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D > 31680 feet

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D > 31680 feet

by j_shreyans » Thu Oct 16, 2014 8:59 pm
If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that the 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 per second.

OA E

Guys ,

Isn't it Statement 2 only sufficient.

Let Distance be D , Speed be S ,and Time be T.

So Carlos T in sec. = 1/+2-*3600 = 1800 sec.

If 1 mile = 5280 feet then 6 mile will be 31680 feet

Target question = D > 31680 feet

Statement 1) Average speed is greater than 16 feet per second means S will be 17,18,19......

So this is YES/NO .

D=1800*17 =30600 (NO)
D= 1800*18 = 32400(YES)

so NOT SUFFICIENT

statement 2- Average speed is less than 18 feet per second

So the S will be less than 18

D= 1800*17 = 30600 (NO)
D= 1800*16 = 28800 (NO)

This statement always gives NO answer so i think this statement is sufficient to answer the target question.

Pls check and correct where i am wrong.
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Source: — Data Sufficiency |

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by [email protected] » Thu Oct 16, 2014 10:56 pm
HI j_shreyans,

Most of your work here is spot-on, but the question never stated that we were restricted to integer values. This means that we MUST consider FRACTIONS of a foot/second. When a Fact states "greater than 16 ft/sec", we might be dealing with 16.0000001 ft/sec" and when a Fact states "less than 18 ft/sec", we might be dealing with 17.999999 ft/sec.

As such, we have to calculate 16 ft/sec (for Fact 1) and 18 ft/sec (for Fact 2) and use THAT data to determine the sufficiency of the information. If you work through those steps, then you'll get to the correct answer.

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by GMATGuruNY » Fri Oct 17, 2014 1:15 am
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 = 5,280 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 per second.
Since the two statements are given in terms of FEET PER SECOND, rephrase the question stem in terms of FEET PER SECOND.

1/2 hour = 1800 seconds.
Thus:
6 miles/1800 seconds * 5280 feet/1 mile
= 6 * 5280 / 1800
= 528/30
= 17.6 feet per second.

Question rephrased: Did Carlos travel at an average speed greater than or equal to 17.6 feet per second?

The two statements combined indicate only that Carlos's average speed was between 16 and 18 feet per second.
Thus, it's possible that his average speed was less than, equal to, or greater than 17.6 feet per second.
INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Oct 17, 2014 6:02 am
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 per second.
Target question: Was the distance that he cycled greater than 6 miles?

This question could use some rephrasing. Since the two statements provide speeds in feet per second, let's first see what it means for Carlos to cycle exactly 6 miles in 1/2 an hour.

Distance = 6 miles = (6)(5280) feet
Time = 1/2 hour = 1800 seconds.

Speed = (6)(5280)/1800 = 5280/300 = 176/10
= 17.6 feet per second.

So, in order for Carlos to travel more than 6 miles in 1800 seconds, his average speed must be greater than 17.6 feet per second.

REPHRASED target question: Was Carlo's average speed greater than 17.6 feet per second?

Statement 1: His average speed was greater than 16 feet per second.
So, his speed may have been greater than 17.6 feet per second, or less than 17.6 feet per second.
Since we cannot answer the rephrased target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: His average speed was less than 18 feet per second.
So, his speed may have been greater than 17.6 feet per second, or less than 17.6 feet per second.
Since we cannot answer the rephrased target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We now know that his speed is between 16 feet per second and 18 feet per second.
So, once again, his speed may have been greater than 17.6 feet per second, or less than 17.6 feet per second.

Since we still cannot answer the rephrased target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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