In a certain deck of cards, each card has a positive integer written o

EMPOWERgmatRichC, my understanding was since 14 is the largest number, we should take 13 not 15 to multiply by 14.. Can you please explain?

Hi tkorzhan1995,

With these types of 'story problems', it can often help to imagine the specific situation that is described in the prompt. Here, the prompt tells us:

"draw a card and multiply the integer ON THE CARD by the next larger integer." We're also told that the number of possible products is limited (the results must be BETWEEN 15 and 200).

So, imagine that you draw a card and work through the math that is described (and you can do the following brute-force math to prove what the largest possible number is):

-If your card had a '11' on it, then you would multiply that 11 by the next larger integer (12).... and you'd have (11)(12) = 132
-If your card had a '12' on it, then you would multiply that 12 by the next larger integer (13).... and you'd have (12)(13) = 156
-If your card had a '13' on it, then you would multiply that 13 by the next larger integer (14).... and you'd have (13)(14) = 182
-If your card had a '14' on it, then you would multiply that 14 by the next larger integer (15).... and you'd have (14)(15) = 210

Since the product has to be between 15 and 200, the largest possible number of a card CANNOT be 14 (here, the product would be 210 - which is too big). Thus, the largest number would be 13.

GMAT assassins aren't born, they're made,
Rich

Can anybody link similar questions to this one? thanks!

I was not able to find very similar questions to this one but you can check for other min/max questions in the links below:

14. Min/Max Problems

• Theory
  Maximizing/Minimizing Strategies on the GMAT - All in One Topic!
  
  • Questions
    Worst Case Scenario Questions
    DS Questions
    PS Questions

Hope it helps.

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