Blog

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:

Let’s list out the product, using “dot-dot-dot” for missing parts in the middle.

Product = (x1/21) (x1/22) (x1/23)…(x1/30)

Since the bases are all the same, we just add the exponents to get the final exponent.

Exponent of product = 1/21 + 1/22 + 1/23 + … + 1/30 (ten terms in the sum)

Now, we are not asked to compute the exact value of this number (a brutal task that would require us to find a common multiple of every integer from 21 to 30!). Rather, we want to know what the product lies between.

One way to find simple upper and lower bounds is to replace all the different fractions with the same fraction that is definitely larger or smaller. Then compute these “fake” sums and see what you get.

Start at the small end. The real sum is definitely greater than this fake sum:

1/30 + 1/30 + 1/30 + … + 1/30

We’ve replaced 1/21, 1/22, etc. with 1/30 in each position. 1/30 is definitely less than 1/21, 1/22, etc. through 1/29, so the sum is definitely less.

Lower fake sum = 1/30 + 1/30 + 1/30 + … + 1/30 (ten terms) = 10/30 = 1/3

We have a good lower bound. Let’s set an upper bound by replacing every fraction in the real sum with 1/20, which is definitely larger than every fraction in the real sum.

Upper fake sum = 1/20 + 1/20 + 1/20 + … + 1/20 (ten terms) = 10/20 = 1/2

We now have bounds on either end. The exponent must be between 1/3 and 1/2, so the product in question must be between x1/3 and x1/2.

The correct answer is C.




Upcoming Events


Upcoming Deadlines

  • Dartmouth Tuck (Round 3)
  • London Business School (Round 3)
  • Texas McCombs (Round 3)
  • Vanderbilt Owen (Round 4)
  • Berkeley Haas (Round 4)
  • Penn State Smeal (Round 4)
  • Penn Wharton (Round 3)
  • Columbia (Round 3)
  • Northwestern Kellogg (Round 3)
  • Virginia Darden (Round 3)
  • Chicago Booth (Round 3)
  • Michigan Ross (Round 3)
  • MIT Sloan (Round 3)
  • Stanford GSB (Round 3)
  • Yale SOM (Round 3)
  • Cornell Johnson (Round 3)
  • UCLA Anderson (Round 3)
  • USC Marshall (Round 3)
  • Toronto Rotman (Round 4)
  • UNC Kenan-Flagler (Round 4)
  • Georgetown McDonough (Round 4)

Click here to see the complete deadlines


2023–2024 MBA Essay Tips

Click here for the 2022–2023 MBA Essay Tips


MBA Program Updates