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Do at least 40 percent of the people over the age of 50 in

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Manager
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Do at least 40 percent of the people over the age of 50 in [#permalink] New post 05 Nov 2006, 22:46
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Do at least 40 percent of the people over the age of 50 in state S have some form of retirement savings?

(S1) In state S, 16 percent of the population under the age 50 has some form retirement savings, and 29 percent of the total population has such savings

(S2) There are more people under the age of 50 than those over the age of 50 in state S


Please elucidate the logic of your answer.
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 [#permalink] New post 06 Nov 2006, 01:05
answer is C.

you need to draw a grid for 4 combinations:

1. under 50, have.
2. under 50, have no.
3. over 50, have.
4. over 50, have no.

assume under 50 are u people. and over 50 are o people. and assume total population is 1.

then

1). u + o = 1.

Now assume the percent of over 50 who have insurance is y.

-----------------
From 1st condition, you get this:

2). 1*29% = u*16% + y*o

combine the 1) and 2) together, 3 variables with 2 equations, not enough to find y. so 1st is not Suff.

-----------------
From 2nd condition: you get this:
3). u > o.
obviously not Suff.

-----------------

Now combine the 2 conditions:

u get the 3 equations: 1) 2) and 3) i listed above.

then u solve y = (29% - u*16%)/o = 29%/o - 16%*u/o

because o < u, so o < 1/2. so 29%/o > 58%.
because o < u, so u/o > 1. so -16%*u/o < -16%.

so you can see y > 42%. so it is Suff. Hence C.
Senior Manager
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[#permalink] New post 06 Nov 2006, 08:49
Asuume total pop = 100

From II under 50 pop 49 and over 50 pop 51


16percent of 49*16/100=7.84

29% of all = 29 so 29-7.84 atleast 21 people over 50 have saving

21 is 21*100/51 = approx 41% of over 50

Answer C
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Re: DS: Retirement savings in state S [#permalink] New post 06 Nov 2006, 09:24
IT'S a good ds problem and i cudn't do it in 2 mins.

i took x and y as the no of people over and 50 years of age.

1. gave population over 50 with RS(retire sav)=.29(x+y) - .16 y =.29 x + .13 y.....not enough

2. y>x

combined....29X +.13 y > .29 x +.13 x = .43 y

these kind of probs r better....feel good.
Re: DS: Retirement savings in state S   [#permalink] 06 Nov 2006, 09:24
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