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15 Jun 2020, 09:31
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (01:59) correct
62%
(02:14)
wrong
based on 178
sessions
History
Date
Time
Result
Not Attempted Yet
If n is an integer and n^2 + 45 equals to the square of an integer. How many value of n are possible?
A. 0
B. 1
C. 2
D. 3
E. 6
A. 0
B. 1
C. 2
D. 3
E. 6
15 Jun 2020, 09:38
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Bunuel
Asked: If n is an integer and n^2 + 45 equals to the square of an integer. How many value of n are possible?
Let n^2 + 45 = m^2
m^2 - n^2 = 45
(m+n)(m-n) = 3^2*5
Let m+n = 45; m-n=1 ; m=23 ; n = 22
Let m+n = 15; m-n=3 ; m=9; n=6
Let m+n=9; m-n = 5; m=7; n=2
n = {-22,-6,-2,2,6,22}; 6 values since both positive & negative integers are possible
IMO E
15 Jun 2020, 09:52
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Bunuel
Go by the options
49 and 81 are easily found.
so n=-2,2,6 & -6 and more
none of the option is 4
Only option E
E:)
15 Jun 2020, 11:50
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n^2 + 45 = a^2
=> a^2 - n^2 = 45
=> (a+n)(a-n) = 45 = 3^2*5
Now,
Some Number Theory
Total Number of ways a composite number can be written as a product of two factors = (Total Number of Factors)/2
Total Number of Factors of 45 = 3*2 = 6
=> Total Number of ways 45 can be written as a product of two factors = 6/2 = 3
=> Number of possible values of n = 6 (since negative values also have to be considered)
=> Answer: E
=> a^2 - n^2 = 45
=> (a+n)(a-n) = 45 = 3^2*5
Now,
Some Number Theory
Total Number of ways a composite number can be written as a product of two factors = (Total Number of Factors)/2
Total Number of Factors of 45 = 3*2 = 6
=> Total Number of ways 45 can be written as a product of two factors = 6/2 = 3
=> Number of possible values of n = 6 (since negative values also have to be considered)
=> Answer: E
