How to Solve Quantitative Questions

In almost every case you come across quantitative questions – let’s talk about how to deal with them. There are three (3) steps to solving any quantitative question:

1. Repeat the question, all of the key information, and ask any clarifying questions. Make sure you understand what each quantity is and the proper units. So simple, yet so important.

2. Take some time to plan out your approach. Figure out what quantities you have, what quantities you need, and what equation you will use. Tell your interviewer your approach and ask for any key quantities.

3. Solve the equation. Here is a link to a really good website with math tricks to improve your calculation speed and accuracy.

4. Verify the answer!

Example

The following example is from case # 3 in the Darden 2012 Casebook, found here.

Question: The team has decided to focus on increasing the number of registered donors and is specifically interested in kidneys donations. The Health Commission knows that it needs 9,200 kidneys per year. What percent of New Yorkers need to be registered donors in order for 9,200 kidneys to be donated in a year?

The team has already collected some useful information: The population of New York is 10 million. The percentage of people that become terminally ill or injured each year is .1% (one-tenth of one percent). The percentage of families that give consent to harvest organs is 10%.

Here’s what I’d say:

1. Repeat the question / all the information / ask clarifying questions:

Question:

OK, so to make sure we’re on the same page, you’re asking me to figure out what percent of New Yorkers would need to be registered donors for us to have 9200 kidneys donated / year?

Information:

Also, the information you gave me was:

– The population of NY is 10 million.

– 0.1% of people are terminally ill or injured ever year.

– Of the people who aren’t donors, typically 10% of their families end up donating upon their death.

– We need 9200 kidneys (4600 donors because every donor has 2 kidneys)

2. Plan / Tell the Approach:

# deaths of donors + # deaths nondonors * family donation rate = total

let x = the % of the population that are organ donors

# deaths of donors = population * death rate * % organ donors

# death of nondonors = population * death rate * % nondonors * families who donate anyway

total = 4600 people

3. Calculate

# deaths of donors + # deaths nondonors * family donation rate = total

10 million * 0.1% * x + 10 million * 0.1% * (1-x) * 10% = 4600

10,000x + 1,000 – 1000x = 4600

9000x = 3600

x = 3600 / 9000 = 36 / 90 = 4 / 10 = 40%

4. Verify

We calculation 10 million * 0.1% = 10,000 people die / year

if 40% are donors that’s 4000 sets of kidneys.

For the remaining 6000 that aren’t donors, on average 10% of their families will consent for donation = 600 more sets of kidneys.

That adds to 4600 sets of kidneys!

Conclusion

The key to success to quantitative questions are to:

1. Repeat the question / data.

2. Plan / Explain.

3. Calculate.

4. Verify

Hope it helps!

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