1000 PS- section 2- #12

[sky828i]

12. A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?
(A) 10
(B) 40
(C) 45
(D) 50
(E) 55


The answer is C, but i can't even solve this problem. Anybody can help?

Data Sufficient

24. If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

Why is the answer 'A'?
Gmat master can explain?

[davidnodine]

Curious where are you getting these questions?

1) because the distance remains the same you can say rt=(r+5)(t-1)
so... rt=rt-r+5t-5, subtract rt, move r, and you have your R(rate)=5t-5. Put that into the D=RT equation: 450=(5t-5)t, solve for t and get 5t^2-5t-450=0. Divide by 5, and get t^2-t-90=0 which is the same as (t-10)(t+9)=0, Time cannot be negative so T must be equal to 10 solve in original equation R10=450 so R=45.

2) I'm not too sure about this one. Because you could say that c=1, so 1x2x3=6 which is a multiple of 3 but 6/24 does not equal an integer. 1 is odd so statement B doesn't help. Are you sure that you wrote that correctly

[devesh]

1. C

24. If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3,
(2) c is odd.

2. try c=3 and c=7 diff results so no C
1. b is multiple of 3
product of three cons. positive integer is always a multiple of 3.
i wonder how this helps. NO B

ans shud be E

[agps]

Hi.

for question 12 I would use backsolving.

you know that distance = time x speed and distance is given 450.
and that for s+5 t ould be t-1.

plug in the answers for speed and determine the time.

for b) 450 = 40xT, so T=11+1/4, if s were 45 T= 10, not good 11+1/4-10 > 1

for d) 450=50xT, so T= 9, if s were 55 T=8+2/11, not good either 9-8+2/11 < 1

so try for c)
450=45xT, so T=10, if s were 50 T=9, good, 10-9 = 1, C is the answer.

this method can produce very quick results.

for the data sufficency question,
unless you forgot to mention anything i would agree with devesh that the best answer is E.