Aptitude - Problems on Numbers - Discussion

6. 

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

[A]. 69
[B]. 78
[C]. 96
[D]. Cannot be determined
[E]. None of these

Answer: Option D

Explanation:

Let the ten's digit be x and unit's digit be y.

Then, x + y = 15 and x - y = 3   or   y - x = 3.

Solving x + y = 15   and   x - y = 3, we get: x = 9, y = 6.

Solving x + y = 15   and   y - x = 3, we get: x = 6, y = 9.

So, the number is either 96 or 69.

Hence, the number cannot be determined.


Dominic said: (Jul 29, 2011)  
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.

Sundar said: (Jun 13, 2012)  
@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.

Ramesh said: (Jun 13, 2012)  
I agree with Sundar.

Moola V Reddy said: (Jun 26, 2012)  
I agree with Dominic
always read the question carefully
1.sum of the two digits
2.difference between them
sundar said good example of difference
but there is no sum

Sally said: (Mar 10, 2013)  
Could somebody explain why we are not taking the tens digit as 10x and the ones digit as y, Like it was done in the previous questions?

Mehran said: (Aug 16, 2013)  
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.

S Vishnu Vardhan said: (May 24, 2014)  
Could somebody explain why we are not taking the tens digit as 10x and the ones digit as y, Like it was done in the previous questions?

Ajay said: (Aug 22, 2014)  
Please explain why we are not taking the tens digit as 10x and the ones digit as y, Like it was done in the previous questions?

Balu said: (Oct 26, 2014)  
Please why we not take tens digit as 10x and unit digit as y. Please explain as it taken in previous question.

Sudeshna said: (Nov 2, 2014)  
If we take the tens digit as 10x then also we will get the value of 10x = 9 and y = 6

So we can easily write the answer as 96 as 9-6 gives 3 and 6-9 gives -3!

So the answer can be determined.

Farah said: (Nov 18, 2014)  
I don't understand the technique used guide me.

Prince said: (Jul 26, 2015)  
Dominic answer is correct.

Vicky said: (Aug 10, 2015)  
I agree with you @Sundar. But if one of the option (69 or 96) is present in option then answer can be determined.

Cannot be determined case exists when both of the options are present and we are unable to decide among them.

Reetu said: (Sep 16, 2015)  
What is the correct answer?

Jayesh said: (May 22, 2016)  
x + y = 15.
x - y = 03.
- + - (Changing signs).
----------
2y = 12.
----------

i.e y = 6 (unit place).

Substitute the value of y.

x + y = 15.
So, x + 6=15.
x = 15 - 6.
x =9 (tens place).

Then assume it as 96 and it is the correct one.

Amrutha Siva said: (Jun 8, 2016)  
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).

Devi said: (Jun 30, 2016)  
Please, anyone tell me the correct answer to this problem.

Rabiul said: (Aug 6, 2016)  
You are correct @Dominic.

Md Jahangir Alam said: (Nov 26, 2016)  
Right answer should be 69. Because when asked about difference we should subtract tenth digit from unit digit. So, answer should be 69.

Jagdish said: (Jan 13, 2017)  
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.

Dipak said: (Feb 20, 2017)  
Agree @Jagdish.

Maggie said: (Apr 3, 2017)  
Answer should be 96.

Since 6-9=-3 and 9-6=3.

Pooja P Kumar said: (Apr 17, 2017)  
I Strongly agree @Sundar. That's absolutely correct.

Naina said: (May 4, 2017)  
Hi,

Can anyone explain, why we didn't take (10x+y) and (10x-y)?

Rocky said: (Jul 13, 2017)  
We can't take (10x+y) and (10x-y). Because the question is given that the sum of the digits of a two - digit number.

Exam: a two digit number=98, then sum of the digits 9 and 8=9+8, difference of the digits 9 and 8=9-8.

Vicky said: (Nov 19, 2017)  
I agree @Dominic.

96 is the correct answer.

Vijay said: (Jun 23, 2018)  
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.

Manikandan said: (Jul 4, 2018)  
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.

Joe said: (Jul 23, 2018)  
Yes, 96 is the correct Answer.

Anaga said: (Aug 29, 2018)  
(a+b)=(b+a).
(a-b)!=(b-a).

solution:
a+b=15
a-b=3
______
a=9,b=6 i.e ab=96.

b+a=15
b-a=3
______
b=9,a=6 i.e ab=69.

As both the options are correct and present in the solution we cannot determine the correct answer.

Muhammadkhan said: (Apr 23, 2019)  
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.

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