Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded the nearest tenth.)

1) Pei walked this distance at an avg. rate of less than 6.4 kilometers per hour.
2) On avg., it took Pei more than 9 minutes per kilometer to walk this distance.

What is the best way to approach this type of problem (where you know the 2 statements are going to provide limits)? stem asks if t > 2hr and gives r x t = 10 mi/hr, so should the stem be restated as: is r > 5mi/hr? and also convert that inequality to km/hr?

Took me several minutes to keep track of all the "less than" "more than" statements, any help is appreciated. thanks

What is the OA?

I get B.

1. Pie walked 6.4 km/hr, and 1mile - 1.6 km, so I coverted 6.4 km/hr to m/hr by dividing 6.4/1.6 = 4 m/hr.
so stem-1 is sufficient to answer the question ..it would take more than two hours to travel 10 miles.

2. pie takes more than 9 minutes to travel 1 km, so I took next least possible time (i.e 10 mins), so if a person travels 1 km in 10 mins then he would travel not less than 6 km/hr. Convert 6 km/hr to m/hr by dividing 6/1.6 = 4.25 m/hr. so again it would take more than 2 hours to travel 10 miles..

the answer is D - both are sufficient.

no, the stem should ask whether r is LESS than 5 miles/hr. the longer you take, the slower your rate.
if you're confused as to which way the inequality goes, just think about whether the answer would be 'yes' or 'no' if r were (a) 0.00001 miles/hr or (b) 1,000,000 miles/hr.

ironically, you would be fine with this misinterpretation of the problem statement, because it's data sufficiency; "is x true" and "is x not true" are indistinguishable in the weird wild world of DS.
for all you logic hounds out there, yes, the exact opposite of x < 5 is not x > 5 but rather x > 5, but this is a non-issue because neither of the statements has anything to do with r = 5.

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if you're overly confused by the inequality signs, just practice the following templates until you've got them totally down cold:

is x > 20?
(1) x > 18
(2) x > 21
answer: (b) - 2 is sufficient, 1 isn't

is x > 20?
(1) x < 18
(2) x < 21
answer: (a) - 1 is sufficient, 2 isn't

etc.

Simpler way (time saver):
We need to know the value of three variables (rate, distance, and time)
RT = D
St 1 gives R and so does St 2 – we can figure out Time cause we know the distance (10miles) – ignore the units cause they can be converted esp when the conversion is explicitly given!
note: St2 does need a flip
So just knowing that values are given - st1 and st2 are sufficient - why bother calculating...
(if this was a problem solving que., then it’s a different story – convert units to find out the actual answer)
If this is not correct - please post a response.

Thanks for offering another idea Deepak. Your reasoning doesn't quite work, unfortunately. The two statements do not offer one specific rate value, which would then allow us to calculate one specific time. Instead, each statement offers a range of possible rates (less than 6.4 kmh, more than 9m per km).

Let's use an analogous example with different numbers to illustrate the problem:

I drive 50 miles to get to work. I drive less than 25 mph to get there (I'm slow). Do I take more than 2.5 hours to get to work?

T = D/R = 50 / 25 = 2 hours BUT I'm not actually driving 25 mph exactly. I'm driving <25 mph (24.9? 20? 14?), so I'm taking >2 hours to get there.

So, what's the answer to the question? At certain speeds <25 mph, I will get to work in less than 2.5 hours. At certain other speeds >25 mph, I will take more than 2.5 hours to get to work. Not sufficient.

So, lesson for future: a *range* of rates does not (necessarily) allow you to calculate a single solution. If the rate is given as "less than" or "more than" some number, then you do actually have to do some more work.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Can we do this as follows, as well?

Distance under concern = 10 miles = 16 kms (as per given conversion rates)

Let R be the rate.

The question asks if 16/R > 2 hrs

or 16 > 120. R (converted hrs to minutes).

St. 1:

R < 6.4 km/ hr
or R < 6.4 / 60 km/min.

Now, if we calculate the right hand side of our problem statement:

120. R = 120. 6.4/60 = 12.8

Definitely 16 > 12.8. Since the rate is anyway lesser than 6.4, the right hand side will get only lesser.

Therefore, St. 1 is sufficient.

St. 2:

Avg. time is more than 9 minutes per km.

So on an avg. it must take 9 * 16 = 144 minutes for 16 kms.

Definitely 144 > 120 (i.e. 2 hours).

Hence, st. 2 is sufficient.

Therefore, answer D.

My question is: can the averages given in the statements be used as constant rates or times as I have done above (for e.g. I have taken the avg. of 9 minutes in st.2 as a uniform speed through out the entire distance).

sprparvathy, your method is fine.

S2 means that her average rate for the entire distance is 1km/9min. Neither the question nor either of the statements mentions any distance other than the whole ten miles (except to define speed).

Q) time> 2hours ?

10miles=16km

St.1) time=distance/speed

16/LT 6.4 =GT 2hours

(LT= Less Than)

A-Sufficient.

St.2) 1 km = GT 9min

16 x GT 9= GT 134min = GT 2hours.
(GT=Greater Than)

B-Sufficient

Ans:D

Thanks, Anupam..

_________________
Tim Sanders
Manhattan GMAT Instructor

Dear instruc.
Can you please show a full solution to this problem.
Stat.1 I rephrase as Is R less than8km/h?
Stat2.I am confused.
Thanks

this thread already contains several solutions to the problem, so please tell us what you already understand and what you don't. i.e., which parts of the solutions already given on the thread do you understand? which parts are confusing you?

Dear Instructor,
The second statement I try to convert into rate inequality as I did with the first statement ( is R less than 8km/h). Is it possible? or should I just convert statement 2 into time question rather than rate? Buttom line I am confused approach wise on this type of enequalities.
Thank you.

you should probably stick with time on statement 2 rather than rates, because the information is given in terms of time and the question is asking about time..

_________________
Tim Sanders
Manhattan GMAT Instructor