kaplan question

[jc114]

A certain hotel has 1400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are need to clean all the rooms if each person works for exactly 7 hours?
A. 65
B. 70
C. 80
D. 90
E. 265

If the sum of the first n positive integers is S, what is the sum of the first n positive even integers, in terms of S?
A. S/2
B. S
C. 2S
D. 2S+2
E. 4S

[mschling52]

(1) B - 70

(1400 singles) x (1/4 hour per room) = 350 hours cleaning
(420 doubles) x (1/3 hour per room) = 140 hours cleaning

Total = 490 hours of cleaning

At 7 hours per person, this requires 70 people

[Cybermusings]

A certain hotel has 1400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are need to clean all the rooms if each person works for exactly 7 hours?
A. 65
B. 70
C. 80
D. 90
E. 265

1 person ---- single room 15 min --- double room 20 min
1400 single rooms require 1400*15 = 21000 minutes = 350 hrs
and 420 double rooms require 420*20 = 8400 minutes = 140 hrs
Total = 490 hrs
Total ppl required = 490/7 = 70

If the sum of the first n positive integers is S, what is the sum of the first n positive even integers, in terms of S?
A. S/2
B. S
C. 2S
D. 2S+2
E. 4S

first say 5 integers have sum = 1+2+3+4+5 = 15
First 5 even integers have sum of 2+4+6+8+10 = 30
Thus 2S should be the answer