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31 Aug 2008, 19:39
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x is a positive integer ,is x divisible by 2?
1)\(x^3+x\) is divisible by 4
2)\(5x+4\)is divisible by 6
KINDLY SHARE THE METHOD OF SOLVING
1)\(x^3+x\) is divisible by 4
2)\(5x+4\)is divisible by 6
KINDLY SHARE THE METHOD OF SOLVING
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Updated on: 31 Aug 2008, 20:28
Originally posted by arjtryarjtry on 31 Aug 2008, 20:10.
Last edited by arjtryarjtry on 31 Aug 2008, 20:28, edited 1 time in total.
Last edited by arjtryarjtry on 31 Aug 2008, 20:28, edited 1 time in total.
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1) all given values of x whihc satisfy the given condition are even, so suff.
2) since only even nos. are divisible by 6, 5x+ 6 is even.
also, since even = even+ even, 5x= even or x=even, so divisible by 2. suff
1) all given values of x whihc satisfy the given condition are even, so suff.
2) since only even nos. are divisible by 6, 5x+ 6 is even.
also, since even = even+ even, 5x= even or x=even, so divisible by 2. suff
31 Aug 2008, 20:18
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spriya
1: (x^3+x) = 4k
x (x^2+1) = 4k, where k is an integer
either x or x^2+1 is divisible by 4. if x^2+1 were to divided by 4, x^2 must be odd. in that case, x is also odd. but square of any odd plus 1 cannot be a multiple of 4. for ex:
3^2+1 = 10, which is not divisible by 4.
5^2+1 = 26, which is not divisible by 4.
7^2+1 = 50, which is not divisible by 4.
9^2+1 = 81, which is not divisible by 4.
so x must be an even and also a multiple of 4. so suff...
2: 5x + 4 = 6m, where m is an integer
if 6 were to divide 5x+4 evenly, 5x+4 must be an even integer. in that case, 5x also be an even integer and eventually x is to an even integer.
so Suff.
D...
