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If the number 892,132,24x is divisible by 11, what must be the value

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If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 05 Jan 2016, 21:17
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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
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 06 Jan 2016, 03:48
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timothyhenman1 wrote:
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


Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11


Given number: 892,132,24x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 4 = 16 (ii)

(i) - (ii) = 15 + x - 16 = x - 1
Hence x should be = 1 to make this a multiple of 11 (0) Option A
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 06 Jan 2016, 10:44
1
TeamGMATIFY wrote:
timothyhenman1 wrote:
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


Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11


Given number: 892,132,24x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 4 = 16 (ii)

(i) - (ii) = 15 + x - 16 = x - 1
Hence x should be = 1 to make this a multiple of 11 (0) Option A




Ah! I never learned the rule for divisibility of 11... I've done about 200 or so Quant problems and have never encountered a problem with this rule. In your experience has this rule been a common thing or more of a rarity?
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 06 Jan 2016, 22:46
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timothyhenman1 wrote:
Ah! I never learned the rule for divisibility of 11... I've done about 200 or so Quant problems and have never encountered a problem with this rule. In your experience has this rule been a common thing or more of a rarity?


The divisibility rule is not tested much on the GMAT much, but you never know :)
So it is better to have the rules of 2, 3, 4, 5, 8 and 9 handy.

Here are the rules for your reference:

2 - The last digit should be even
3 - Sum of the digits should be multiple of 3
4 - Last two digits should be divisible by 4
5 - Last digit should be 5 or 0
6 - Number is even and if the sum of its digits is divisible by 3
7 - Quiet complex and should not be used
8 - Last three digits should be divisible by 8
9 - Sum should be divisible by 9
10 - Last digit should be 0
11 - (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 06 Jan 2016, 23:09
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 07 Jan 2016, 02:03
Bunuel wrote:
timothyhenman1 wrote:
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


Similar questions to practice:
if-the-number-x3458623y-is-divisible-by-88-what-is-the-134183.html
the-number-23a4534a01-is-divisible-by-11-how-many-values-134180.html

Hope it helps.



Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.

In our problem, 892,132,24x is divisible by 11

alternate sum from left to right
=> 8+2+3+4+x
=> 17+x
=> x=5 which is 22 divisible by 11

Answer E
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If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 07 Jan 2016, 02:20
1
umasarath52 wrote:


Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.

In our problem, 892,132,24x is divisible by 11

alternate sum from left to right
=> 8+2+3+4+x
=> 17+x
=> x=5 which is 22 divisible by 11

Answer E


Hi umasarath52,

You are missing one thing in the divisibility rule.
The rule says: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11

You missed subtracting the sum of other numbers.

To check this, try dividing 892,132,245 by 11. You will not have an integer.

Hop this helps!
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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New post 08 Jun 2016, 10:00
i just did long division withion 30-40 seconds was left with a remainder 1 with which you have to bring down the units digit x to divide the number by 11 and find out if it finally leaves a reminder, just clear enough that only a 1 brought down with the previous remainder 1 will make the last leg of division 11 / 11 hence 1 must be the last digit.
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Re: If the number 892,132,24x is divisible by 11, what must be the value  [#permalink]

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Re: If the number 892,132,24x is divisible by 11, what must be the value   [#permalink] 20 Nov 2019, 12:22

If the number 892,132,24x is divisible by 11, what must be the value

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