Aptitude - Problems on Numbers - Discussion

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.


What is the two-digit number?


The difference between the two-digit number and the number formed by interchanging the digits is 27.


The difference between the two digits is 3.


The digit at unit's place is less than that at ten's place by 3.

[A]. I and II only
[B]. I and III only
[C]. All I, II and III
[D]. I, and either II or III
[E]. Even with all I, II and III, answer cannot be give.

Answer: Option E


Let the tens and units digit be x and y respectively.

  I. (10x + y) - (10y + x)       x - y = 3.

 II. x - y = 3.

III. x - y = 3.

Thus, even all the given three statements together do not give the answer.

Correct answer is (E).

Shibi said: (Jan 28, 2011)  
But we can say the answer will be 52 then how can we tell that we can't be able to get the answer with the clues.

Swapna said: (Feb 7, 2011)  
Yes. The answer is 52. And it can be solved with 1 & 3 statements only.

Anay said: (Apr 27, 2011)  
The answer can be 63 also so I guess there is enoug amiguity in the question itself.

Rekha said: (Oct 20, 2011)  
I m not able to understand the 1st statement.

Karthik said: (Jan 29, 2012)  
No, I think the answer is E. Because if you try to solve the statement 1 then you will end up with the same result as that of 2nd and 3rd statement. So you can't solve the problem.

Vineet Verma said: (Sep 3, 2012)  
You dont need to be genius to solve this,
41-14=27 and 4-1=3
52-25=27 and 5-2=3
63-36=27 and 6-3=3
74-47=27 and 7-4=3
85-58=27 and 8-5=3
96-69=27 and 9-6=3

Riya said: (Nov 28, 2012)  
But actually they are right because 2 of the data give similar information. So we cannot get the answer. Yes of course we can assume by hit and trial but cannot get the answer from given data.

Pavithra said: (Apr 18, 2013)  

In the first step why have they considered 10 in the equation (10x+y) - (10y-x) please share the information?

Divya said: (Jan 10, 2014)  

Just look at the first statement. It is the diff of the 2 digits and interchange of the digits is given as 27, not the given number and interchange is 27.

Suresh Maidaragi said: (Apr 25, 2014)  
I hope everyone can solve this, here 1st and 2nd or 1 and 3 statements are more than enough to find the two digit number.

Solution: Consider two digit number as xy lets take 1st and 2nd statements xy-yx=27 by trial and error we can take 9 as first digit and 6 as second digit now the number become 96 right so.

From statement 1 96-67=27 from statement 2 9-6=3 or we can assume 1st and 3rd statement from 3rd we assure that 96 follows. Therefore option D is correct.

Shweta said: (Aug 25, 2014)  
The explanation is not sufficient for me as I know there is no connection between any of the statement. Anyone can clarify it please.

Mridhula Joju said: (Sep 18, 2014)  
Even with the first statement we can get both the statements 2 & 3. And from the first statement itself we can get different numbers as the answer.

Afreen said: (Jan 21, 2015)  
What is the use of 3rd statement? Can anyone explain about it?

Kylin said: (May 8, 2018)  

Consider xy as number,
then according to 3 number it will be like
1) xy - yx=27
2) x - y=3
3) x>y

There are 10 digits 0-9.
So according to 2 second and third statement (x - y=3 and x>y).
x y xy-yx.
9 6 96-69 = 27
8 5 85-58=27
7 4 74-47=27
6 3 63-36=27
5 2 52-25=27
4 1 41-14=27.

Nagendra Singh said: (Sep 20, 2018)  
The correct answer is 2 option. 1 and 3 can give the answer of the question.

From statement 1
( 10x + y) - ( 10y + x ) = 27,
9( x-y) = 27,
x-y = 3.
From the 1st statement, we get the second statement so no need of a 2nd statement

3 statement:-
The unit place is less than 3 by tens place.

So we have the condition to check;
1, 4
2, 5
3, 6
4, 7
5, 8
6, 9
By checking all condition we found a number 52.

52 - 25 = 27.

The difference of digit is also 3.
Difference of unit's place and ten's is also 3

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