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Integer

by Veronica » Mon Sep 20, 2010 7:45 pm
If n is a positive integer, what is the remainder when (3^(8n+3)) + 2 is divided by 5?
a. 0; b.1; c. 2; d.3; e.4

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
a. 10; b.12; c.14; d.16; e.18

If x, y, and k are positive numbers such that (10x/(x+y)) + (20y/(x+y)) = k and if x < y, which of the following could be the vale of k?
a. 10; b.12; c.15; d.18; e.30

Please explain, thank you!
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by debmalya_dutta » Mon Sep 20, 2010 8:15 pm
If n is a positive integer, what is the remainder when (3^(8n+3)) + 2 is divided by 5?
a. 0; b.1; c. 2; d.3; e.4
let us find the unit's digit of 3^(8n+3)
let's simplify it by putting n=1
so , we have 3 ^ 11 ... the units digit of 3 ^ 11 is 7 ..... Now back to 3^(8n+3)) + 2 ...
we know the units digit of 3^(8n+3)) which is 7 ..adding 2 to 7 , we get the unit's digit of the expression 3^(8n+3)) + 2 which is 9 ....

so any number ending with 9 when divided by 5 will leave a remainder of 4
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by debmalya_dutta » Mon Sep 20, 2010 8:20 pm
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
a. 10; b.12; c.14; d.16; e.18
this is a tedious one ...
p = 1.2.3.4.5.6..............................30 which includes are multiples of 3 starting with 3 and ending in 30
Concentrate only on the multiples of 3

3
2*3
3*3
4*3
5*3
2*3*3
7*3
8*3
3*3*3
10 * 3
so p = 1.2.3.4.5.6..............................30
= 1.2.3.4.5.(2.3).7.8.(3.3).... (10.3)
Highest power of 3 in this is 3 ^14
So , C is our answer
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by debmalya_dutta » Mon Sep 20, 2010 8:25 pm
If x, y, and k are positive numbers such that (10x/(x+y)) + (20y/(x+y)) = k and if x < y, which of the following could be the vale of k?
a. 10; b.12; c.15; d.18; e.30
Refer this link.. Had some good discussion just a couple of days back
https://www.beatthegmat.com/quants-quest ... tml#298936
@Deb
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