English and Logical Reasoning Prep Guide
- Exam
- English and Logical Reasoning Prep Guide
- Subject
- Logical Reasoning
- Chapter
- Data Sufficiency
English and Logical Reasoning Prep Guide · Logical Reasoning · Data Sufficiency
Directions: Each of the following consists of a question and some...
Directions: Each of the following consists of a question and some statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
A number contains 7 digits from 0 to 9 is written on a notebook such that a digit is not repeated in the number. Find the sum of hundreds and tens digits of the number?
Statement I:& The unit digit of the number is the smallest odd prime number. The difference between the tens digit and hundreds digits is 3, neither of the digits is composite. The number starts with 7.
Statement II:& The number contains three even digits. The tens digit of the number is the smallest even number. The sum of the thousands and hundreds digit is 8.
Statement I:& The unit digit of the number is the smallest odd prime number. The difference between the tens digit and hundreds digits is 3, neither of the digits is composite. The number starts with 7.
Statement II:& The number contains three even digits. The tens digit of the number is the smallest even number. The sum of the thousands and hundreds digit is 8.
Options
- AIf the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
- BIf the data in statement II alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
- CIf the data either in statement I alone or in statement II alone is sufficient to answer the question.
- DIf the data in both statement I and II together are not sufficient to answer the question.
Correct answer
A.
If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
Step-by-step solution
A number contains 7 digits from 0 to 9 is written on a notebook such that a digit is not repeated in the number.
Find the sum of hundreds and tens digits of the number?
Statement I:& The unit digit of the number is the smallest odd prime number. The difference between the tens digit and hundreds digits is 3, neither of the digits is composite. The number starts with 7.
Statement II:& The number contains three even digits. The tens digit of the number is the smallest even number. The sum of the thousands and hundreds digit is 8.
Checking statement I:
Find the sum of hundreds and tens digits of the number?
Statement I:& The unit digit of the number is the smallest odd prime number. The difference between the tens digit and hundreds digits is 3, neither of the digits is composite. The number starts with 7.
Statement II:& The number contains three even digits. The tens digit of the number is the smallest even number. The sum of the thousands and hundreds digit is 8.
Checking statement I:
The digits of the number would be from 0 to 9 and one digit is not repeated.
The smallest odd prime number is 3, so the number ends with 3 and starts with 7.
7_ _ _ _ _ 3
The numbers whose difference is 3 are − (5 - 2), ( 7 - 4), but both the digits should be prime, so the tens and hundreds digit would be 2 and 5 not necessarily in the same order.
Sum of hundreds and tens digit is 7.
The smallest odd prime number is 3, so the number ends with 3 and starts with 7.
7_ _ _ _ _ 3
The numbers whose difference is 3 are − (5 - 2), ( 7 - 4), but both the digits should be prime, so the tens and hundreds digit would be 2 and 5 not necessarily in the same order.
Sum of hundreds and tens digit is 7.
Hence data in statement I alone is sufficient.
Checking statement II:
The digits of the number would be from 0 to 9 and one digit is not repeated.
The smallest even number is 2, thus tens digit is 2.
_ _ _ _ _ 2 _
The digits whose sum is 8 are (0-8), (2-6) and (3,5), out of which (6-2) is an invalid combination as 2 is already placed as tens digit.
The thousands and hundreds digits could be 0- 8 or 3-5.
Hence data in statement II alone is not sufficient.
Hence data in statement I alone is necessary to answer the question.
Hence option A is correct.
Hence option A is correct.