Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.106)

106. 

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

[A]. 2 or 6
[B]. 4
[C]. 4 or 8
[D]. 8
[E]. None of these

Answer: Option A

Explanation:

80 = 2 x 5 x 8

Since 653xy is divisible by 2 and 5 both, so y = 0.

Now, 653x is divisible by 8, so 13x should be divisible by 8.

This happens when x = 6.

x + y = (6 + 0) = 6.


Vishnu said: (Dec 25, 2013)  
"Now, 653x is divisible by 8, so 13x should be divisible by 8".

In the above statement why 13x should be divisible by 8. Shouldn't it be like 53x should be divisible by 8.

Martin said: (Jan 17, 2014)  
The answer is 6.

Let the number be 65300.

65300/80 = 816.25; this is not a whole number.

Try 816 x 80 = 65280 - not quite there so add 80.

65280+ 80 = 65360.
6 + 0 = 6.

Saurabh said: (Aug 18, 2014)  
"Now, 653x is divisible by 8, So 53x should be divisible by 8".

But by the test of divisibility value for x is 6.
But for what about 2?

Tanuja said: (Oct 17, 2014)  
I think we have to consider 3xy according to divisibility condition for 8 if why is 0 then 3x0 if we substitute 2 in place of x then 320/8 gets satisfied.

Swayze said: (Nov 6, 2014)  
75 xy is divisible by 5 and 9 how to justify it need your help thanks.

Xyz said: (Jan 18, 2015)  
65320/80 = 816.5, 65360/80 = 817, so x = 6 & y = 0 => x+y = 6.

Sangeeta Kumari said: (Mar 4, 2016)  
653xy.

80 = 2 * 5 * 8.

y = 0 (since 2*5 is a factor, so last digit should be zero).

Check from options now.

1) 2 or 6.

Rule: A number is divisible by 8 if last three digits are divisible by 8 i.e. 3xy.

Since y = 0.

3 * 0.

320 (if we put = 2).

320 is divisible by 80.

Therefore, x + y = 2 + 0.

Now, put x = 6.

Number becomes.

360.

Divide it by 8, it is divisible.

So, x + y = 6 + 0 = 6.

Check for the rest of options, they are not divisible when put.

Ramesh said: (Jul 10, 2016)  
Nothing, I understand please anyone explain clearly.

Rahul said: (Aug 28, 2016)  
2 can't be an answer. If we divide 65320 by 80 then the answer is 816.5.

Vishnu Swamy said: (Jun 6, 2017)  
Excellent explanation, thank you very much @Sangeeta.

Surabhi said: (Jun 25, 2018)  
Pleased explain it. I'm not able to understand this.

Jenet said: (Jul 5, 2018)  
Explained well @Sangeetha. Keep up the good work.

Rajesh Guru said: (Jul 5, 2018)  
Thnks All.

Shikhar said: (Oct 2, 2018)  
653xy is divisible by 80.
653xy=65300+10x+y.
We consider y=0 because it is divisible by 80.
Now,
653x is divisible by 8.
We divide 653 by 8 and we got remainder 5.
5x is now divisible by 8. We assume x as a number so 5x is divisible by 8.
Here we got 6 as x because 56 is a number which is divisible by the 8.

Raushan Pandey said: (Feb 7, 2019)  
Answer is 6.

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