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:
23 comments Page 1 of 3.
Vishnu said:
1 decade ago
"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.
In the above statement why 13x should be divisible by 8. Shouldn't it be like 53x should be divisible by 8.
Martin said:
1 decade ago
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.
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:
1 decade ago
"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?
But by the test of divisibility value for x is 6.
But for what about 2?
Tanuja said:
1 decade ago
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:
1 decade ago
75 xy is divisible by 5 and 9 how to justify it need your help thanks.
Xyz said:
1 decade ago
65320/80 = 816.5, 65360/80 = 817, so x = 6 & y = 0 => x+y = 6.
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)
Ramesh said:
9 years ago
Nothing, I understand please anyone explain clearly.
Rahul said:
9 years ago
2 can't be an answer. If we divide 65320 by 80 then the answer is 816.5.
Vishnu Swamy said:
8 years ago
Excellent explanation, thank you very much @Sangeeta.
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