shoes while Ad

Question

For a global sports event, Nike has to make 810 pair of shoes while Adidas has to make 900 pair of shoes, in the same period of time. Nike could complete the order 3 days before the scheduled time while Adidas completed the order 3 days before Nike. How many pair of shoes did Nike and Adidas make per day if Adidas made 21 more shoes per day than Nike?

A. 54 and 75
B. 44 and 65
C. 34 and 55
D. 31 and 55
E. 21 and 42

Are You Up For the Challenge: 700 Level Questions

A. 54 and 75
B. 44 and 65
C. 34 and 55
D. 31 and 55
E. 21 and 42

Are You Up For the Challenge: 700 Level Questions

arpang · Accepted Answer

Nike: n per day
Adidas: n+21 per day

Let's say Nike took x days to make 810 pairs, So - 
 nx = 810

And Adidas took x-3 days, So
 (n+21)(x-3) = 900

Pretty easy equation, replace nx = 810 in the above and you get :

n = 9x/7  which means 9 is definitely a factor of n, which is true only in option A.

MrSengupta · Answer

The correct answer is (A)

This is how I reached my answer . This is not the best way but solves the answer. 
Let the scheduled number of days be x days.

Nike -> Rate : a shoes / day and the number of days : x-3
Adidas -> Rate : a+21 shoes/day and the number of days x-6

a(x-3)=810
=>ax=810+3a

(a+21)(x-6) = 900
=>7x=72+a

Then I checked with the answers with what matches . Came out as (A)

effatara · Answer

Let Nike take 'x' days to complete. Then Nike's daily production is 810/x and Adidas's daily production is 900/(x-3). 
900/(x-3) = 810/x + 21....> 7x^2 - 51x -27*30 =0....> 7x(x-15) + 54(x-15) = 0....> (x-15)(x+54) = 0....> x=15.
Nike's daily production is 810/15 = 54 and Adidas's is 75. ANS: A

The math was a bit complicated since it involved large numbers. Difficult to do in allotted time.

effatara · Answer

arpang , recheck your calculations.

(n+21)(x-3) = 900 does NOT give you n=9x/7. When you replace "nx" with 810, it becomes 810-3n+21x-63=900....> 21x-3n=153. 
However, you can still solve for 'n' by substituting "x=810/n" in the above equation whereupon you get n^2+51n-7*810=0 which can be solved by factorizing as follows: n^2+105n-54n-7*810=0...> n(n-54)+105(n-54)=0....> (n-54)(n+105)=0....> n=54.

Jsgambach · Answer

Straightforward approach, it may save some time if you are quick enough mentally dividing:

Try dividing 810 between Nike's possible daily production's Ans Choices.
810 is only divisible by 54, hence that's the answer. Double check by dividing 900 into 75. There you go, A is the ANS.

error404bnf · Answer

If we solve this question by forming the quadratic equation and then solving that, it will take ages in terms of GMAT time.

This is how I solved: -

Work  
  Time  
  Rate  
 
   Nike  
 810 
 t 
 r 
 
   Adidas  
 900 
 t-3 
 r+21

Scheduled time, let be ' t+3 '

From above you get following equations

810=t x r  .................................................... .. (A) 
 900=(t-3) x (r+21)   ........................................ (B)

Solve (B) and you get  21t - 3r = 153

Simplify and Get r one side,  r=7t-51

or we can manipulate it and write,  r= 7(t-7)-2

This gives you the information that r (Nike's rate) is 2 less than a multiple of 7. The only possibility is A. Hola!

Jash1666 · Answer

For this type of question where you have to find 2 different rate we are tend to make mistakes, in this question you can see only option A divides rest will not divide, I saved time there if options are close then you can just go by option ways it’s faster than equation and less tedious and error prone

Stormik1 · Answer

Conceptually easy, calculation wise tough!!

For a global sports event, Nike has to make 810 pair of shoes while Ad

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	Work	Time	Rate
Nike	810	t	r
Adidas	900	t-3	r+21
		Scheduled time, let be 't+3'

GMAT Problem Solving (PS) Questions

For a global sports event, Nike has to make 810 pair of shoes while Ad

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