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Source: — Data Sufficiency |

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by [email protected] » Sat Apr 23, 2016 9:48 am
Hi didieravoaka,

This DS question involves a lot of little steps and a mix of skills (some math skills and TESTing VALUES).

We're told that...
Machine M produces X widgets every 4 minutes
Machine N produces Y widgets every 5 minutes

We're asked if they both word for 20 minutes, does Machine M produce more widgets than Machine N? This is a YES/NO question.

Before we get to the Facts, we can rewrite this question. Over the course of 20 minutes, Machine M will produce 5X widgets and Machine N will produce 4Y widgets, so the question is really asking....

Is 5X > 4Y?

By thinking of these question in these terms, you'll find that the two Facts are considerably easier to deal with.

Fact 1: X > .8Y

This inequality can be simplified with a couple of Algebra steps...

X > .8Y
10X > 8Y
5X > 4Y

Now we KNOW that 5X > 4Y, so no more work is necessary - the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: Y = X+1

This looks like a perfect opportunity to TEST VALUES. From this equation, we know that Y will be 1 greater than X, so the values are "close."

If....
X = 1
Y = 2
Is 5(1) > 4(2)?......Is 5 > 8? The answer is NO

X = 10
Y = 11
Is 5(10) > 4(11)?....Is 50 > 44? The answer is YES
Fact 2 is INSUFFICIENT

Final Answer: A

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by GMATGuruNY » Sat Apr 23, 2016 11:54 am
Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time ?

1) x > 0.8y
2) y = x + 1
Both machines work for the same amount of time.
To produce more widgets than N, M must work faster than N.

Question rephrased:
Is M faster than N?

Statement 1: x > 0.8y
Let y=10, implying that x>8.
Since y=10, N produces 10 widgets every 5 minutes, implying that N's rate = 10/5 = 2 widgets per minute.
Since x>8, M produces MORE than 8 widgets every 4 minutes, implying that M's rate = (more than 8)/4 = MORE than 2 widgets per minute.
Thus, M is faster than N.
SUFFICIENT.

Statement 2: y = x+1
Case 1: x=1, y=2
Since y=2, N produces 2 widgets every 5 minutes, implying that N's rate = 2/5 widget per minute.
Since x=1, M produces 1 widget every 4 minutes, implying that M's rate = 1/4 widget per minute.
In this case, N is faster than M.

Case 2: x=100, y=101
Since y=101, N produces 101 widgets every 5 minutes, implying that N's rate = 101/5 ≈ 20 widgets per minute.
Since x=100, M produces 100 widgets every 4 minutes, implying that M's rate = 100/4 = 25 widgets per minute.
In this case, M is faster than N.

Since N is faster than M in Case 1 but slower than M in Case 2, INSUFFICIENT.

The correct answer is A

Alternate approach:
Since M produces x widgets every 4 minutes, M's rate = x/4 widgets per minute.
Since N produces y widgets every 5 minutes, N's rate = y/5 widgets per minute.
Since M and N work for the same amount of time, M will produce more widgets than N if M's rate is greater than N's rate.
For M's rate to be greater than N's rate, the following must be true:
x/4 > y/5
x > (4/5)y.

Question stem, rephrased: Is x > (4/5)y?

Statement 1: x > (0.8)y
Thus, x > (4/5)y.
SUFFICIENT.

Statement 2: y = x+1
If x=1 and y=2, then (4/5)y = 8/5.
In this case, x < (4/5)y.
If x=100 and y=101, then (4/5)y ≃ 80.
In this case, x > (4/5)y.
INSUFFICIENT.

The correct answer is A.
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by chetan.sharma » Sat Apr 23, 2016 11:24 pm
didieravoaka wrote:Image

Thanks to help.
Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time ?

1) x > 0.8y
2) y = x + 1

Hi,
A BETTER WAY would to find the work of both in same time frame..
so lets look at the LCM of 4 and 5= 20 minutes...

M produces x in 4 minutes.
so M will produce 5x in 5*4 min..

N produces y in 5 minutes.
so N will produce 4y in 5*4 min..

the Q basically asks us : "Is 5x>4y?"..

lets see the statements
1) x > 0.8y
or 5*x> 5*0.8y..
5x>4y..
this is exactly what we are looking for..
Suff

2) y = x + 1
we can say y>1..
but we cannot deduce 5x>4y from the given info
Insuff

A
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