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An artist's portfolio consisting of 1,000 photos is divided into 20 subjects. After an extensive photo shoot, two more

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An artist's portfolio consisting of 1,000 photos is divided into 20 subjects. After an extensive photo shoot, two more

by AAPL » Wed Jan 20, 2021 9:55 am

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An artist's portfolio consisting of 1,000 photos is divided into 20 subjects. After an extensive photo shoot, two more subjects are then added to the portfolio. Is the average (arithmetic mean) number of photos in each subject greater than 55?

1) Each of the new subjects has fewer than 117 photos
2) Each of the new subjects has more than 71 photos

OA E
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Source: — Data Sufficiency |
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Re: An artist's portfolio consisting of 1,000 photos is divided into 20 subjects. After an extensive photo shoot, two mo

by deloitte247 » Sun Jan 24, 2021 11:14 am

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Let the number of photos in new subjects = x
Portfolio consists of 1000 photos which are divided into 20 subjects.
After photoshoot 2 more subjects were added so the total subjects = 22

Target question: Is the average (arithmetic mean) number of photos in each subject greater than 55?
$$\frac{1000+2x}{22}>55$$
$$1000+2x>55\cdot22$$
$$1000+2x>1210$$
$$2x>210$$
$$x>\frac{210}{2}>105$$
Is x>105??

Statement 1=> Each of the new subjects has fewer than 117 photos.
i.e x < 117
If x=110, then x>105 but if x=90; then x < 105. Since the answer is not definite statement 1 is NOT SUFFICIENT.

Statement 2=> Each of the new subjects has more than 71 photos.
i.e x > 71, if x=110, then x>105 but if x=90, then x<105. Since the answer is not definite statement, statement 2 is NOT SUFFICIENT.

Combining both statements:
x < 117 and x > 71
71 < x < 117
If x = 110, then x > 105 but if x=90, then x<105. Since the answer is NOT DEFINITE, both statements combined together is NOT SUFFICIENT.

Answer = option E
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