# Problems on Numbers Part 2

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.
 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:
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.
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.
 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:
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.
 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.

Directions to Solve
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
1.
 What is the two-digit number? I. The difference between the two-digit number and the number formed by interchanging the digits is 27. II. The difference between the two digits is 3. III. The digit at unit's place is less than that at ten's place by 3.
 A. I and II only B. I and III only C. All I, II and III D. I, and either II or III E. Even with all I, II and III, answer cannot be give.
Explanation:
Let the tens and units digit be x and y respectively.
I. (10x + y) - (10y + x)        x - y = 3.
II. x - y = 3.
III. x - y = 3.
Thus, even all the given three statements together do not give the answer.
Correct answer is (E).
2.
 What is the two-digit number? I. Sum of the digits is 7. II. Difference between the number and the number obtained by interchanging the digits is 9. III. Digit in the ten's place is bigger than the digit in the unit's place by 1.
 A. I and II only B. II and III only C. I and III only D. All I, II and III E. None of these