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Jack and Jill both left their respective homes at 1 PM. Jack walked

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Jack and Jill both left their respective homes at 1 PM. Jack walked  [#permalink]

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New post 30 Jul 2017, 11:45
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Difficulty:

  95% (hard)

Question Stats:

47% (03:16) correct 53% (03:17) wrong based on 98 sessions

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Jack and Jill both left their respective homes at 1 PM. Jack walked till a school that was between 2.5 kilometers and 3 kilometers from his home, inclusive, and returned home between 1:55 PM and 2:05 PM. If Jill walked 5 kilometers more than Jack and returned to her home at 3 PM, which of the following statements must be true?

    I. The walking speed of Jill was greater than that of Jack
    II. Jack’s walking speed was close to 3 kilometers per hour
    III. Had Jack covered 0.5 more kilometers every 30 minutes, his walking speed would have been greater than Jill’s


A. I only
B. II only
C. III only
D. I, II and III
E. None of the above



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Re: Jack and Jill both left their respective homes at 1 PM. Jack walked  [#permalink]

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New post 31 Jul 2017, 00:06
EgmatQuantExpert wrote:
Jack and Jill both left their respective homes at 1 PM. Jack walked till a school that was between 2.5 kilometers and 3 kilometers from his home, inclusive, and returned home between 1:55 PM and 2:05 PM. If Jill walked 5 kilometers more than Jack and returned to her home at 3 PM, which of the following statements must be true?

    I. The walking speed of Jill was greater than that of Jack
    II. Jack’s walking speed was close to 3 kilometers per hour
    III. Had Jack covered 0.5 more kilometers every 30 minutes, his walking speed would have been greater than Jill’s
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above


At 1:00PM, Jack walked to school that was between 2.5-3 km from his home, and then returned home between 1:55PM-2:05PM. Hence, Jack walked about 5-6km in between 55min and 1h 05min.

At 1:00PM, Jill walked 5km more than Jack and returned home at 3PM, he walked about 10-11km in 2 hours.

(I) The walking speed of Jill was greater than that of Jack
We could set a specific example to eliminate this one.

If Jack walked for 5km in 1 hour, Jill walked for 10km in 2 hours, then the walking speed of them are equal.
If Jack walked for 6km in 1 hour, Jill walked for 11km in 2 hours, then the walking speed of Jack is greater.

Hence this one is wrong.

II. Jack’s walking speed was close to 3 kilometers per hour
It's clear that this one is wrong.
Jack walked about 5-6km in between 55min and 1h 05min. Hence, his walking speed is between 4.6 and 6.5 km per hour, much greater than 3 km per hour.

III. Had Jack covered 0.5 more kilometers every 30 minutes, his walking speed would have been greater than Jill’s
This one is correct.

If Jack covered 0.5 more km every 30 min, Jack will cover 1 more km every 1 hour. Hence, he could walk about 6-7km in between 55min and 65min.

Jill walked about 10-11km in 2 hours, or walked about 5-5.5km in 1 hours.

It's clear that Jack's walking speed is greater than Jill's. In the worst case, Jack could walk 6 km in 65 min, so his walking speed is 5.54km/h, still greater than Jill's.

The answer is C.
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Re: Jack and Jill both left their respective homes at 1 PM. Jack walked  [#permalink]

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New post 12 Dec 2017, 05:15
EgmatQuantExpert wrote:
Jack and Jill both left their respective homes at 1 PM. Jack walked till a school that was between 2.5 kilometers and 3 kilometers from his home, inclusive, and returned home between 1:55 PM and 2:05 PM. If Jill walked 5 kilometers more than Jack and returned to her home at 3 PM, which of the following statements must be true?

    I. The walking speed of Jill was greater than that of Jack
    II. Jack’s walking speed was close to 3 kilometers per hour
    III. Had Jack covered 0.5 more kilometers every 30 minutes, his walking speed would have been greater than Jill’s


A. I only
B. II only
C. III only
D. I, II and III
E. None of the above



Thanks,
Saquib
Quant Expert
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Though it's not a hard problem as far as the concepts go, the calculations involved are ugly at best.
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Re: Jack and Jill both left their respective homes at 1 PM. Jack walked  [#permalink]

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New post 12 Dec 2017, 06:07
EgmatQuantExpert wrote:
Jack and Jill both left their respective homes at 1 PM. Jack walked till a school that was between 2.5 kilometers and 3 kilometers from his home, inclusive, and returned home between 1:55 PM and 2:05 PM. If Jill walked 5 kilometers more than Jack and returned to her home at 3 PM, which of the following statements must be true?

    I. The walking speed of Jill was greater than that of Jack
    II. Jack’s walking speed was close to 3 kilometers per hour
    III. Had Jack covered 0.5 more kilometers every 30 minutes, his walking speed would have been greater than Jill’s


A. I only
B. II only
C. III only
D. I, II and III
E. None of the above





Yes the calculations are lengthy, especially so in statement III and not likely to be seen in actual but you can save some time by..
info:-
1) Mr Jack travels 5 to 6 km in 55 to 65 min
2) Jill travels 10-11 in 2 hr

statements..
    I. The walking speed of Jill was greater than that of Jack
    To confirm, take MAX of Jack
    so Jill speed 5.5km/h and jacks speed 6 km in 55min, so >6km/h
    NOT necessary

    II. Jack’s walking speed was close to 3 kilometers per hour
    Don't do any calculations. REQUIRED info in statement I, speed of Jack>6km/h
    Again NOT necessary

    III. Had Jack covered 0.5 more kilometers every 30 minutes, his walking speed would have been greater than Jill’s
    so Jack travels 6 to 7 km in 55-65 min
    Take least speed of Jack 6 km in 65 min..
    Don't divide 6 by 65, will take a lot of time..
    check how much would JIll travel in 65 minutes = 65*5.5=357.5 whereas jack travels 6*60 = 360

    YES

Multiplication just lessens down some tedious calculations

Only III true

C
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Re: Jack and Jill both left their respective homes at 1 PM. Jack walked &nbs [#permalink] 12 Dec 2017, 06:07
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Jack and Jill both left their respective homes at 1 PM. Jack walked

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