Alice, Bob, and Charlie were on a hike and were wondering how far away

Question

GMATbuster's Weekly Quant Quiz#8 Ques #7 
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Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Let d be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of d?

A) (0,4)
B) (4,5)
C) (4,6)
D) (5,6)
E) (5,∞)

A: min 6
B:max 5
C: max 4

Plotting it on the number line
we can the only range not covered is between 5 and 6.
--------4---5---6-----

Hence answer D

A) (0,4)
B) (4,5)
C) (4,6)
D) (5,6)
E) (5,∞)

Chethan92 · Answer

Alice-Atleast 6 miles away means Distance> or equal to 6. interval is (6, infinite)
Bob-Atmost 5 miles. Max 0-5 interval is (0,5)
Charlie-Atmost 4 miles away. max 0-4 interval (0,4)
Since none of their assumption is correct. the only possible value of Distance d is (5,6)

D is the answer.

nitesh50 · Answer

Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Let d be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of d?

A) (0,4)
B) (4,5)
C) (4,6)
D) (5,6)
E) (5,∞)

A: min 6
B:max 5
C: max 4

Plotting it on the number line
we can the only range not covered is between 5 and 6.
--------4---5---6-----

Hence answer D

A) (0,4)
B) (4,5)
C) (4,6)
D) (5,6)
E) (5,∞)

A: min 6
B:max 5
C: max 4

Plotting it on the number line 
we can the only range not covered is between 5 and 6.
 -------- 4 --- 5---6 -----

Hence answer D

nkin · Answer

We need to get the opposite statements for all three cases which turn out to be:

d<6, d>5 and d>4. Combining the three we get (5,6) as the interval.

Hence D

saukrit · Answer

Alice-At least 6 miles away means Distance>=6. Interval is (6, infinite)
Bob-At most 5 miles. Interval is (0,5)
Charlie-At most 4 miles away. Interval (0,4)

Since none of the above can be correct, The only possible value of Distance d is (5,6)

Correct answer is D

mishugarg · Answer

according to alice distance >=6
according to bob :: <=5
according to Charlie :: <=4

for all statements to be false, the range can be (5,6) i.e. D

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Alice, Bob, and Charlie were on a hike and were wondering how far away

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