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06 May 2021, 08:30
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If a is an even integer and a/18 is an odd integer, which of the following is NOT an even integer?
A (a^2)/54
B (a^2)/12
C (a^2)/9
D (a^2)/6
E (a^2)/2
A (a^2)/54
B (a^2)/12
C (a^2)/9
D (a^2)/6
E (a^2)/2
hykhan
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06 May 2021, 08:43
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IMO B
use 18 since its the easiest number. (18 is even and 18/18 is an odd integer of 1)
A trick that helps me is that instead of writing 18^2/54, I write (18)(18)/54 which allows me to cancel out divisions faster
a) 18^2/54 = (18)(18)/54 = 18 *18/54 = 18 * 1/3 = 6
b) 18^2/12 = (18)(18)/12 = 18 * 18/12 = 18 * 3/2 = 27 - no need to test further
use 18 since its the easiest number. (18 is even and 18/18 is an odd integer of 1)
A trick that helps me is that instead of writing 18^2/54, I write (18)(18)/54 which allows me to cancel out divisions faster
a) 18^2/54 = (18)(18)/54 = 18 *18/54 = 18 * 1/3 = 6
b) 18^2/12 = (18)(18)/12 = 18 * 18/12 = 18 * 3/2 = 27 - no need to test further
06 May 2021, 09:56
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Since a is even then it must be divisible by 2. Further if a/ 18 is odd then it is clear that 'a' is exactly divisible by 2^1 and no more power of 2 divides 'a'.
That means we can write a = 2 * odd number.
Now a^2 can be written as 2^2 * odd number.
Now only option B contains 2^2 and therefore if a^2 is divided by option B it will yield an odd number.
Posted from my mobile device
That means we can write a = 2 * odd number.
Now a^2 can be written as 2^2 * odd number.
Now only option B contains 2^2 and therefore if a^2 is divided by option B it will yield an odd number.
Posted from my mobile device
