Aptitude - Numbers - Discussion
Discussion Forum : 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 = ?
Answer: Option
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.
Discussion:
24 comments Page 2 of 3.
Shikhar said:
7 years ago
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.
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.
Rajesh guru said:
8 years ago
Thnks All.
Jenet said:
8 years ago
Explained well @Sangeetha. Keep up the good work.
Surabhi said:
8 years ago
Pleased explain it. I'm not able to understand this.
Vishnu Swamy said:
9 years ago
Excellent explanation, thank you very much @Sangeeta.
Rahul said:
9 years ago
2 can't be an answer. If we divide 65320 by 80 then the answer is 816.5.
Ramesh said:
10 years ago
Nothing, I understand please anyone explain clearly.
Sangeeta kumari said:
10 years ago
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.
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.
(1)
Xyz said:
1 decade ago
65320/80 = 816.5, 65360/80 = 817, so x = 6 & y = 0 => x+y = 6.
Swayze said:
1 decade ago
75 xy is divisible by 5 and 9 how to justify it need your help thanks.
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