Lesson: Data Sufficiency Challenging - 16t03

Easy Math/Tough Applications: Example 1

Challenging questions in the Quantitative Section may test your ability to cut through dense information to get to the heart of what often turns out to be a relatively simple matter. Why does the Exam do this? To see whether you have the ability to whittle complex language down to an easy solution. In these problems, the important thing is to find the "question behind the question." That is, to find what the question is really asking. Here’s an example:

At the end of every hour a culture of bacteria becomes some number of times larger than it was the previous hour. If the number of bacteria was originally greater than 1 and if the rate of growth also increases every hour, what was the original number of bacteria?

1) of the original culture would have resulted in a total of 385 bacteria after 3 hours.

2) The original number of bacteria was less than 4.

Review the question stem above. Do you recognize the math concept that this is testing? Type it into the Text Box, and click Continue.

This problem is really about .

Review Statement 1 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

1) of the original culture would have resulted in a total of 385 bacteria after 3 hours.?

Sufficient

Insufficient

Countinue

What does this mean? Well, if of the original culture would’ve resulted in 385 bacteria after 3 hours, then the actual number of bacteria must equal 1155 after 3 hours. If we look at this as an equation, we get . So if we multiply both sides by 3, to get rid of the fraction, we get cbax = 1155. The product 1155 should set off a prime factorization alarm, since it contains some primes as factors (most clearly 5 and 11).

If we divide 1155 by 11, we get 11 × 105, which gives us 11 × 5 × 21, which gives us 11 × 5 × 7 × 3. So the prime factorization of 1155 is 3 × 5 × 7 × 11. But this is insufficient to tell us which of these numbers is the original number of bacteria.

We know that the three hourly rates of increase have to be in increasing size order, but there are four ways to start with one of these numbers as the original number and the other three as the increasing rates of growth: 3 × 5 × 7 × 11 or 5 × 3 × 7 × 11 or 7 × 3 × 5 × 11 or 11 × 3 × 5 × 7. So Statement (1) is insufficient to tell us what the original number of bacteria was.

Now let’s look at Statement (2).

Countinue

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