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# A marketing company tested six different ovens to determine which oven

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Senior Manager
Joined: 25 Sep 2018
Posts: 430
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
A marketing company tested six different ovens to determine which oven  [#permalink]

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08 Apr 2019, 00:34
1
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Difficulty:

45% (medium)

Question Stats:

64% (01:24) correct 36% (01:24) wrong based on 25 sessions

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A marketing company tested six different ovens to determine which oven cooked a baguette the fastest. The cooking times for the first three ovens were a minutes, b minutes, and c minutes, respectively. These three cooking times produced a standard deviation of d minutes. Was the standard deviation of the cooking times of the next three ovens greater than d minutes?

1) The mean cooking time for the last three ovens was equal to the mean cooking time for the first three ovens.
2) The cooking times for the last three ovens was equal to a + x, b + x, and c + x minutes, respectively.

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Why do we fall?...So we can learn to pick ourselves up again
Intern
Joined: 18 Jun 2014
Posts: 6
Location: India
Schools: ISB '18 (A)
GMAT 1: 700 Q51 V35
Re: A marketing company tested six different ovens to determine which oven  [#permalink]

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08 Apr 2019, 04:16
Whenever approaching DS, try to keep things as simple as possible.

Don't calculate things you don't need, don't waste time on options. Move forward, eliminate, revisit, make up your mind and mark your answer. DS problems are notoriously known for making you waste a lot of time. Maybe this link might help you get off the ground if you're a little confused.

--

Ok. Let's get to the point.

Given:
First three ovens take a, b, c minutes to cook something and the standard deviation is d.

Question: Is the standard deviation of the cooking times of the next three ovens greater than d?

Let's find out.

Statement 1: The mean cooking time for the last three ovens was equal to the mean cooking time for the first three ovens.

Ok, the means are equal. Let's think of a scenario when the means can be equal.

Assume the mean of a, b, c = 10

Now when the cooking times of the next three ovens are:
1. 10, 10, 10 ... the mean, is again 10, but the standard deviation is 0.
2. 0, 10, 20 ... the mean, is again 10, but the standard deviation is not 0. {What would the SD be? I'm not interested, nor am I going to calculate}

So we can't be sure of the standard deviation if we're given this information, and we can't say for sure that the standard deviation of the cooking times of the next three ovens is going to be greater than 10.

Let's eliminate option A and option D.

Statement 2: The cooking times for the last three ovens was equal to a + x, b + x, and c + x minutes, respectively.

Ok, now we have some interesting data.

Let's revisit something that we learned in school.

Quote:
Adding or Subtracting a Constant. If we add or subtract a constant to each score in any distribution, we in effect create a new distribution based on the original one. The mean changes by the amount that was added or subtracted but the variance and standard deviation stay the same.

[Beginning of - Not sure if you need to know this]
Funny huh.. Why?

The mean of this new distribution would be original mean + x
And when we calculate the variance, the x in the mean and the cooking times will cancel out, making the variance stay the same and hence the S.D

[End of - Not sure if you need to know this]

So yea, the standard deviation remains the same.

Now we know that the standard deviation is the same as before, i.e., d and we can say for sure that d is not greater than d, our original question.

Eliminate options C, and E.

--

If you like the way I approach GMAT problems, please check out my blog, Doorknop for more of such solutions
Re: A marketing company tested six different ovens to determine which oven   [#permalink] 08 Apr 2019, 04:16
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