Exercise :: Problems on Numbers  Data Sufficiency 1
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 Problems on Numbers  Data Sufficiency 1
 Problems on Numbers  Data Sufficiency 2
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. 


Answer: Option C Explanation: Let the tens and units digit be x and y respectively. Then,
I gives, 4y = 24 y = 6. So, x + 6 = 8 x = 2.
II gives, x^{2} = 36 x = 6. So, 3y = 6 y = 2. Therefore, Either I or II alone sufficient to answer. 
2. 


Answer: Option E 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). 
3. 


Answer: Option A 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. 