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Is the last digit of integer x2 – y2 a zero?
1) x – y is an integer divisible by 30
2) x + y is an integer divisible by 70
- 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
Is the last digit of integer x2 – y2 a zero?1) x – y is an...
Given: x^2−y^2=(x−y)(x+y) = integer x^2−y^2=(x−y)(x+y)=integer. Question is the units digit of this integer zero, which can be translated as is x^2−y^2 x^2−y^2 divisible by 10.
(1) x−y=30mx−y=30m (where mm is an integer) --> if xx and yy are integers, then x+y=integer x+y=integer and x^2−y^2=30m∗(x+y)=30m∗integer x^2−y^2=30m∗(x+y)=30m∗integer, which is divisible by 10 BUT if x=30.75x=30.75 and y=0.75y=0.75, then x^2−y^2=(x−y)(x+y)=30∗31.5=945=integer x^2−y^2=(x−y)(x+y)=30∗31.5=945=integer, which is not divisible by 10. Not sufficient.
(2) x+y=70nx+y=70n (where nn is an integer) --> if xx and yy are integers, then x−y=integer x−y=integer and x^2−y^2=(x−y) ∗ 70n=integer∗70n x^2−y^2=(x−y)∗70n=integer∗70n, which is divisible by 10 BUT if x=69.75x=69.75 and y=0.25y=0.25, then x^2−y^2=(x−y)(x+y)=69,5∗70=4865=integer x^2−y^2=(x−y)(x+y)=69,5∗70=4865=integer, which is not divisible by 10. Not sufficient.
(1)+(2) x^2−y^2=30m ∗ 70n=integer x^2−y^2 = 30m∗70n = integer, Which is divisible by 10. Sufficient.
Most Upvoted Answer
Is the last digit of integer x2 – y2 a zero?1) x – y is an...
It depends on the last digit of integer x.
If the last digit of x is 0, 1, 5, or 6, then the last digit of x^2 will also be 0, 1, 5, or 6, respectively.
If the last digit of x is 2, 3, 7, or 8, then the last digit of x^2 will be 4, 9, 9, or 4, respectively.
If the last digit of x is 4 or 9, then the last digit of x^2 will be 6 or 1, respectively.
Therefore, it is not possible to determine the last digit of x^2 without knowing the last digit of x.
If the last digit of x is 0, 1, 5, or 6, then the last digit of x^2 will also be 0, 1, 5, or 6, respectively.
If the last digit of x is 2, 3, 7, or 8, then the last digit of x^2 will be 4, 9, 9, or 4, respectively.
If the last digit of x is 4 or 9, then the last digit of x^2 will be 6 or 1, respectively.
Therefore, it is not possible to determine the last digit of x^2 without knowing the last digit of x.
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Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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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Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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 Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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 Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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?.
Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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 Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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 Is the last digit of integer x2 – y2 a zero?1) x – y is an integer divisible by 302) x + y is an integer divisible by 70a)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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