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.
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.
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
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
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.]
Gajanand said:
1 decade ago
My answer is the statement 1 is alone sufficient to give the answer.
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.
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.
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.
Tanujkumar said:
1 decade ago
How can you say x-y = 9? It could be y-x = 9 also then answer will be 09?
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.
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