Working at their respective constant rates, machine A makes : GMAT Data Sufficiency (DS)
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# Working at their respective constant rates, machine A makes

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Working at their respective constant rates, machine A makes [#permalink]

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09 Mar 2011, 14:03
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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.
[Reveal] Spoiler: OA
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Re: Working at their respective constant rates, machine A makes [#permalink]

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09 Mar 2011, 16:00
banksy wrote:
268. 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.

can't find the the total copies that they will produce without knowing the value of x and y. So with (1) and (2), it is sufficient to find values.
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09 Mar 2011, 22:56
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banksy wrote:
268. 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.

Rate of Machine A is 100/12 copies per minute and that of Machine Y is 100/15 copies per minute.

When x number of A machines and y number of B machines work simultaneously at their respective rates for 2 hours (120 minutes), they will produce $$120*((100/12)*x+(100/15)*y)$$copies

$$120*((100/12)*x+(100/15)*y)$$ on simplification becomes $$200*(5x+4y)$$

Statement 1 says $$x=y$$, which doesn't help us get the exact numbers, so insufficient

Statement 2 says $$5x+4y = 90$$, we cant solve for x and y from this, but all we need to answer the question is value of 5x+4y which we get from this statement, so sufficient.

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Re: Working at their respective constant rates, machine A makes [#permalink]

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09 Mar 2011, 23:03
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(1) is clearly insufficient.

For (2), several answers are possible:

5 * 14 + 4 * 5 = 90

5 * 10 + 4 * 8 = 90

But (1) and (2) together give x = y = 10, so answer is C
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Re: Working at their respective constant rates, machine A makes [#permalink]

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09 Mar 2011, 23:11
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Mongolia2HBS wrote:
banksy wrote:
268. 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.

can't find the the total copies that they will produce without knowing the value of x and y. So with (1) and (2), it is sufficient to find values.

subhashghosh wrote:
(1) is clearly insufficient.

For (2), several answers are possible:

5 * 14 + 4 * 5 = 90

5 * 10 + 4 * 8 = 90

But (1) and (2) together give x = y = 10, so answer is C

Guys, we are not concerned here with exact values of x and y. All we need to find is the total number of copies the machines working together would produce. So, anything that gives us their combined relationship is sufficient. Statement 2 effectively is telling us about that relationship.

So, statement B is sufficient to answer the given question.

Irrespective of whatever value x and y individually may have, as long as 5x+4y is 90, the number of pages they will produce would remain 200*90

We can easily check the same by putting different values for x and y.
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Re: Working at their respective constant rates, machine A makes [#permalink]

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10 Mar 2011, 07:30
As per question:

A makes 1000 pages in 2 hours
B makes 800 pages in 2 hours

x machines of A and y machines of B are used.

Total output = 1000x + 800y......(1)

Given by statement 2: 5x + 4y = 90...........(2)

From 1 and 2,

The answer will be 90 * 200 = 1800 pages.

Hence B alone is sufficient.
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10 Mar 2011, 19:45
A "lone wolf" trap.
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Re: Working at their respective constant rates, machine A makes [#permalink]

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11 Mar 2011, 22:24
I was wrong, B alone is sufficient.
Thanks to beyondgmatscore and pesfunk.
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Re: Working at their respective constant rates, machine A makes [#permalink]

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15 Dec 2014, 09:50
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Re: Working at their respective constant rates, machine A makes [#permalink]

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29 Dec 2015, 09:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Working at their respective constant rates, machine A makes [#permalink]

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04 Feb 2016, 13:35
Rate of A $$\frac{100}{12}$$
Rate of B $$\frac{100}{15}]$$

$$\frac{100x}{12}*120 + \frac{100y}{15}*120$$
$$1000x + 800y$$

1. x=y Tell us nothing about the actual values.
2. 5x + 4y = 90

$$1000x + 800y$$
$$(5x+4y=90)*200$$
$$1000x+800y=18000$$
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Re: Working at their respective constant rates, machine A makes [#permalink]

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13 Feb 2016, 21:05
banksy wrote:
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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Re: Working at their respective constant rates, machine A makes [#permalink]

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29 Feb 2016, 19:17
banksy wrote:
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.

X*2*(100/12) + Y*2*(100/15) - No.of copies.

Multiply by 60.

200*(5X+4Y)=No. of copies. B Sufficient.
Re: Working at their respective constant rates, machine A makes   [#permalink] 29 Feb 2016, 19:17
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