Question

$◯◊$

$\times$ $\square ◊$

__________

$△\square ◊$

In the multiplication above, each symbol represents a different unknown digit, and $◯\times \square \times ◊=36$. What is the three-digit integer $◯\square ◊$?

• A. $263$
• B. $236$
• C. $194$
• D. $491$
• E. $452$

Answer 1

Answer: (B)

$236$

The three symbols $◯,\square$ and $◊$ multiply to 36 and each must represent a different digit. Take a look at those choice: you can work backwards to solve! The digits of each answer choice represent $◯,\square ,◊$ respectively. Plug each in to find the one that works.

(A) 263. The multiplication problem becomes (23)(63). The units digit is 9, but it should be 3, so this answer is incorrect.

(B) 236. The multiplication problem becomes (26)(36). The units digit is 6, so this one could work. At this point, decide whether you want to finish the rest of the math for this answer or whether you want to check for the units digit for (C), (D), and (E). If the units digit doesn't work for the other three, then this one must be the right answer and you don't have to do any more work.

Here's the rest of the work for (B). (26)(36) = 936. This does match the remaining restrictions on the problem, so it is the correct answer.

(C) 194. The multiplication problem becomes (14)(94). The units digit is 6, but it should be 4, so this answer is incorrect.

(D) 491. The multiplication problem becomes (41)(91). The units digit is 1, so you also have more work to do on this choice. (41)(91) =3,731. The product has to be a 3-digit number, not a 4-digit number,so this answer is incorrect. (You can stop the multiplication at the point that you can tell that it will be larger than a 3-digit number.)

(E) 452. These three digits don't multiply to 36, so this cannot be the correct answer.