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 2 of 3.
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.
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.
Baba said:
1 decade ago
You can reverse the subset of x and y as you have considered.
Statement I alone is enough.
Statement I alone is enough.
Tanujkumar said:
1 decade ago
How can you say x-y = 9? It could be y-x = 9 also then answer will be 09?
Sourabh said:
1 decade ago
In 2nd statement, we have no of ways like 10 whose sum and difference is equal, and 20, 30, 40.. 90 whose sum and diff is equal.
So we are not sure about the number. So State 1 alone is sufficient.
So we are not sure about the number. So State 1 alone is sufficient.
Kumail khurram said:
1 decade ago
From 1 we have 90 or 09 and 09 is not a two digit no. So no. Has to be 90. So 1 alone is sufficient.
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.
Gajanand said:
1 decade ago
My answer is the statement 1 is alone sufficient to give the answer.
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.]
Mukesh rai said:
1 decade ago
Here we have to find out the 2 digits no. whose difference is 9 and this is possible when one digit is 9 and other is 0
Here we have only option that the no. is 90
Here we have only option that the no. is 90
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