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13 May 2021, 04:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (02:12) correct
18%
(02:26)
wrong
based on 113
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Zeta took several pictures with her new digital camera. Each picture was saved as a file, the size of which depended on the picture's resolution. A low resolution image requires a 0.5 megabyte file, and a high resolution image requires a 0.9 megabyte file. If the total size of all the files was 8.1 megabytes, which of the following is a possible number of pictures Zeta took with her camera?
A. 15
B. 14
C. 13
D. 12
E. 11
A. 15
B. 14
C. 13
D. 12
E. 11
16 May 2021, 07:45
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Bunuel
Say L is the number of low resolution images and H is the number of high resolution images (notice that L and H must be non-negative integers).
Given that \(0.5L+0.9H=8.1\) --> \(5L+9H=81\) --> \(L=\frac{9(9-H)}{5}\).
Now, in order \(\frac{9(9-H)}{5}\) to be an integer, \(9-H\) must be a multiple of 5, which is only possible for \(H=4\) or \(H=9\).
Next, if \(H=4\), then \(L=\frac{9(9-H)}{5}=9\) and \(L+H=13\);
If \(H=9\), then \(L=\frac{9(9-H)}{5}=0\) and \(L+H=9\).
Both are possible number of pictures but since only 13 is listed then C is the answer.
Answer: C.
For more on such type of questions check:
https://gmatclub.com/forum/eunice-sold-s ... 09602.html
https://gmatclub.com/forum/martha-bought ... 00204.html
https://gmatclub.com/forum/a-rental-car- ... 05682.html
https://gmatclub.com/forum/joe-bought-on ... 06212.html
https://gmatclub.com/forum/a-certain-fru ... 01966.html
https://gmatclub.com/forum/joanna-bought ... 01743.html
Hope it helps.
General Discussion
13 May 2021, 04:33
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Let the 0.5mb photos be 5x, let the 0.9mb photos be 9y and make the total 0f 8.1 be 81
5x + 9y = 81
As 5 will always end in 5 or 0, the only way we can get a number that ends in 1 is if y gives a number that ends in 6. The only number that will give a number with 6 at the end that is smaller than 81 is 9*4=36.
81 - 36 = 45
45/5 = 9
9+4 = 13
Answer C
5x + 9y = 81
As 5 will always end in 5 or 0, the only way we can get a number that ends in 1 is if y gives a number that ends in 6. The only number that will give a number with 6 at the end that is smaller than 81 is 9*4=36.
81 - 36 = 45
45/5 = 9
9+4 = 13
Answer C
