Working at their respective constant rates, machine A makes 100 copies

Question

Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 100 copies in 15 minutes. If a number of x machine A and a number of y machine B work simultaneously at their respective rates for 2 hours, what is the total number of copies that they will produce?

(1) x = y.
(2) 5x + 4y = 90.

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(1) x = y.
(2) 5x + 4y = 90.

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yashikaaggarwal · Accepted Answer

1 hour = 500 copies (Machine A) 
2 hours = 1000 copies

1 hour = 400 copies (Machine B) 
2 hours = 800 copies

Together they make 1800 copies per hour.

1) X=Y but what no. Of machines are working together? 
1800, 3600, 5400 or more? 
No idea. 
(Insufficient)

2) 5x+4y = 90

X = 2 , Y = 20
Copies to be manufactured = 1000*2+20*800 = 2000+16000 = 18000

6 = X, Y = 15
Copies to be manufactured = 1000*6+15*800 = 6000+12000 = 18000

X = 10, Y = 10
Copies to be manufactured = 1000*10+10*800 = 10000+8000 = 18000

X = 14 , y = 5
Copies to be manufactured = 1000*14+5*800 = 14000+4000 = 18000

X = 18, Y = 0
Copies to be manufactured = 1000*18+0*800 = 18000

Manufactured copies no. Are same. 
(Sufficient)

Answer is B

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Dan1sh · Answer

Machine A
12 mins --> 100 copies
2 hours --> 1000 copies

Machine B
15 mins --> 100 copies
2 hours --> 1000 copies

x no.of Machine A & y no.of Machine B

Total production in 2 hours = 1000x+800y=?

Statement I :
x=y cannot determine value of 1000x+800y
Not Sufficient

Statement II :
5x + 4y = 90

200* (5x + 4y = 90)

---> 1000x+800y=90*200

Sufficient

Option B

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suchita2409 · Answer

It has to be C.

We need to find x and y to solve the problem.

First stmt is clearly insufficient.

Second stmt ,we can have no. of such pairs that could satisfy the equation.
Insufficient.

1)+2)
We get x=y=10

We can find out if we have values of x and y.

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ataman · Answer

Very smart one! I had C then I aware  yashikaaggarwal  ‘s point. Tricky one

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yashikaaggarwal · Answer

I was thinking about C initially as well. But I had been through similar DS question where C was the trap. So put it down on paper. And it turned out well. ?

Ahmed9955 · Answer

• MAIN POINT-Always check the equation you derive from questions with the equations given in statements.

Ra= rate of work of machine A => given - Ra =100/12
Rb = rate of work of Machine B => given - Ra =100/15

Time*Rate=Work done
To find- 2* (xRa + yRb ) =>2* (x*100/12 + y*100/15)=>  2*( x*25/3+y*20/3)  -------(1)

S1 -> x=y

Clearly insufficient, we will still be left with one variable

S2-> 5x +4y=90
Now if I multiply the given eq with 5/3 I'll get

25/3x +20/3y=90 
Put this value back in (1) - Sufficient

IMO -B

drambo24 · Answer

hi bunuel could explain as to why option 2 is sufficient?shall we solve the equation from question stem and match with option 2?

DmitryFarber · Answer

Yes, basically. Since the rates for A and B are 1,000/2 hrs and 800/2 hrs respectively, the total work we want is 1,000x + 800y. Statement 2 gives us the value for 5x + 4y. The trick is to recognize that the ratio of coefficients is the same. As shown in a previous explanation, if we multiply both sides of our equation by 200, we get the answer: 5x + 4y = 90 --> 1000x + 800y = 18,000

This issue of coefficient ratios is common in DS. In this case, it was the way to spot a sufficient statement. In many other cases, it appears as a trap. For instance, if the question had told us 5x+ 4y = 90 and then asked for x, then each statement might have shown another equation. If (1) had an equation with a different ratio of coefficients, such as 2x - y = -3, we could use that in conjunction with the previous equation to solve. But then if (2) gave us 1,000x + 800y = 18,000, it would be important for us to recognize that this was the same info we had from the question stem. In that case, we'd choose A, because (1) would be sufficient but (2) would not.

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Working at their respective constant rates, machine A makes 100 copies

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Working at their respective constant rates, machine A makes 100 copies

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