GMAT Tough Problem Solving - 6 ( Venn Diagram, Ratio , Probability and Triangles)

26. There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability that the number of men is equal to that of women?


A.18/35 B16/35 C.14/35 D.13/35 E.12/35

27. The area of an equilateral triangle is 9.what is the area of it circumcircle.


A.10PI B.12PI C.14PI D.16PI E.18PI

28.A group of people participate in some curriculums, 20 of them practice Yoga, 10 study cooking, 12 study weaving, 3 of them study cooking only, 4 of them study both the cooking and yoga, 2 of them participate all curriculums. How many people study both cooking and weaving?


A.1 B.2 C.3 D.4 E.5

29. There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?


A 1001 B. 1009 C.1008 D.1007 E.1006

 

30. In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?


A) 5

B) 10

C) 15

D) 20

E) 25

Solutions

26.Soln: there has to be equal no of men & women so out of 4 people selected there has to be 2M & 2W.

Total ways of selecting 4 out of 8 is 8C4

total ways of selecting 2 men out of 4 is 4C2

total ways of selecting 2 women out of 4 is 4C2

so probability is (4C2*4C2)/ 8C4 = 18/35

27.Soln: area = sqrt(3) / 4 * (side)^2 = 9

so , ( side )^2 = ( 9*4 ) / sqrt(3)


Height = H = sqrt(3)/2 * (side) , so H^2 = 3/4 * Side^2 = 3/4 * (9*4) / sqrt(3)

Radius of CircumCircle = R = 2/3 of ( Height of the Equilateral Triangle )

so , area of Circumcircle = PI * R^2

=> PI * 4/9 * H^2

=> PI * 4/9 * 3/4 * (9*4) / sqrt(3)

=> PI * 4 * sqrt(3)

28.Soln: We know there are 10 people who do cooking as an activity.


3 -> people who do only cooking

4 -> do cooking and Yoga

2 -> do all of the activities

x -> number of people doing cooking and weaving


When you sum all this up, we should have 10. So 3+4+2+x=10 --> x=10-9=1

29.Soln: fiction : non-fiction = 3 : 2 = 6 : 4

non-fiction : biology = 4 : 3

fiction : non-fiction : biology = 6 : 4 : 3

6x + 4x + 3x = 1000

x = 76 12/13

if we add 1, 13 will divide evenly (1001/13 = 77)

1000 + 1 = 1001

30.Soln: n(1U2U3) = n(1) + n(2) + n(3) - n(1n2) - n(2n3) - n(1n3) + n (1n2n3)

85=50+30+20- [n(1n2) - n(2n3) - n(1n3)] +5

[n(1n2) - n(2n3) - n(1n3)] = 20

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