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29 Jun 2020, 01:43
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:38) correct
28%
(01:39)
wrong
based on 253
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a prime number, is n − 1 equal to the square of an integer?
(1) n < 10
(2) n is a solution of x^2 − 2x − 35 = 0.
29 Jun 2020, 02:17
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Explanation:
Given: n is a prime number
Find: (n-1) is square of an integer
Statement 1: n<10
if n=5 , yes (n-1) is square of an integer
if n=2,3,7 No.
Not Sufficient.
Statement 2: x^2 − 2x − 35 = 0
(x-7)(x+5)=0
x=7,-5 ; n=7,-5
(n-1) = 7-1 = 6 ; No
(-5-1) = -6 ; No
Sufficient
IMO-B
Given: n is a prime number
Find: (n-1) is square of an integer
Statement 1: n<10
if n=5 , yes (n-1) is square of an integer
if n=2,3,7 No.
Not Sufficient.
Statement 2: x^2 − 2x − 35 = 0
(x-7)(x+5)=0
x=7,-5 ; n=7,-5
(n-1) = 7-1 = 6 ; No
(-5-1) = -6 ; No
Sufficient
IMO-B
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29 Jun 2020, 02:18
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If n is a prime number, is n − 1 equal to the square of an integer?
Solution : Key Highlight: Prime numbers are always positive
(1) n < 10
Prime number less than 10 = 2,3,5&7
where, 2-1 = 1 is a square of integer 1.
where, 3-1 = 2 is not a square of any integer.
where, 5-1 = 4 is a square of integer 2.
where, 7-1 = 6 is not a square of any integer.
(Not Sufficient)
(2) n is a solution of x^2 − 2x − 35 = 0.
x^2 − 7x + 5x − 35 = 0.
x(x - 7) + 5 (x − 7) = 0.
( X - 7 ) (X + 5)
x = 7 & -5
since x is a prime number
x is only 7
but X-1 = 6 which is NOT a square of any integer.
(Sufficient)
IMO B
Solution : Key Highlight: Prime numbers are always positive
(1) n < 10
Prime number less than 10 = 2,3,5&7
where, 2-1 = 1 is a square of integer 1.
where, 3-1 = 2 is not a square of any integer.
where, 5-1 = 4 is a square of integer 2.
where, 7-1 = 6 is not a square of any integer.
(Not Sufficient)
(2) n is a solution of x^2 − 2x − 35 = 0.
x^2 − 7x + 5x − 35 = 0.
x(x - 7) + 5 (x − 7) = 0.
( X - 7 ) (X + 5)
x = 7 & -5
since x is a prime number
x is only 7
but X-1 = 6 which is NOT a square of any integer.
(Sufficient)
IMO B
