Aptitude - Problems on Numbers - Discussion

Let the two-digit number be( 10x + y ), where ( x ) is the tens digit and ( y) is the unit digit.

We are given two conditions:
1. The sum of the digits is 15: [ x + y = 15 ]
2. The difference between the digits is 3: [ x - y = 3]

Now, we can solve these two equations simultaneously:

From the second equation,
x = y + 3

Substitute this value of ( x ) into the first equation:
(y + 3) + y = 15.
2y + 3 = 15.
2y = 12.
Then, y = 6.

Now substitute y = 6 into ( x = y + 3 ):
x = 6 + 3 = 9

Thus, the two-digit number is ( 10x + y = 10(9) + 6 = 96).

The two-digit number is 96.

Good morning friends.

Let the numbers X and Y
(1).X+Y = 15.
(2).X-Y = 3.

From equation (1)
X+Y = 15
Y = 15 -X .

Adding equation (1)and (2)
We get --- X - ( 15 - x) = 3.
When we solve this we get X = 9 and Y = 6.

BUT
When we solve another method.
Let the numbers X and Y.
(1).X+Y = 15.
(2).X-Y = 3.

From equation (1).
X + Y = 15.
X = 15 - Y.

Adding equation (1)and (2).
We get --- (15 - Y) - Y = 3.
When we solve this we get X = 6 and Y = 9.
So, the answer is either 96 or 69.

So, here the answer is cannot be determined.
Thanks.

See if the unit place is greater than the tens place the given answer is the correct.

Imagine the number 78. Here, 8 - 7 is 1, but 7 - 8 is - 1 also 7 + 8 is also 15 so the given answer is correct.

Here they are talking about the values of the digit so we take the only 7 = x and not 10x = 70.

I hope this clarifies the queries.

It can be either way around so it cannot be determined.

For example if we take 87 as the number then 8 - 7 = 1 and again 7 - 8 = 1 also 1 again 7 = 8 is 15 satisfying the (x + y) but not (x - y).

@Dominic

You are wrong. The given answer is correct.

I want to ask a question to you.

Assume your height is 165 cm and your friend's height is 170 cm.

Now tell me what is the height-difference between you and your friend?

Is it 5 cm or -5cm ?

We usually write difference between x and y as

X ~ Y NOT as X - Y.

Hence the given answer 'Cannot be determined' is correct.

If the question is: The sum of two digits is 15 and the difference between the ten's digit and unit's digit is 3. Then the answer would be 96.

But the question given is simply: the difference between the digits is 3. He didn't said about the position of the digits.

So the given answer is correct. It cannot be determined. The answer can be 69 or 96.

Assumed Number = XY.

X-Y = 15----- (i)

X+Y = 3 ------ (ii)

By solving (i)&(ii) we reach at;

X = 9 & Y = 6.

So, Assumed Number is 96,

Which satisfy both equations (i) & (ii).

If we take 69 that is not appropriate because in Equation (ii).

It comes with negative value of -3.

So, correct and answer is 96 that is determined here.

Let tens digit is = x.
And unit digit is = y.

Here x+y=15 ------> 1
x-y = 3 ------> 2

From two:

x=3+y put it in 1 we will get y = 6.
Now put y in equation 1 we get x = 9.
As x is ten digit and y is unit so, 10 * x +y = 10 * 9 + 6 = 96.

So 96 is the correct answer.

If we take 69 as answer.

Sum becomes:6+9=15.

But difference become: 6-9=-3.

But from the question, the sum should be 15 and the difference 3, not -3. On this note, I strongly believe that, the correct answer is 96, because.

Sum: 9+6=15,

And difference: 9-6=3.

We use 10x only if we want to represent the whole number. For example, if x=9, y=4, we cannot write x+y because the answer will be 13, but we must write 10x+y = 90+4 =94.

But here we are referring to only the digit in ten's place which is 9 for example.

I don't agree with this solution this is because if we take the number as 69 then,

6+9=15 which is said to be as correct but on the other case 6-9=-3 but in the question it is given the resultant as 3. Therefore the correct solution for this will be 96.