Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.16)

16. 

If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

[A].
[B]. 1
[C]. 2
[D]. None of these

Answer: Option C

Explanation:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.

  x = 2.


Vikas said: (Aug 5, 2010)  
Why we are adding the given all digits ?

Suresh said: (Aug 20, 2010)  
How can we divide (22+x) by 3 ?

Ramakrishna said: (Sep 22, 2010)  
Not understanding me explain me properly.

Priyanka P. said: (Nov 30, 2010)  
hi..
the rule for division for 3 is the total of the given number should be divided by 3..
so when add 517x324=22 which can't be divided by 3, so we have to add 2, to make it dividable by 3.

after adding 2 it becomes 24 which can be divided by 3.

hope it helps u..

Paavani said: (Dec 17, 2010)  
I can't understand anyones explaination. If any one got this sum means please explain it clearly.

Janu said: (Dec 29, 2010)  
Hi @Pavani..

If a number(for example take xyzpqr) is divisible by 3, then the sum(x+y+z+p+q+r) is also divisible by 3 and vice versa..

ex: 243 is divisible by 3
2+4+3=9 is also divisible by 3..

So if u want to check dat a number is divisible by 3 then it is enough to see whether the sum of digits in the number is divisible by 3..

Sonakshi said: (Mar 7, 2011)  
Hi Janu! can we set this formula with every number?

Jay said: (Jun 3, 2011)  
Let x
and chosen number form option
and 22 + 2 = 24
it.s divided by 8 so answer is 2

Nikitha said: (Aug 19, 2011)  
Hi paavani..

Principle: If a number is divisible by 3 means, sum of the digits also divisible by 3.

For eg: take 12. we know that 12 is divisible by 3
sum of digits i.e 1+2 = 3 ,3 is divisible by 3.

First u clear about this?

We cum to problem then..
517*324 is completely divisible by 3
so sum of the digits also divisible by 3.

Then, 5+1+7+x+3+2+4 = 22+x

We hav given the options 0, 1 , 2

If x=0, sum= x+22= 0+22 = 22 is not divisible by 3
If x=1, Sum =x+22 = 1+22 = 23 is not divisible by 3
If x=2, Sum =x+22 = 2+22 = 24 is divisible by 3
So answer is 2

Hope you understand this..

Divya said: (Feb 18, 2012)  
How can we divide (22+x) by 3 ?

Ram said: (Jul 29, 2012)  
Will this be applicable for all the numbers or only for 3.

Abhi said: (Aug 10, 2012)  
@Divya.

We don't divide (22+x) by 3, it is an equation form. It means what you add in 22 so it can be divided by 3.

Ex

=> 22+x/3.

=> If we assume smallest number 0, 1 then we got sum is 22, 23 which is not divided by 3, so we add 3(x) , and we get 24 which is divisible by 3.

Hope you understand.

Pavan said: (Feb 22, 2013)  
@Ram, Sonakshi.

The adding of digits to check divisibility can be done only for 3 which is rule for test of divisibility for 3.

Similarly,To check divisibility of 9 the sum of digits should be 9.

Ex: 45 => 4+5=9 . So 45 is divisible by 9.

Each digit has its own Divisibility rule to check whether it exactly divides the given or not.

Vidyadhar said: (Mar 26, 2013)  
(5 + 1 + 7 + x + 3 + 2 + 4)
=22+x means
22/3 Remain 1
Then
3-1 = 2
Answer is 2

Krish said: (Sep 5, 2014)  
We can't understand clearly give me a correct notes.

Prajith said: (Oct 25, 2014)  
Is this method is only applicable when the divisor is 3?

Sudharshan said: (Jan 19, 2015)  
Can you send anybody divisible rules for remaining numbers 7, 6, 8?

Nithya said: (Aug 4, 2015)  
517*324 its divided by 3.

5+1+7+X+3+2+4 = 22+X.

X = 0, 1, 2, 3, .

22+0 = 22. Its not divided by three.

22+1 = 23. Its not divided by three.

22+2 = 24(8*3) = 24 is divided by three.

So, the x value is 2. The two will be added. So the number is divided by three. So the answer is three.

Shailu said: (Oct 24, 2015)  
Just all see @Nikitha comment she describes it well.

Ramesh Nigam said: (Dec 25, 2015)  
Can we apply this trick on all numbers, or its just applicable on number 3?

Shiva said: (Feb 22, 2016)  
5 + 1 + 7 + x + 3 + 2 + 4 = 22.

22 + 3 - x = 24.

24/12 = 2.

Pooja said: (Jul 5, 2016)  
It's quite simple. Consider * as x and add all the numbers which will become (22+x). Now choose the number from options one by one and put in place of x and then try to divide it by 3. As I put the first option in place of x = (22+2) = 24 which is divided by 3.

Pravas said: (Jul 8, 2016)  
Simple method-->divide the left-hand side number by 3, the remainder will be 1, then divide RHS number by 3 the remainder will be 0 as the number is divided by 3 so, place 2 before remainder 1, it will be 21 and divide by 3. That's solved.

Ex: 517/3 = 1 (remainder) * 324/3 = 0, So place 2 before 1 (remainder) = 21/3 = 7 (all are divided).

Kamal said: (Jul 29, 2016)  
Not understand the solution, please someone help me.

Durga said: (Aug 11, 2016)  
Thanks, @Nikitha.

Ramana said: (Aug 26, 2016)  
How it comes 22+ x? Please explain it.

Meghana said: (Sep 22, 2016)  
I am not getting this, please explain properly.

Subha said: (Oct 21, 2016)  
You gave the best explanation @Nikitha.

@All. Please refer Nikitha's answer you will understand the solution.

Balaji Psg said: (Oct 25, 2016)  
Thank you @Nikitha I can understand now.

Praveengolla said: (Nov 18, 2016)  
Thank you @Nikitha and @Pavan.

Aravind said: (Feb 4, 2017)  
456*85 divisible by 3. Find the smallest whole digit number.

A. 10 b. 84 c. 12 d. 21.

Give me the answer of this question.

Phuntsho Dorji said: (Mar 17, 2017)  
Why using addition symbol instead of multiplication?

Please anyone explain to me.

Vishnu said: (Jun 5, 2017)  
Good, thanks @Nikitha.

Saravanan said: (Jun 23, 2017)  
@Aravind
456*85.
1. 4+5+6+x+8+5=28+x
2. 28+10(A is given option )=38/3=12.66 ஃ A is No
3. 28+84=112/3=37.333. No
4. 28+12=/3=13.33. No
5.28+21=16.33. No

Ans: None of those

But.
28+2=30/3=10. Ans is 2.

Fufh said: (Nov 11, 2017)  
But we can add all numbers.

Dev said: (Mar 6, 2018)  
Let the two numbers be a and b(a>b)
So A. T. Q
a-b=1365-----> [ eq no(1)]
Also;
b)a (6
- 6b
_____
15
______

Therefore;
From above we can say
a-6b=15-----> [eq no(2)]
Solving both equations we get;
b= 270[as per required].

Thanks.

Debashish said: (Aug 19, 2018)  
According to you guys if a number is divisible by another number then sum of its all digits also divisible. But it's not true in all cases.

e.g. The number is 625 which is divisible by 5. But if we add all its digits 6+2+5=13 which is not divisible by 5.

So this principle is wrong.

Mridul said: (Sep 11, 2018)  
@All.

The rule which one is applied here is only applicable for 3, not for 4 or 5 etc.

Surya said: (Sep 18, 2018)  
Well done @Nikitha.

Manu said: (Feb 12, 2019)  
Thank you @Nithya.

Ann Mary said: (Sep 15, 2019)  
Thanks @Nikitha.

Ruhi said: (Sep 27, 2019)  
The answer is 1.

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