Data Sufficiency

How many hours did it take Helen to drive from her house to her parents' house?

(1) Helen's average speed on this trip was 72 kilometers per hour
(2) If Helen's average speed on this trip had been 8 kilometers per hour greater, it would have taken her 1 hour less

statement 1 is clearly insuff

statement 2:

rt=1 ----eqt 1
(r+8)(t-1)=1-----eqt 2
when you simplify the two...you get to 8t^2-8t-1=0
I am unable to find the roots for this equation...
given that the discriminant is positive...there should be 2 roots
Thus, answer should be B

However, OA is C

r*t = d

ST 1 :

r = 72

Clearly insufficient

St 2 :

(r+8) (t-1) = d

rt-r+8t -8 = d

Insufficient as we dont know r & d

Combining st1 & st2

we know that rt= d ;

rt-r+8t -8 = d

rt-r+8t -8 = rt

8t= 8+r

from ST1 ;r=72

8t=8+72

---> t= 10 hours

Pick C

Plz note that u picked d=1 which is not STATED..!

the reason why i picked D=1 is b/c it is irrelevant what the distance is if we can get two equations
not sure if i agree with your solution

instructors, please help!

san2009 wrote:the reason why i picked D=1 is b/c it is irrelevant what the distance is if we can get two equations
not sure if i agree with your solution

instructors, please help!

How are you very sure that DISTANCE is " irrelevant"???Plz post your reasoning..want to hear that!!

san2009 wrote:the reason why i picked D=1 is b/c it is irrelevant what the distance is if we can get two equations
not sure if i agree with your solution

instructors, please help!

Hi,
When you need to find the time in a rate question, the distance traveled is never irrelevant as you'll can find out for yourself by just thinking about it.


However, the value of the distance is irrelevant in general if you're trying to find the average rate. But even then you have to be careful in the case in which you're given two separate distances; you can choose two arbitrary values for the distances as long as their ratio is maintained in this scenario.

So GMAT Titan did a good job at solving the question.

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Dakar Azu, GMATLounge

I guess i went wrong in assuming a value for the distance. I should've taken only "d" for distance -- then your solution makes sense! thanks

san2009 wrote:I guess i went wrong in assuming a value for the distance. I should've taken only "d" for distance -- then your solution makes sense! thanks

Good that now you understood it. Dakar is right that distance is not always irrelevant. So, clearly 1 is insufficient.
Now, if you look at 2 then you can form an equation:

r*t = (r+8)*(t-1)

r*t = r*t - r + 8*t - 8. So, r - 8t + 8 =0.

Because you still don't know the value of r, this statement is also insuficient.

Combining both the equations, you can find the value of t. Hence, C

Tell whether this equation is right ?

100/r -100/r+8 = 1

seems right to me. what do u get when you solve it for r?

san2009 wrote:seems right to me. what do u get when you solve it for r?

r^2 +8r - 800 = 0

Sorry but I am not able to factorize this quadratic equation.

Nikhil,

Ur logic and equation is right.

However we cant assume Distance value as 100 here.

If we assume D=100,we can solve it from the stmt1 itself.

D=100,r=72,t=100/72

In work rate problem,its safe not to assume any value.The better approach is solving it by the given equation.

Using ur logic we can derive the equation as below,

D/(T-1)-D/T=8

D=72T

72T/(T-1)=80

T=10

Hope this clarify