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.
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)
Priyesh Tiwari said:
5 years ago
The Answer will be 6.
Question is saying the number is divisible by 80, which means it will come in the table of 80.
So now, Let the number be 65300.
65300 ÷ 80 = 816.25, this is not a perfect multiple, but here we get that our number is more than the multiple of;
816 * 80 i.e. 65280.
So now, we will go for a next.multiple.
817 * 80 = 65360.
So here is the number we were finding out!
X = 6.
Y = 0.
X+Y = 6+0 = 6.
Question is saying the number is divisible by 80, which means it will come in the table of 80.
So now, Let the number be 65300.
65300 ÷ 80 = 816.25, this is not a perfect multiple, but here we get that our number is more than the multiple of;
816 * 80 i.e. 65280.
So now, we will go for a next.multiple.
817 * 80 = 65360.
So here is the number we were finding out!
X = 6.
Y = 0.
X+Y = 6+0 = 6.
(5)
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.
Subas said:
4 years ago
Its simple guys,
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.
Here why 13x divide 65 by 8 we have 1 remainder so we need to consider 1 also so 13x
This happens when x = 6.
x + y = (6 + 0) = 6.
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.
Here why 13x divide 65 by 8 we have 1 remainder so we need to consider 1 also so 13x
This happens when x = 6.
x + y = (6 + 0) = 6.
(3)
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.
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.
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.
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?
Ashia said:
4 years ago
But how is the answer both 2 and 6?
It should only be 6 cuz if we divide 80 with 65320, we get 816.5.
It should only be 6 cuz if we divide 80 with 65320, we get 816.5.
(1)
Rahul said:
9 years ago
2 can't be an answer. If we divide 65320 by 80 then the answer is 816.5.
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