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C
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Difficulty:
85%
(hard)
Question Stats:
40% (02:12) correct
60%
(02:43)
wrong
based on 48
sessions
History
Date
Time
Result
Not Attempted Yet
If x is an integer, is (9x^2 + 10)^2/5 an integer?
(1) x is a prime factor of 60
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient
e) Statements 1) and 2) TOGETHER are not sufficient
(1) x is a prime factor of 60
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient
e) Statements 1) and 2) TOGETHER are not sufficient
21 Nov 2023, 00:35
Kudos
Bookmarks
If x is an integer, is \(\frac{(9x^2 + 10)^2}{5}\) an integer?
What the question asks: Is \(9x^2+10\) divisible by 5.
Only possibility when x is a multiple of 5.
(1) x is a prime factor of 60
So x can be 2, 3 or 5.
Insufficient
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x could be any of many possible odd numbers.
1 or 5 when k is 0 or 5
7 or 11 when k is 1
13 or 17 when k is 2
and so on. (One less or 1 more than all multiples of 6)
Insufficient
Combined
x cannot be 2 and 3 as x=6k+1=(2*3)k+1 or (2*3)k+5
Only possibility is 5.
Sufficient
C
What the question asks: Is \(9x^2+10\) divisible by 5.
Only possibility when x is a multiple of 5.
(1) x is a prime factor of 60
So x can be 2, 3 or 5.
Insufficient
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x could be any of many possible odd numbers.
1 or 5 when k is 0 or 5
7 or 11 when k is 1
13 or 17 when k is 2
and so on. (One less or 1 more than all multiples of 6)
Insufficient
Combined
x cannot be 2 and 3 as x=6k+1=(2*3)k+1 or (2*3)k+5
Only possibility is 5.
Sufficient
C
22 Nov 2023, 03:35
Kudos
Bookmarks
Asked: If x is an integer, is (9x^2 + 10)^2/5 an integer?
(1) x is a prime factor of 60
x = 2, 3 or 5
Not Sufficient
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x = 1, 5, 7, 11, 13, 17
Not sufficient
(1) + (2)
(1) x is a prime factor of 60
x = 2, 3 or 5
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x = 1, 5, 7, 11, 13, 17
x = 5
Sufficient
IMO C
(1) x is a prime factor of 60
x = 2, 3 or 5
Not Sufficient
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x = 1, 5, 7, 11, 13, 17
Not sufficient
(1) + (2)
(1) x is a prime factor of 60
x = 2, 3 or 5
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x = 1, 5, 7, 11, 13, 17
x = 5
Sufficient
IMO C
