Few math problems...

[gmatrant]

1. A parallelogram has four equal sides and an angle of 60 degrees. What is the ratio of the shorter diagonal to the longer diagonal?
Is it possible to have a parallelogram with equal sides and an angle of 60 degrees. If the sides are equal then shouldn't all angles be equal. Please correct me if I am wrong.

2.A particular species of tiger has a 0.6 probability to live up to 20 year of age and a .48 probability to live up to 25 years of age. What is the probability of a 20 year old tiger to live up to 25 years of age.

[csandeepreddy]

1. Yes is possible for a parallelogram to have 4 sides equal with an interior angle of 60.
Is the answer 2:3??

2. Is the answer 0.8??

[vittalgmat]

I get the ratio as 1:sqrt(3)
Let me explain.
Let the parallelogram(rhombus) of equal sides have side length of x.
The diagonals bisect each other and also the angles. So u will have 4 right 30-60-90 triangles with hypotenuse = x. The the sides of this triangle are in the ratio
k: k sqrt(3): 2k.

So the shorter side of this litle triangle =x/2
longer side = x sqrt(3) / 2
Hypotenus = x

each of the sides are actually half the diagonals.
So shorter diagonal = 2 * x/2 => x
Longer diagonal = 2 * x sqrt(3)/2 => x sqrt(3)

ratio = shorter diagonal / longer diagonal = x / x sqrt(3)
=> 1: sqrt(3)

Pls let me know ur thoughts

[4meonly]

For second question I think 4/5 or 0.8

[gmatguy16]

can someone please explain why its 4/5 for the second question .

[Morgoth]

can someone please explain why its 4/5 for the second question .

60% of the tigers survive till 20

or 60 out of 100 tigers survive till 20

48 out of 100 tigers survive till 25


if 60 survived at 20, and out of these 60, 48 survived till 25.

total probability = 48/60 = .8 or 80%

Hope this helps.