Data Sufficiency

If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles (note 1 mile = 5280 feet)

1) the average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.

2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet feet per second.

OA: A
time=30x60=1800 sec
speed>16 ft/sec
distance covered>16x1800 ft
>22800 ft
with II we donot reach any conclusion.

D=S*T
Is D>6?

We know T=1/2hr, so we are looking to answer the question is S>6/(1/2)=12mph?

1) S>16 feet per second - convert to mph --> 16/5280*3600 = approximately 10 mph

So we know S>10mph--pick numbers: s=11 D=5.5 NO; S=13, D=6.5 Yes - Insufficient

2) Same process as above.
S< 18 feet per second - convert to mph--> 18/5280*3600 = slightly above 12mph.

S<12.06 mph

S=12, D=6, is D>6 NO
S=11, D=5.5 is D>6 NO

Sufficient.

Ans B.

Since the answer choices are in feet per second, we should convert the question for clarity.

6 miles in 30 minutes is what speed in feet per second:
6*5280/(30*60)= 17.6 feet per second. Calculation is not bad if you cancel factors. If he exceeds that rate, then he will cover more than 6 miles in the 30 minutes.

The relevant question is "Did Carlos average more than 17.6 fps?"

(1) Insufficient. Would be sufficient if less than 16, but greater could mean 16.5 or 18.
(2) Insufficient.

Combined 16<X<18. Doesn't help if we're testing for X>17.6. Insufficient

E

iwant700plus wrote:D=S*T
Is D>6?

We know T=1/2hr, so we are looking to answer the question is S>6/(1/2)=12mph?

1) S>16 feet per second - convert to mph --> 16/5280*3600 = approximately 10 mph

So we know S>10mph--pick numbers: s=11 D=5.5 NO; S=13, D=6.5 Yes - Insufficient

2) Same process as above.
S< 18 feet per second - convert to mph--> 18/5280*3600 = slightly above 12mph.

S<12.06 mph

S=12, D=6, is D>6 NO
S=11, D=5.5 is D>6 NO

Sufficient.

Ans B.

there is no restriction on S being an integer. S could be 12.04