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## If A, B and C represent different digits in the multiplication,

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### If A, B and C represent different digits in the multiplication,

by BTGmoderatorDC » Tue Jul 19, 2022 6:16 pm

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B

C

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If A, B and C represent different digits in the multiplication, AAB * B = CB5B, then A + B + C = ?

A. 9
B. 12
C. 14
D. 15
E. 17

OA E

Source: Magoosh

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### Re: If A, B and C represent different digits in the multiplication,

by swerve » Sun Jul 24, 2022 2:24 pm
BTGmoderatorDC wrote:
Tue Jul 19, 2022 6:16 pm
If A, B and C represent different digits in the multiplication, AAB * B = CB5B, then A + B + C = ?

A. 9
B. 12
C. 14
D. 15
E. 17

OA E

Source: Magoosh
Step 1: Value of $$B$$.
If we look at the units digit of the numbers being multiplied and the product, we get $$B*B=_B$$.
Thus, B can only be $$0, 1, 5$$ and $$6$$.
If $$0$$, then the product will be $$0$$. Discard
If $$1$$, then the product will be $$AA1$$. Discard
If $$5$$, then $$AA5*5=C555$$. But the product of two multiples of $$5$$ should end in $$00, 25, 50$$ or $$75$$. Discard
So, $$B=6$$.

Step 2: Value of $$C$$.
So, the product is $$\Rightarrow \, AA6\ast 6=C656$$
Now, $$C656$$ should be a multiple of $$6$$, so $$C$$ can be $$1, 4$$ or $$7$$.

If $$C$$ is $$1$$, then $$\dfrac{1656}{6}=276 \neq AA6$$

If $$C$$ is $$4$$, then $$\dfrac{4656}{6}=776 = AA6$$

So, $$C=4$$ and $$A=7$$

SUM $$= 7+4+6 = 17$$

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