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Aptitude - Problems on Numbers - Discussion

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

What is the number?

I. 

The sum of the two digits is 8. The ratio of the two digits is 1 : 3.

 II. 

The product of the two digit of a number is 12. The quotient of two digits is 3.

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 units digit be x and y respectively. Then,

 I. x + y = 8 and x = 1
y 3

I gives, 4y = 24       y = 6.

So, x + 6 = 8       x = 2.


II. xy = 12 and x = 3
y 1

II gives, x2 = 36       x = 6.

So, 3y = 6       y = 2.


Therefore, Either I or II alone sufficient to answer.

Discussion:
43 comments Page 3 of 5.
Nishant Kakar said:   8 years ago
Sir there no specific answer to the question as the set of solutions possible contains: (2, 6) or (6, 2) So the two solutions can't produce single element in the answer set. So the answer should be D.
Vira said:   7 years ago
According to me, the answer is both are not sufficient. Obviously, the exact no couldn't be found.
Sachin said:   1 decade ago
How we can say that x/y =3. That is true only if the remainder is 0. And in question it is not mention. So the answer should be A.
FARID said:   1 decade ago
I fully agree with Mr. Anubhav. What is the actual no. ?
Rahul said:   1 decade ago
Yes Anubhav is correct so answer will be D.
Abhijit said:   1 decade ago
I also feel that anubhav is correct.
Karthik said:   1 decade ago
How you get the number 24 there can you explain?
Kamaneeya Kalaga said:   1 decade ago
Actually I think the question is about whether we can find a number using the condition. So, whatever the answer is the main point is that we can find a number (26 or 62) using either I or II alone.

Hence, that could be the reason why the answer was option C.
Kamaneeya Kalaga said:   1 decade ago
Hi Karthik,

If you put x=y/3 in the equation, you get

y/3 + y = 8 ; then, 4y/3 = 8
Hence, 4y = 24

I hope you got it. Good luck.
Paranjoy said:   1 decade ago
Statement II. is not sufficient. It says "quotient of two digits is 3." Hence, we are not sure whether it is x/y or y/x.
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