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Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?
1) The range of the seven remainders is 6. ?
2) The seven numbers selected are consecutive integers. ?
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Seven different numbers are selected from the integers 1 to 100, and e...
Correct Answer :- b
Explanation : The trick here is to know that remainder is always non-negative integer less than divisor 0≤r<d0≤r<d, so in our case 0≤r<70≤r<7.
So the remainder upon division of any integer by 7 can be: 0, 1, 2, 3, 4, 5, or 6 (7 values).
(1) The range of the seven remainders is 6 --> if we pick 6 different multiples of 7 (all remainders 0) and the 7th number 6 (remainder 6) then the range would be 6 and the sum also 6. But if we pick 7 consecutive integers then we'll have all possible remainders: 0, 1, 2, 3, 4, 5, and 6 and their sum will be 21. Not sufficient.
(2) The seven numbers selected are consecutive integers --> ANY 7 consecutive integers will give us all remainders possible: 0, 1, 2, 3, 4, 5, and 6. It does not matter what the starting integer will be: if it's say 11 then the remainder of 7 consecutive integers from 11 divided by 7 will be: 4, 5, 6, 0, 1, 2, and 3 and if starting number is say 14 then the remainder of 7 consecutive integers from 14 divided by 7 will be: 0, 1, 2, 3, 4, 5 and 6. So in any case sum=0+1+2+3+4+5+6=21. Sufficient.
Most Upvoted Answer
Seven different numbers are selected from the integers 1 to 100, and e...
Explanation:
Let's consider both statements one by one.
Statement 1: The range of the seven remainders is 6.
As there are only 7 numbers selected, the range (maximum remainder - minimum remainder) of the remainders cannot be more than 6. Therefore, this statement alone is sufficient to answer the question.
Statement 2: The seven numbers selected are consecutive integers.
If the seven numbers selected are consecutive integers, their remainders when divided by 7 will be 1, 2, 3, 4, 5, 6, and 0 (in some order). The sum of the remainders will be 21, which is a fixed value. Therefore, this statement also alone is sufficient to answer the question.
Hence, either statement 1 or statement 2 alone can answer the question, which means option 'B' is the correct answer.
Let's consider both statements one by one.
Statement 1: The range of the seven remainders is 6.
As there are only 7 numbers selected, the range (maximum remainder - minimum remainder) of the remainders cannot be more than 6. Therefore, this statement alone is sufficient to answer the question.
Statement 2: The seven numbers selected are consecutive integers.
If the seven numbers selected are consecutive integers, their remainders when divided by 7 will be 1, 2, 3, 4, 5, 6, and 0 (in some order). The sum of the remainders will be 21, which is a fixed value. Therefore, this statement also alone is sufficient to answer the question.
Hence, either statement 1 or statement 2 alone can answer the question, which means option 'B' is the correct answer.
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Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?
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Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?.
Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?.
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Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?1) The range of the seven remainders is 6. ?2) The seven numbers selected are consecutive integers. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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