BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

Answer

by EconomistGMATTutor » Sat Jan 13, 2018 8:41 am
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.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sun Jan 14, 2018 2:40 pm

TTT

by mariliatgd » Sun Jan 14, 2018 3:07 pm
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.
Top
Senior | Next Rank: 100 Posts
Posts: 82
Joined: Mon Jan 15, 2018 2:01 am

by DrMaths » Mon Jan 15, 2018 4:14 am
8 - 9 + 2 - 1 + 3 - 2 + 2 - 4 + x = 11n (because 11n always = sum of digits alternating + - + -, etc.)
so x = 11n + 1. When n = 0, then x = 1.
Top
Post new topic Post Reply
• Page 1 of 1