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Unknown Digits - MGMAT

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Unknown Digits - MGMAT

by itudor13 » Sun Jan 05, 2014 7:05 am
I have been struggling with unknown digits recently, and I was hoping the experts could help clear somethings up for me.

Here is a problem I struggled with:

(circle)(diamond)
x (square)(diamond)
(triangle)(square)(diamond)

In the multiplication above, each symbol represents a different unknown digit, and (circle)*(square)*(diamond)= 36. What is the three-digit integer (circle)(square)(diamond)

A)263
B)236
C)194
D)491
E)452

I understand how to eliminate the answers down to B and D because a diamond multiplied by a diamond equals a diamond. However, after this step, I don't know how to get to the right answer unless I multiply each answer out individually. This is time consuming and I'm not sure I would have enough time to do that.

Answer is B

Thank you in advance.
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by GMATGuruNY » Sun Jan 05, 2014 7:43 am
itudor13 wrote:I have been struggling with unknown digits recently, and I was hoping the experts could help clear somethings up for me.

Here is a problem I struggled with:

�♢
�♢
______
∆�♢

In the multiplication above, each symbol represents a different unknown digit, and � * � * ♢= 36. What is the three-digit integer ��♢?

A)263
B)236
C)194
D)491
E)452
We can PLUG IN THE ANSWERS, which represent the value of ��♢.
The multiplication example -- �♢ * �♢ = ∆�♢ -- implies that all 3 values have the same units digit.
The answer choices offer the following options for ♢:
3, 6, 4, 1, 2.
Of these options, only ♢=6 and ♢=1 are viable:
B: �6 * �6 = ∆�6
D: �1 * �1 = ∆�1.

Test answer choice B:
If ��♢ = 236, then � = 2, � = 3 and ♢ = 6.
Plugging these values into �♢ * �♢ = ∆�♢, we get:
26 * 36 = 936.
Success!

The correct answer is B.

To determine the correct answer, we had to test only one answer choice.
2 minutes should be sufficient time to perform the necessary calculations.
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