# Aptitude - Problems on Numbers - Discussion

### Discussion :: Problems on Numbers - Data Sufficiency 1 (Q.No.3)

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.

3.

 What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9. I. The number is multiple of 51. II. The sum of the digits a and b is 6.

 [A]. I alone sufficient while II alone not sufficient to answer [B]. II alone sufficient while I alone not sufficient to answer [C]. Either I or II alone sufficient to answer [D]. Both I and II are not sufficient to answer [E]. Both I and II are necessary to answer

Explanation:

From statement I:

A two digit number, greater than 9 and multiple of 51 should be 51 itself.

Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.

From statement II:

A two digit number, greater than 9 and sum of the digit is 6.

It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.

Thus, I alone give the answer while II alone not sufficient to answer.

 Bhargavi said: (Jun 4, 2015) 51 is divisible only by 3, hence 3+3=6, but it is not divisible by either 5, 2, 4, etc. So my view is we determine the answer by statement-II also.

 Yash said: (Nov 4, 2015) @Bhargavi. How 51 is divisible by 3?

 Murthy said: (Dec 10, 2015) According to statement 1, the number is a multiple of 51, hence it can be 17 and 51. According to statement 2 the number can be 15, 24, 36, 42, 51. Hence if we combine both the statements we will get 51 as the answer!

 Nilesh Tripathi said: (Mar 18, 2016) Multiple of a number means a number greater than that number(17 and 3 are factors of 51 not the multiple). So obviously 51 is the number who has the sum 6 and multiple of its own. Hence (A) alone is sufficient.

 Krishu said: (Jun 29, 2018) I. The number is multiple of 51. --> This statement gives the numbers as 51, 102, 153... and so on The question statement states the number is greater than 9, SO WE STILL CAN'T DETERMINE THE RESULT by I statement alone. II. The sum of the digits a and b is 6. This statement alone cannot determine the result too, as numbers can be 15, 24, 33, 42, 51, 60. When we combine the two results then we get only one answer that satisfies all the condition --> 51 : a no greater than 9, sum of the digits of the number is 6 and it is also a multiple of 51. also no other number matches the given description. SO THE FINAL ANSWER SHOULD BE 'E'

 Kaira said: (Jul 12, 2018) The answer is correct. Here is the solution: Since the number is greater than 9 and is of two digits, it must be between 10-99. Now, it is given that the number is a multiple of 51 AND is a double-digit number so OBVIOUSLY, it is 51 because the next multiple is 51x2=105 which is a 3 digit number. This leaves us with only ONE answer i.e 51. We do not need a second assumption. However, if you only consider the second assumption i.e a+b=6 then the value could be 15 or 24 or 33 and so on. Thus we cannot use the second assumption independently to figure out the number.