Can somebody tell me what the most efficient way to solve this kind of DS GMAT questions ;
the question says , if the remainder of the division of (n-1)*(n+1) by 24 is r, what's the value of r ?
1- n is not divisible by 2
2- n is not divisible by3
I appologize if the question rose somewhere else here in this forum while,butI didn't see it.
Thanks
question from Gmatprep test1
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- jayhawk2001
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Not sure if this is the most efficient way but here goes...
1 - insufficient. Take n = 1 and n = 3 for example.
They yield remainders of 0 and 8 resp. No unique value. So rule out 1.
2 - insufficient. Take n = 1 and n = 2.
They yield remainders of 0 and 3 resp. No unique value. So, rule out 2
A number that is not divisible by 2 AND not divisible by 3 can be
written as n = 6x + 1 or n = 6x - 1
For n = 6x+1
(n-1)*(n+1) / 24
= 6x * (6x+2) / 24
= 12x * (x+1) / 24
We know that x*(x+1) will be even or 0, so the above equation will
always yield a remainder of 0.
Similarly for n=6x-1
(n-1)*(n+1) / 24
= (6x - 2)*6x
= 12x*(x-1) / 24
Again, x*x(-1) will be even or 0 and hence remainder r will be 0.
So, C looks like the correct answer.
On the actual GMAT, in the interest of time, it might be worthwhile
trying n = 1, 3, 5, 7, 9 etc. We can see that the remainder is 8 when n
is not divisible by 3 and remainder is 0 when n is divisible by 3 (for
all values n > 0). Using this pattern, I guess we can settle on C.
1 - insufficient. Take n = 1 and n = 3 for example.
They yield remainders of 0 and 8 resp. No unique value. So rule out 1.
2 - insufficient. Take n = 1 and n = 2.
They yield remainders of 0 and 3 resp. No unique value. So, rule out 2
A number that is not divisible by 2 AND not divisible by 3 can be
written as n = 6x + 1 or n = 6x - 1
For n = 6x+1
(n-1)*(n+1) / 24
= 6x * (6x+2) / 24
= 12x * (x+1) / 24
We know that x*(x+1) will be even or 0, so the above equation will
always yield a remainder of 0.
Similarly for n=6x-1
(n-1)*(n+1) / 24
= (6x - 2)*6x
= 12x*(x-1) / 24
Again, x*x(-1) will be even or 0 and hence remainder r will be 0.
So, C looks like the correct answer.
On the actual GMAT, in the interest of time, it might be worthwhile
trying n = 1, 3, 5, 7, 9 etc. We can see that the remainder is 8 when n
is not divisible by 3 and remainder is 0 when n is divisible by 3 (for
all values n > 0). Using this pattern, I guess we can settle on C.
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jayhawk2001, that is a wonderful explanation! Thank you. Gives us a valuable technique, we can use for similar questions.