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An artist's portfolio consisting of 1,000 photos is divided into 20 su

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An artist's portfolio consisting of 1,000 photos is divided into 20 su  [#permalink]

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New post 13 Feb 2015, 08:46
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

68% (02:17) correct 32% (02:21) wrong based on 125 sessions

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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.


Kudos for a correct solution.

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Re: An artist's portfolio consisting of 1,000 photos is divided into 20 su  [#permalink]

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New post 14 Feb 2015, 09:32
3
2
I chose E

rephrase:

x = number of photos in new subjects

(1000+2x)/22 > 55
1000+2x>1210
2x>210
x>105; are there greater than 105 in ea of the new subjects or a total greater than 210?

1) fewer than 117
could be 116 - Works
could be 1 - Doesn't Work

NS - depends on values chosen

2) each is more than 71
could be 72 -- Doesn't Work
could be 1,000,000,000,000 - Works

NS - depends on values chosen

1 &2)

Could be 72 - doesn't works
Could be 116 - works

NS - depends on values chosen
General Discussion
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Re: An artist's portfolio consisting of 1,000 photos is divided into 20 su  [#permalink]

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New post 16 Feb 2015, 02:09
E

So basically the Q is asking is the TOTAL > 1210

1) If 116, then 116*2 + 1000 = 1232
If 1, then 1*2 + 1000 = 1002 ………….. NOT SUFF

2) If 72, then 72*2 + 1000 = 1144
If 200, then 200*2 + 1000 = 1400 ……… NOT SUFF

Combined, again we can get both Yes and No - Not SUFF
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Re: An artist's portfolio consisting of 1,000 photos is divided into 20 su  [#permalink]

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New post 16 Feb 2015, 06:33
Bunuel wrote:
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.


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

From the question stem, the average of the current portfolio is 50 photos (1000/20). Statement (1) indicates that each of the two new subjects has less than 117 photos. At most, each of the two new subjects would contain 116 photos. This would bring the new average to a maximum 56 photos (1232/22). While this is the maximum, there could always be fewer photos. This allows for both greater than 55 photos on average and fewer than 55 photos on average. Since this statement yields both "yes" and "no" as a response, statement (1) is not sufficient. Statement (2 tells us that each new subject has more than 71 photos. At least, each of the two new subjects would contain 72 photos. This means that the new average must be at least 52 photos (1144/22). Of course, this also allows for both greater than 55 and fewer than 55 photos on average, so statement (2) is not sufficient. Taking the two statements together, we know that the new average is between 52 and 56; however this is still not sufficient to say whether the average is greater than 55 or not. The two statements together are not sufficient and the answer is accordingly E. Tip: A quicker way to evaluate the statements is to maintain the average of 50 first, and then see whether there are enough additional photos to push the average to 55. For statement (1), subtract 50 photos from the maximum possible of 116. That 50 subtracted is enough to maintain the average; so at this point, we have an average of 50 with an additional 66 photos per subject. Since we have 2 new subjects, we have 132 additional photos (66 * 2) over 22 subjects to try and push the average over 55. If 132/22 yields a number larger than 5, then the total average will be greater than 55. This technique requires much easier calculating than dividing 1232 by 22. Repeat the same procedure for statement (2).
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: An artist's portfolio consisting of 1,000 photos is divided into 20 su  [#permalink]

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