In the two-digit integers 3◼︎ and 2▲ DS08231

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GMAT DS08231

In the two-digit integers 3◼︎ and 2▲, the symbols ◼︎ and ▲ represent different digits, and the product
(3◼︎)(2▲) is equal to 864. What digit does ◼︎ represent?

(1) The sum of ◼︎ and ▲ is 10.
(2) The product of ◼︎ and ▲ is 24.

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Комментарии
Автор

Thanks Avi for this extremely tough question! I could not solve on my own and was thinking whether the question itself is wrong or whether both the options are wrong, as I was unable to think anything other than 32 and 27 as factors of 864. Thanks for letting me know of the other possibilities and the way to find them.

ashishsinha
Автор

Thank you Avi for all of your videos!
There is much easier way to find an answer for this particular task:
Lets represent (3◼︎)(2▲) = 864 as (30+◼︎)(20+▲) = 864
It might looks complicated with those figures, but it's a simple equation with two unknowns.
Thus either option we use: ◼︎ + ▲ = 10 or ◼︎ + ▲ = 24 - we have two equations with two unknowns, which are solvable.
So the answer that either option alone is sufficient :) Am I right?

maximignatenko