Aptitude - Problems on Numbers - Discussion
Discussion Forum : Problems on Numbers - Data Sufficiency 1 (Q.No. 2)
Directions to Solve
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
- Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
- Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
- Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
2.
What is the two-digit number? | |
I. | The difference between the two digits is 9. |
II. | The sum of the digits is equal to the difference between the two digits. |
Answer: Option
Explanation:
Let the tens and unit digits be x and y respectively. Then,
I. x - y = 9.
II. x + y = x - y.
From I and II, we get x - y = 9 and x + y = 9.
On solving, we get x = 9 and y = 0.
Required number is 90.
Thus, both I and II are needed to get the answer.
Correct answer is (E).
Discussion:
22 comments Page 1 of 3.
Abhinav Tripathi said:
1 decade ago
Digit is only 0 to 9 and in this case the only two digit possible is 0 and 9 whose difference can be 9 and so option a is sufficient.
As 9-0 = 9. So order of two digit no is 90. But if difference is less than 9 than we require two equation.
For example if difference is 8 than it may be due to 9-1 or 8-0 hence if difference is 9 we require only option (a) and if difference is less than 9 than we require option(e).
Hence correct option for this question must be option(a).
Thanking you.
As 9-0 = 9. So order of two digit no is 90. But if difference is less than 9 than we require two equation.
For example if difference is 8 than it may be due to 9-1 or 8-0 hence if difference is 9 we require only option (a) and if difference is less than 9 than we require option(e).
Hence correct option for this question must be option(a).
Thanking you.
Sundar said:
1 decade ago
@All
How many of you accept that '09' also a 2-digit number ?
Since we have doubts that 90 and 09 both are 2-digit number, we cannot conclude that 90 is the required answer from statement I itself.
We have to mathematically prove it. So in the given explanation, statement II also used to prove it.
Hence the given answer Option E is correct.
[Note: Some times even accused will be released with benefit of doubt.]
How many of you accept that '09' also a 2-digit number ?
Since we have doubts that 90 and 09 both are 2-digit number, we cannot conclude that 90 is the required answer from statement I itself.
We have to mathematically prove it. So in the given explanation, statement II also used to prove it.
Hence the given answer Option E is correct.
[Note: Some times even accused will be released with benefit of doubt.]
Harsh said:
9 years ago
A should be the correct answer because the digits cannot be other than 0 and 9.
For either of the options.
Because a difference of 9 can only be produced when 9-0 are the digits you can try as many as combinations you want.
And 09 will be considered a single digit because if you are so stupid to consider 09 as a two digit then I can consider as a three digit or 4 digits etc by adding zeros in the beginning.
For either of the options.
Because a difference of 9 can only be produced when 9-0 are the digits you can try as many as combinations you want.
And 09 will be considered a single digit because if you are so stupid to consider 09 as a two digit then I can consider as a three digit or 4 digits etc by adding zeros in the beginning.
Gauravv said:
5 years ago
1 is sufficient because two-digit numbers with difference 9 must be 90 there is no other option.
and 2 alone is not sufficient because;
x + y = x - y
2y = 0
i.e. y must be 0 but here is a catch x can be any number so the number may be; 10,20,30,40,50,60,70,80 and 90.
So, the answer is 1 is sufficient.
and 2 alone is not sufficient because;
x + y = x - y
2y = 0
i.e. y must be 0 but here is a catch x can be any number so the number may be; 10,20,30,40,50,60,70,80 and 90.
So, the answer is 1 is sufficient.
(12)
V S S Ranganadh P said:
1 decade ago
In the question
The difference between the two digits is 9
only possible for 0 and 9
The possible ways are {(0,9)}
{(10,1),(11,2),...} this set is not possible for single sigit no.s
So, number should be 90 or 09
09=9( not a 2 digit number)
then 90 is the number.
Option I is sufficient
The difference between the two digits is 9
only possible for 0 and 9
The possible ways are {(0,9)}
{(10,1),(11,2),...} this set is not possible for single sigit no.s
So, number should be 90 or 09
09=9( not a 2 digit number)
then 90 is the number.
Option I is sufficient
Gaurav Bhansali said:
10 years ago
Tell me any other two digit number except 90 in which difference of the two digits is 9. So, I suppose only statement one is sufficient to answer the question. While second statement is applicable on 10, 20, 30, 40, 50 and so on, which makes it insufficient to answer the question.
Prasanth Mathew said:
1 decade ago
Either one is sufficient:
1. By logic: if diff bet 2 digits is 9 in a 2 digit number then one number is 0. and since its 2 digit number x = 9 and y = 0.
2. X + Y = X - Y
=> 2Y = 0
=> Y = 0 and X = 9
So any one can be used to find out that the number is 90.
1. By logic: if diff bet 2 digits is 9 in a 2 digit number then one number is 0. and since its 2 digit number x = 9 and y = 0.
2. X + Y = X - Y
=> 2Y = 0
=> Y = 0 and X = 9
So any one can be used to find out that the number is 90.
Hemanth Kothuru said:
10 years ago
In the question it is given that difference between two digits is 9. So it is possible with 9 and 0 only.
And if difference between digits is equal to sum of digits it can be possible with any multiple of 10. So option 1 is the answer.
And if difference between digits is equal to sum of digits it can be possible with any multiple of 10. So option 1 is the answer.
Ankur Khare said:
1 decade ago
Answer is obviously A.
If you are putting Zero at tens position in two digit number you are violating the permutation combinations reasoning. Through which probable solution will only have 1! or (1 factorial) solution. i.e.. 90.
If you are putting Zero at tens position in two digit number you are violating the permutation combinations reasoning. Through which probable solution will only have 1! or (1 factorial) solution. i.e.. 90.
Subendu Mondal said:
1 decade ago
For this particular problem through statement 1 we can recognize
the answer because only 9 and 0 is the two numbers whose difference can be 9. so statement 1 is alone sufficient to give answer is correct.
the answer because only 9 and 0 is the two numbers whose difference can be 9. so statement 1 is alone sufficient to give answer is correct.
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