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Magoosh Brain Twister: The Smallest Big Change – Explanation


Alright Magooshers, let’s see how you fared on this week’s Brain Twister!


(17 x 19 x 23 x 29)^31 = n

Lowering which of the following numbers by one will result in the least decrease of n?

  1. 17
  2. 19
  3. 23
  4. 29
  5. 31


Answer and Explanation

The GRE likes to test your ability to reason with numbers. Can you see general patterns, without having to resort to calculation? To test this ability, the GRE folks need to be craftier than ever, hiding those patterns in astronomical sums, since there is no a calculator on the exam.

In this question, making the smallest number one less will actually have a major effect on the outcome of the number, more so than will making those largest numbers one smaller. To test this pattern out, try smaller numbers:

2 x 5

If we make ‘2’ one less, the product becomes 1 x 5 = 5. On the other hand, by decreasing the ‘5’ by one, we end up getting 2 x 4 = 8. This pattern will carry out to the larger numbers as well (you can also test this by comparing 17 x 28 and 16 x 29). Therefore, the greater the number that is reduced by one, the less the “impact” on the total sum. Before, we choose (D), which is the answer, let’s just take a look at (E).

For the exponent, decreasing ‘31’ to ‘30’ will make the sum a lot smaller. To test this out, let’s drop the last three numbers and focus on 17^30 vs. 16^31 , since in both cases we have 19, 23, and 29.

17^30 is less than 16^31 by quite some. Again, use easier numbers to see this pattern: 3^4 vs. 4^3 is 81 vs 64; 4^5 vs. 5^4 = 1024 vs. 625. Whereas dropping 29 to 28 doesn’t affect the overall sum too much.

Answer: (D)


See you in two weeks for the next Magoosh GRE Brain Twister! Happy studying in the meantime. 🙂


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4 Responses to Magoosh Brain Twister: The Smallest Big Change – Explanation

  1. sunny shinde December 12, 2014 at 10:19 am #

    Can you make these brain twisters more frequent ?

  2. Isaac December 12, 2014 at 4:04 am #

    After this lucid explanation, the answer is definitely D!

  3. Isaac December 12, 2014 at 4:03 am #

    oh , men! The answer seemed to have been A

  4. Alireza December 11, 2014 at 2:15 pm #

    D is the answer. Decreasing the biggest number causes the least decrease in the answer

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