Problem Solving

Hello,

Can anyone help me solve the following problems? Please provide as detail explanation as possible:-

Q1. If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

Q2. This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A. 1/r+2
B. 1/2r+2
C. 1/3r+2
D. 1/r+3
E. 1/2r+3

Q3. Mrs. Napueta has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. Napueta been given if there are 120 ways that she could distribute the vouchers?
(A) 13 (B) 14 (C) 15 (D) 16 (E) more than 16

Thanks
MSD

1. prob of head (H)=1/2; prob of not Head= prob of Tail(T)=1/2

prob of HHHTT= (1/2)*(1/2)*(1/2)*(1/2)*(1/2)= 1/32

2. consume(c)+ save(s)= Income (I)
c= I-s

for 1 dollar he saves he gets 1+r. for s dollars it will be s+sr
he will consume half of last year i.e c/2. c/2 = (I-s)/2

Half of last year consumption will be equal to what he will have available to spend.

s+sr= (I-s)2
2s+2sr=I-s; 3s+2sr=I; s(3+2r)=I
s= I/(3+2r)

so fraction of income he should save is 1/(3+2r).

3. This is tricky. my guess is (E)b but i'm not sure

Hi TrizMA,

Thanks for the answers.
The correct answer to Q.3 is actually 15 i.e C......but I dont know how it has been arrived at.

Regards
MSD

https://gmat-maths.blocked/search/l ... mbinations

check problem 21