Data Sufficiency

What is the distance between Harry's home and his office?

(1) Harry's average speed on his commute to work this Monday was 30 miles per hour.

(2) If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

Let d = distance between Harry's home and his office

Target question: What is the distance between Harry's home and his office?

Statement 1: Harry's average speed on his commute to work this Monday was 30 miles per hour.
To determine the distance (d), we need the travel time.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.
Travel time = (distance)/(speed)
Let v = Monday's speed,

Start with a word equation:
(Monday's travel time) = (travel time at twice Monday's speed) + 15 minutes
Or..., (Monday's travel time) = (travel time at twice Monday's speed) + 0.25 hours
So, we can write d/v = d/2v + 0.25
Multiply both sides by 2v to get: 2d = d + 0.5v
Simplify: d = 0.5v
Divide both sides by v to get: d/v = 0.5
NOTE: distance/speed = time [in other words, time = d/v]
So, the Monday's travel time = 0.5 hours
So, statement 2 allows us to determine Monday's travel time, but we don't know Harry's speed.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that Harry's speed was 30 mph
Statement 2 tells us that Harry drove for 0.5 hours
Distance = (speed)(time)
So, distance = (30)(0.5) = 15 miles
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Hi Needgmat,

You can approach this question using "system" math, which is a category in Algebra that you'll see a few times on Test Day.

**As a warning, It's actually quite common for a DS question that "looks like" a "system" question to NOT be a system question, so you need to be sure to write everything down on the pad and do the necessary work to avoid making a silly mistake.**

We're asked for the DISTANCE between home and office. The information in the two Facts imply that we'll be using the Distance Formula, so I'll start there...

Distance = (Rate)(Time)

or

D = RT = ?

To start, we have 1 equation. To solve for Distance, we'll either need the exact value of RT or two additional unique equations that involve these variables.

Fact 1: Harry's speed = 30mph.

This gives us R. It's only one equation though, so it's not enough. Here's why:

Plugging this in, we get...

D = (30)(T) There's no way to get the exact distance with this information.
Fact 1 is INSUFFICIENT

Fact 2: If Harry's speed was twice as fast, his trip would have been 15 minutes shorter.

Since rate is in miles per HOUR, I'm going to translate 15 minutes into 1/4 hour. We can translate this equation as...

D = (2R)(T - 1/4)

Combined with the initial equation...

D = RT

We now have 2 equations, but 3 variables. No amount of algebra will get us the exact value of D.
Fact 2 is INSUFFICIENT

Combined, we have....
D = RT
D = (2R)(T - 15)
R = 30

We have three variables and three unique equations, so we CAN solve this problem and get the exact values for D, R and T.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Hi Mo2men,

The relationships among the 3 variables are easy to determine IF you hold one of the variables as a constant. However, you can still make deductions even if the variables are not constant.

For example:
-If you double the distance and double the speed, then the time stays the same.
-If you double the distance, but halve the speed, then 4 times the time is required to travel the distance.
-If you triple the speed, and triple the time, then 9 times the distance is traveled,
Etc.

GMAT assassins aren't born, they're made,
Rich

Needgmat wrote:What is the distance between Harry's home and his office?

(1) Harry's average speed on his commute to work this Monday was 30 miles per hour.

(2) If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

We need to determine the distance between Harry's home and his office.

Statement One Alone:

Harry's average speed on his commute to work this Monday was 30 miles per hour.

We are given the rate; however, since we don't know the time it takes him to commute to work, statement one is not sufficient to answer the question. Eliminate answer choices A and D

Statement Two Alone:

If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

We can let the original rate (in mph) equal r and the original time (in hours) equal t, so we have d = r x t.
The new rate is 2r and the new time is (t - ¼), noting that 15 minutes is ¼ hour, and so we have:

d = 2r x (t - ¼).

Since both 2r x (t - ¼) and d = r x t both equal d, we can set those two equations equal to each other.

r x t = 2r x (t - ¼)

Divide both sides by r, and we have:

t = 2(t - ¼)

t = 2t - ½

t = ½

However, since we don't know the rate, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that the rate is 30 mph the time is ½ an hour. Thus, the distance between his home and his office is 30 x ½ = 15 miles. The two statements together are sufficient to answer the question.

Answer: C