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Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??
(1) The third of the five integers is a prime number. ?
(2) The second of the five integers is the square of an integer.
- 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 'A'. Can you explain this answer?
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Five consecutive positive integers are chosen at random. If the averag...
Solution:
Let the five consecutive positive integers be x, x+1, x+2, x+3, x+4.
Their average is (x+x+1+x+2+x+3+x+4)/5 = (5x+10)/5 = x+2
Given that the average is odd, x+2 must be odd, which implies x is odd.
We need to find the remainder when x+4 is divided by 4.
Statement 1: The third of the five integers is a prime number.
If the third integer is a prime number, it can only be 3 (as it is odd and not equal to 1). In this case, x+2 = (x+x+1+3+x+3)/5 = (3x+7)/5 is odd, which implies 3x+7 is odd, which in turn implies x is even (as odd+odd=even). This is a contradiction to our earlier conclusion that x is odd. Therefore, this statement alone is not sufficient to answer the question.
Statement 2: The second of the five integers is the square of an integer.
If the second integer is the square of an integer, it can only be 1 or 4. If it is 1, then the first integer is even, which is not possible as the five integers are consecutive. Therefore, the second integer must be 4. In this case, x+2 = (x+x+1+4+x+3)/5 = (3x+8)/5 is even, which implies 3x+8 is even, which in turn implies x is even (as even+even=even). Therefore, x+4 is even, and the remainder when it is divided by 4 is 0. This statement alone is sufficient to answer the question.
Hence, the correct answer is option A.
Let the five consecutive positive integers be x, x+1, x+2, x+3, x+4.
Their average is (x+x+1+x+2+x+3+x+4)/5 = (5x+10)/5 = x+2
Given that the average is odd, x+2 must be odd, which implies x is odd.
We need to find the remainder when x+4 is divided by 4.
Statement 1: The third of the five integers is a prime number.
If the third integer is a prime number, it can only be 3 (as it is odd and not equal to 1). In this case, x+2 = (x+x+1+3+x+3)/5 = (3x+7)/5 is odd, which implies 3x+7 is odd, which in turn implies x is even (as odd+odd=even). This is a contradiction to our earlier conclusion that x is odd. Therefore, this statement alone is not sufficient to answer the question.
Statement 2: The second of the five integers is the square of an integer.
If the second integer is the square of an integer, it can only be 1 or 4. If it is 1, then the first integer is even, which is not possible as the five integers are consecutive. Therefore, the second integer must be 4. In this case, x+2 = (x+x+1+4+x+3)/5 = (3x+8)/5 is even, which implies 3x+8 is even, which in turn implies x is even (as even+even=even). Therefore, x+4 is even, and the remainder when it is divided by 4 is 0. This statement alone is sufficient to answer the question.
Hence, the correct answer is option A.
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Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. Can you explain this answer?
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Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. 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 Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. Can you explain this answer?.
Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. 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 Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. Can you explain this answer?.
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ample number of questions to practice Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4??(1) The third of the five integers is a prime number. ?(2) The second of the five integers is the square of an integer.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 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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