The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:

The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:

(a) All 3 investments become worthless.
(b) 2 of the 3 investments become worthless, while 1 doesn’t.

Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.
Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.

The sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.

The correct answer is A.

This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.

onTrack by mbaMission

A first-of-its-kind, on-demand MBA application experience that delivers a personalized curriculum for you and leverages interactive tools to guide you through the entire MBA application process.

Get Started!

Upcoming Events

Upcoming Deadlines

  • Columbia J-Term (Round 2)
  • Cambridge Judge (Round 1)
  • HBS (Round 1)
  • Penn Wharton (Round 1)
  • Notre Dame Mendoza (Early Decision)
  • Virginia Darden (Early Decision)
  • Michigan Ross (Round 1)
  • Columbia (Round 1)
  • INSEAD (August Intake)
  • Stanford GSB (Round 1)
  • Yale SOM (Round 1)
  • Northwestern Kellogg (Round 1)
  • Berkeley Haas (Round 1)

Click here to see the complete deadlines

2024–2025 MBA Essay Tips

Click here for the 2023–2024 MBA Essay Tips

MBA Program Updates

Explore onTrack — mbaMission’s newest offering allowing you to learn at your own pace through video. Learn more