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Aptitude - Problems on Numbers - Discussion

Discussion Forum : Problems on Numbers - Data Sufficiency 1 (Q.No. 2)
Problems on Numbers
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.

I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
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 3 of 3.
Suresh pal said:   6 years ago
Here statement 1 only is sufficient to answer the question, as we know that the difference of digits of two digits number is 9 is only in the case of 90.

So, the statement 1 is only true.
(3)
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.
(12)
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