Aptitude - Problems on Numbers - Discussion
Discussion Forum : Problems on Numbers - Data Sufficiency 1 (Q.No. 1)
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. |
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 1 of 5.
Siddharth said:
7 years ago
I have a doubt, if we consider the first statement it says the sum of two digits is 8 and their ratio is 1:3, but it does not say whether the ratio is of units digit to tens digit or tens to units. So even if we get 2 and 6 the number can be either 26 or 62 even by considering only the first statement. In the solution, it has been assumed that the ratio is of tens to units digit. This seems wrong and the answer must be D.
(3)
Soukhin Roy said:
9 years ago
Both the statements are insufficient.
It is a 'what' type of question in DS. And in what type of question we should get one unique answer.
In statement 1 we don't know about digits in units and tens place so we will get two possible 2 digit numbers.
Problem with statement 2 is that it is mentioned that the quotient of the 2 digits is 3. Now the remainder may be or may not be 0. So we can't say that x/y =3.
It is a 'what' type of question in DS. And in what type of question we should get one unique answer.
In statement 1 we don't know about digits in units and tens place so we will get two possible 2 digit numbers.
Problem with statement 2 is that it is mentioned that the quotient of the 2 digits is 3. Now the remainder may be or may not be 0. So we can't say that x/y =3.
Suyash Parag Karnad said:
12 months ago
I think the Answer should be D because the order of the digits is not defined.
Condition 1:- Let x and y be the digits.
x + y = 8. Now for the ratio, it can be x : y = 1 : 3, or y : x = 1 : 3
So we have two answers, 26 and 62.
Condition 2:- Let digits be x and y.
x*y = 12. Again, x/y = 3 or y/x = 3 are the two cases.
Hence, we have two answers again, 62 or 26.
Including both of them is also not enough
Condition 1:- Let x and y be the digits.
x + y = 8. Now for the ratio, it can be x : y = 1 : 3, or y : x = 1 : 3
So we have two answers, 26 and 62.
Condition 2:- Let digits be x and y.
x*y = 12. Again, x/y = 3 or y/x = 3 are the two cases.
Hence, we have two answers again, 62 or 26.
Including both of them is also not enough
(8)
Guni said:
2 months ago
Since while specifying the ratio, the order in which the ratio is to be taken is not specified, it still poses a doubt of 26/62,
Same way for the second statement the numerator and denominator are not specified.
Both statements only tell us the digits are 2 and 6, but not in which place.
So, the answer should be D.
Same way for the second statement the numerator and denominator are not specified.
Both statements only tell us the digits are 2 and 6, but not in which place.
So, the answer should be D.
(2)
Vipul Tibrewal said:
1 decade ago
Although the first statement gives that the ratio is 1:3, it can be assumed that the first and second digit are in ration 1:3, however, the second statement is vague and doesn't provide the details of the position of digits.
The question may be asked as the sum of digits rather than the actual number.
The question may be asked as the sum of digits rather than the actual number.
Ch M P Prakas said:
1 decade ago
I think we can't decide whether it is 26 or 62 but we got a number as answer so it is right.
And Shyam Lohani hai Initially I got the same doubt check the two conditions in second part already xy=12 is given so the possibility of getting remainder in x/y doesn't exist. Hope you understand.
And Shyam Lohani hai Initially I got the same doubt check the two conditions in second part already xy=12 is given so the possibility of getting remainder in x/y doesn't exist. Hope you understand.
Rakesh Joshi said:
8 years ago
Here is asking what is the number. Hence in question, he wants to know the exact number. But the statement I and statement II not alone can find the unique number and be using both of the statement we again not uniquely find the exact number. Hence its answer must be D) Neither I nor II.
Aksh! said:
8 years ago
Option A should be the answer for this question.
As we can see from the 1st statement, the ratio is given according to the ten's and one's digits respectively. Therefore we can find the number, that is to say, 26.
But statement 2 alone is not sufficient as it may denote both 26/62.
As we can see from the 1st statement, the ratio is given according to the ten's and one's digits respectively. Therefore we can find the number, that is to say, 26.
But statement 2 alone is not sufficient as it may denote both 26/62.
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.
Hence, that could be the reason why the answer was option C.
Kavitha said:
1 decade ago
Hai @Divya.
They have given x*y=12 and x/y=3 in the second condition. So you have to use the condition. We cannot simply assume 12/3=4. If we use the condition x/y=3 we get x/3=y. Substitute in x*y=12. We get x*x=36 therefore x=6. Y=2. Hope you get it.
They have given x*y=12 and x/y=3 in the second condition. So you have to use the condition. We cannot simply assume 12/3=4. If we use the condition x/y=3 we get x/3=y. Substitute in x*y=12. We get x*x=36 therefore x=6. Y=2. Hope you get it.
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