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.
First check this video on Arithmetic Mean:
1000 photos and 20 subjects means on average 50 photos per subject. Now 2 more subjects are added and the question is whether average is more than 55.
For average to be 55, we need an extra 5 for each of the 20 subjects and a 55 for each of the two new subjects i.e. we need 20*5 + 2*55 = 210 new photos.
Hence number of photos clicked must be more than 210 for average to be greater than 55.
(1) Each of the new subjects has fewer than 117 photos.The total number of new photos could be 2*116 (which is more than 210) or 2*10 or 2*72 (which is less than 210) etc. Not sufficient alone.
(2) Each of the new subjects has more than 71 photos.The total number of new photos could be 2*72 (which is less than 210) or 2*100 or 2*116 etc. Not sufficient alone.
Even using both statements, we know that total number of new photos could be 2*72 (which is less than 210) or 2*116 (which is more than 210)
Not Sufficient.
Answer (E)