Data Sufficiency

Hi MalcolmW,

In this DS question, we're told that the distance from floor to floor in a building is 9 feet. So the distance from the base of the first floor to the base of the second floor is 9 feet. We're asked how many STEPS there are from the base of the first floor to the base of the second floor.

Fact 1: Each step is 3/4 foot HIGH.

This tells us that the steps are the same height (which is important). Since each step is 3/4 foot high, we CAN figure out how many steps it takes to total 9 feet:

(3/4)(X steps) = 9
X = (9)(4/3)
X = 36/3
X = 12 steps
Fact 1 is SUFFICIENT

Fact 2: Each step is 1 foot WIDE.

This tells us NOTHING about the height of the steps, so there's no way to know how many steps there are from the first floor to the second floor.

If each step is 1 foot high, then there are 9 steps.
If each step is 3/4 foot high, then there are 12 steps.
Fact 2 is INSUFFICIENT.

Final Answer: A

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

If the two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building?

(1) each step is 3/4 foot high
(2) each step is 1 foot wide.

Rich has already explained why the correct answer is A, so I won't rehash that. So, let's talk STRATEGY.

First, we need to recognize that all target questions are IMPOSSIBLE to answer without any additional information. In other words, for any target question there will be more than one possible answer.

So, when you see the target question (in this case, it's How many steps are there in a set of stairs that extends from the first floor to the second floor of the building? ), we should STOP and ask ourselves, WHY is it impossible to answer this question?

In this case, we can't answer the question, because we don't know how "big" each stair is. If each stair is 4.5 feet high, then there will be only 2 stairs to fill in the 9 feet of height between floors. If each stair is 1 foot high, then there will be 9 stairs to fill in the 9 feet of height. If each stair is 3 feet high, then there will be 3 stairs. And so on.

Now that we understand WHY this target question is impossible to answer without any additional information, we should ask, What additional information will help me answer the target question? .

At this point, it's easy to see what we need. We need to know the height of each individual step.

Great. Now, we can start checking each statement.

Statement 1 tells us the height of each step. PERFECT. It must be sufficient. In fact, we need not even perform any calculations. For Data Sufficiency questions, we need only determine whether we have sufficient information to answer the target question. We already know that statement 1 provides sufficient information, so performing any calculations will be a waste of our precious time.

Statement 2 provides no information that will help me determine the height of each step. So, it is NOT sufficient.

Answer: A

For more tips and strategies for solving Data Sufficiency questions, see our comprehensive set of free videos at: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent