If the number 892,132,24x is divisible by 11, what must be the value of x?
A) 1
B) 2
C) 3
D) 4
E) 5
The OA is the option A.
How can I prove that option A is the only one possible? Can any expert give me some help? Please.
If the number 892,132,24x is divisible by 11, what must . .
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- EconomistGMATTutor
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Hello Vjesus12.
Let's take a look at your question.
First, let's remember the multiplication rule of 11:
(Sum of digits at odd places - Sum of digits at even places) should be divisible by 11.
We have the number 892,132,24x, then: $$\left(8+2+3+2+x\right)-\left(9+1+2+4\right)=\left(15+x\right)-\left(16\right)=x-1.$$ The only option that makes 1-x a multiple of 11 is x=1.
This is why the correct option is [spoiler]A=1[/spoiler].
I hope this answer can help you.
Feel free to ask me again if you have any question.
Regards.
Let's take a look at your question.
First, let's remember the multiplication rule of 11:
(Sum of digits at odd places - Sum of digits at even places) should be divisible by 11.
We have the number 892,132,24x, then: $$\left(8+2+3+2+x\right)-\left(9+1+2+4\right)=\left(15+x\right)-\left(16\right)=x-1.$$ The only option that makes 1-x a multiple of 11 is x=1.
This is why the correct option is [spoiler]A=1[/spoiler].
I hope this answer can help you.
Feel free to ask me again if you have any question.
Regards.
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- mariliatgd
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One of the number properties is that to see if a number is multiple of 11 you must:
If the number is "abc", then c-b+a = 0 or 11.
In this case 892 132 24x needs to bee multiple of 11, so:
x - 4 + 2 - 2 + 3 - 1 + 2 - 9 - 8 must equal 0 or 11
x - 1 must equal 0 or 11
x must be 1, because is a number with one digit.
If the number is "abc", then c-b+a = 0 or 11.
In this case 892 132 24x needs to bee multiple of 11, so:
x - 4 + 2 - 2 + 3 - 1 + 2 - 9 - 8 must equal 0 or 11
x - 1 must equal 0 or 11
x must be 1, because is a number with one digit.