August 2014



Elephant Biodiversity threat: The planet's current biodiversity, the product of 3.5 billion years of evolutionary trial and error, is the highest in the history of life. But it may be reaching a tipping point. In a new review of scientific literature and analysis of data, an international team of scientists cautions that the loss and decline of animals is contributing to what appears to be the early days of the planet's sixth mass biological extinction event. Read more ....

Ramesh Raskar "Visionary" technology: Researchers at the MIT Media Laboratory and the University of California at Berkeley have developed a new display technology that automatically corrects for vision defects - no glasses (or contact lenses) required. The technique could lead to dashboard-mounted GPS displays that farsighted drivers can consult without putting their glasses on, or electronic readers that eliminate the need for reading glasses, among other applications. Read more .....

Flowers Tricking plants: Copious corn growing in tiny backyard plots? Roses blooming in December? Thanks to technology that the University of Wisconsin-Madison's Richard Vierstra has been developing for years, these things may soon be possible. And now, new findings out of the genetics professor's lab promise to advance that technology even further. Read more ....

Titan Space science: Scientists analyzing data from NASA's Cassini mission have firm evidence the ocean inside Saturn's largest moon, Titan, might be as salty as the Earth's Dead Sea. The new results come from a study of gravity and topography data collected during Cassini's repeated flybys of Titan during the past 10 years. Read more ....




Solution

Venn diagram

Okay, this is how I have solved it; please let me know whether I have done it right.

Let us start by drawing the Venn diagram as above. We draw three intersecting circles, with each circle representing one of the sports - cricket, hockey and football. The region coloured scarlet red is common to all the three circles, and represents the set of students who play all the three games. We have to find out how many students play all the three games; let this number be "x". It is better to mark this region first.

The region coloured green represents the set of students who play both cricket and football but not hockey (this region is common only to cricket and football). We have been given that the number of students who play both cricket and football = 15. This does not mean that all these students hate hockey; among these 15 students will be a few who play hockey also (that is, among these 15 students will be some who play all the three games). Now there are "x" students who play all the three games. Therefore, the number of students who play both cricket and football, but not hockey, is 15-x. By the way, x has to be less than 15; suppose x > 15, this implies number of students who play all the three games is greater than the number of students who play cricket and football. This is not possible.

Likewise, the region coloured yellow is common only to the cricket and hockey circles, and hence represents the set of students playing cricket and hockey but not football. We have been given that 18 students like to play both cricket and hockey. Therefore, by the same argument we can say that 18-x students play the two games of cricket and hockey but not football.

The region coloured pink is common only to the hockey and football circles and, therefore, represents the set of students who like to play hockey and football but not cricket. Eleven students like to play both football and hockey. Using the same argument as above again, we can state that the number of students who like to play hockey and football but not cricket is 11-x.

Now, we have been told that 30 students like cricket. So, the sum of all the numbers within the cricket circle should be 30. Thus, the number of students who like cricket = number of students who like only cricket + number of students who like cricket and football but not hockey (green region) + number of students who like all the three games (scarlet red region) + number of students who like cricket and hockey but not football (yellow region).

Therefore, 30 = number of students who like only cricket + (15-x) + x + (18-x). So, the number of students who like only cricket = 30 - 15 + x - x - 18 + x. Therefore, number of students who like only cricket = (x - 3).

Similarly, we have been told that 25 students like to play football. Therefore, the number of students who like to play only football works out to be (x - 1).

Thirty-two students like to play hockey. The number of students who like to play only hockey works out to be (x + 3).

There are a total of 50 students and each student plays one game or the other. Hence the sum of the numbers within all the three circles should be 50.

Therefore, (x - 3) + (15 - x) + (x - 1) + x + (18 - x) + (11 - x) + (x + 3) = 50.

Therefore, x + 43 = 50. So, x = 7.

Thus:

The number of students who play all the three games = x = 7.

The number of students who play only football = x - 1 = 7 - 1 = 6.

The number of students who play only hockey = x + 3 = 7 + 3 = 10.

Did I get it right?



Some useful links for
your career:


  • Union Public Service Commission - www.upsc.gov.in
  • IIT-Kharagpur - www.iitkgp.ac.in
  • Indian Statistical Institute - www.isical.ac.in
  • Indian Institute of Technology Madras - www.iitm.ac.in
  • Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
  • Indian Institute of Mass Commission - www.iimc.nic.in
  • IIT Bombay - www.iitb.ac.in
  • Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
  • Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
  • Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
  • Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
  • Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
  • Tata Institute of Social Sciences, Mumbai - www.tiss.edu

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