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I am less than 500. All three digits are odd. All three digits are different. The sum of the digits is thirteen. The product of my digits is greater than 30. I am not divisible by 5. Who am I?

 Feb 11, 2016

Best Answer 

 #1
avatar+2498 
+15

\(\text{ let s say x y z is the digits of your 3 digit number } \\ xyz<500 \\x+y+z=13 \\x*y*z>30 \\\text{i am not divisible by five mean that your number cannot end with 0 or 5} \\ \text{so z cannot be 0 and 5 and your number less than 500 so x<5 x can be (3,1): } \\\text{there is only one number:} \text{ x=1 y=5 z=7 (157)}\)

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 Feb 11, 2016
edited by Solveit  Feb 11, 2016
edited by Solveit  Feb 11, 2016
 #1
avatar+2498 
+15
Best Answer

\(\text{ let s say x y z is the digits of your 3 digit number } \\ xyz<500 \\x+y+z=13 \\x*y*z>30 \\\text{i am not divisible by five mean that your number cannot end with 0 or 5} \\ \text{so z cannot be 0 and 5 and your number less than 500 so x<5 x can be (3,1): } \\\text{there is only one number:} \text{ x=1 y=5 z=7 (157)}\)

Solveit Feb 11, 2016
edited by Solveit  Feb 11, 2016
edited by Solveit  Feb 11, 2016
 #8
avatar+298 
+5

397 can't be also the answer as 3+9+7 is 19, not 13, as again mentioned above.

OneDirection  Feb 11, 2016
 #9
avatar+2498 
0

yeah you are right !

Solveit  Feb 11, 2016
 #10
avatar+298 
+5

Told ya. You didn't admit it before.

OneDirection  Feb 11, 2016
 #11
avatar+2498 
0

i was thinking that there is more posibilities :P

Solveit  Feb 11, 2016
 #2
avatar+298 
+10

You are a human being, duh.

Now don't expect me to write your name.

Still, I think the answer is 157.

 Feb 11, 2016
 #3
avatar+298 
+5

But SolveIt, 3x9x1 is 27, which is not greater than 30, as mentioned above.

 Feb 11, 2016
 #5
avatar+2498 
0

wait .... :)

Solveit  Feb 11, 2016
 #7
avatar+2498 
0

hooh

Solveit  Feb 11, 2016
 #4
avatar+4084 
+5

LMAO, 1D! :D

 Feb 11, 2016
 #6
avatar+298 
0

What? I'm just telling the truth, but wait.....there may be 0.00000001% chances he might be an extra terrestial body, plus I gave him the answer too.

 Feb 11, 2016
 #12
avatar+298 
+5

There may be, but I don't wanna try as I have to go out.

 Feb 11, 2016
 #13
avatar+129849 
+5

Nice work, OneDirection and Solveit.....points from me.....!!!

 

Here's  a way to confirm this......

 

x + y + z  = 13

x * y * z > 30

 

Now ....assume z = 9.....but this means that x and y could only be 1 and 3  since 1 + 3 + 9 = 13......but 1 * 3 * 9  = 27

 

And that's < 30

 

So......let's assume that  z = 7

 

So  z = 13 - x - y  →  7  = 13 - x - y  →   x + y   = 13 - 7  →  x + y  = 6

 

Thus.....either x = 1 and y = 5   or   vice-versa

 

So......if we write the number as xyz, the only possibility is  xyz  =  157

 

 

 

cool cool cool

 Feb 11, 2016
 #14
avatar+26387 
+5

I am less than 500. All three digits are odd. All three digits are different. The sum of the digits is thirteen. The product of my digits is greater than 30. I am not divisible by 5. Who am I?

 

\(\begin{array}{lrcll} (1) & x + y + z &=& 13 \\ & z &=& 13-(x+y) \\ (2) & x\cdot 100 + y\cdot 10 + z &<& 500 \\ & x\cdot 100 + y\cdot 10 + 13-(x+y) &<& 500 \\ & 99x + 9y + 13 &<& 500 \\ & 9y &<& - 99x + 500 - 13 \\ & 9y &<& - 99x + 487 \\ && & \boxed{~ \mathbf{ y } ~ \mathbf{<}~ \mathbf{- 11x + \frac{487}{9} } \\ ~}\\ (3) & x\cdot y \cdot z &>& 30\\ & x\cdot y &>& \frac{30}{z}\\ &&& \boxed{~ \mathbf{x\cdot y } ~\mathbf{>}~ \mathbf{\frac{30}{13-(x+y)} }\\ ~} \end{array} \)

 

I have put  \(y ~<~ - 11x + \frac{487}{9} \) and  \(x\cdot y ~>~ \frac{30}{13-(x+y)} \) in https://www.desmos.com/calculator
se we have a result of 5 Points. see:

 

Now let us see:

\(\begin{array}{|r|r|r|r|} \hline x & y & z=13-(x+y) & \text{result}\\ \hline 1 & 5 & 13 - (1+5) = 7 & {\color{red}\text{yes}}\\ 1 & 7 & 13 - (1+7) = 5 & \text{no, because }~ 175 ~\text{ is divisible by }~ 5\\ 3 & 3 & 13 - (3+3) = 7 & \text{no, because }~ x = y \\ 3 & 5 & 13 - (3+5 )= 5 & \text{no, because }~ y = z \\ 3 & 7 & 13 - (3+7 )= 3 & \text{no, because }~ x = z \\ \hline \end{array} \)

 

There is only one number 157

 

laugh

 Feb 12, 2016

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