Is (x^2-y^2) divisible by 8?
1) x and y are even integers.
2) (x+y) is divisible by 8.
[spoiler] B/C....?[/spoiler]
source- gmatclub.
DS:b/C
This topic has expert replies
-
- Legendary Member
- Posts: 759
- Joined: Mon Apr 26, 2010 10:15 am
- Thanked: 85 times
- Followed by:3 members
hi i`ll try to handle with 2 st 1 is clearly insufficient
(2) (x+y)=8k where k is an integer
x=8k-y
x^2-y^2=(8k-y)^2-y^2=64k^2-16ky+y^2-y^2=64k^2-16ky=16(4k^2-ky) -divisible by 8
my pick for B
(2) (x+y)=8k where k is an integer
x=8k-y
x^2-y^2=(8k-y)^2-y^2=64k^2-16ky+y^2-y^2=64k^2-16ky=16(4k^2-ky) -divisible by 8
my pick for B
- shovan85
- Community Manager
- Posts: 991
- Joined: Thu Sep 23, 2010 6:19 am
- Location: Bangalore, India
- Thanked: 146 times
- Followed by:24 members
(x^2-y^2) = (x+y) * (x-y)anjaneiya wrote:Is (x^2-y^2) divisible by 8?
1) x and y are even integers.
2) (x+y) is divisible by 8.
[spoiler] B/C....?[/spoiler]
source- gmatclub.
1. x and y both even.
say x = 4, y = 2 then (x^2-y^2) = (x+y) * (x-y) = 12 not divisible by 8.
say x = 2, y = 0 then (x^2-y^2) = (x+y) * (x-y) = 4 not divisible by 8.
say x = 2, y = 2 then (x^2-y^2) = (x+y) * (x-y) = 0 divisible by 8.
Insufficient.
2. (x+y) is divisible by 8
Multiple anything with 8 is a multiple of 8. However, when x and y are not integers then it will not suffice.
Take this x = 5.2 and y = 3.8 then though x+y is div by 8, x-y is not.
Thus, insufficient.
Combine both, we will get definite integers for x and y. And any integer multiplication to a multiple of 8 is always div by 8.
IMO C
If the problem is Easy Respect it, if the problem is tough Attack it
- tomada
- Master | Next Rank: 500 Posts
- Posts: 406
- Joined: Mon Jan 25, 2010 11:36 am
- Location: Syracuse, NY
- Thanked: 23 times
- Followed by:4 members
- GMAT Score:740
My answer to this question = B. As a few people noted, Statement 1 is insufficient by itself since (6,2) yields a positive response while (6,4) yields a negative response.
Another way of writing X^2 - Y^2 = (X+Y)(X-Y)
Statement 2 says that (X+Y) is divisible by 8. So, (X+Y) is some multiple of 8. Regardless of the value of (X-Y), one of the factors of this product is 8. For instance, if (X+Y) = 16, the two factors of this product are 8 and 2*(X-Y).
Thus, X^2 - Y^2 is divisible by 8, and Statement 2 is sufficient on its own.
Another way of writing X^2 - Y^2 = (X+Y)(X-Y)
Statement 2 says that (X+Y) is divisible by 8. So, (X+Y) is some multiple of 8. Regardless of the value of (X-Y), one of the factors of this product is 8. For instance, if (X+Y) = 16, the two factors of this product are 8 and 2*(X-Y).
Thus, X^2 - Y^2 is divisible by 8, and Statement 2 is sufficient on its own.
I'm really old, but I'll never be too old to become more educated.
-
- Legendary Member
- Posts: 1337
- Joined: Sat Dec 27, 2008 6:29 pm
- Thanked: 127 times
- Followed by:10 members
x^2-y^2= (x+y)*(x-y)anjaneiya wrote:Is (x^2-y^2) divisible by 8?
1) x and y are even integers.
2) (x+y) is divisible by 8.
[spoiler] B/C....?[/spoiler]
source- gmatclub.
Statement (1) (x+y)*(x-y)/8 - ? either (x+y)*(x-y) or (x+y) and (x-y) must be divisible by 8. One possibility is to test with the consecutive even integers; this returns false about Statement (1) -Not sufficient
Statement (2) (x+y)*(x-y)/8 - ? (x+y)/8=i (integer) and 8i*(x-y)/8= i*(x - y) therefore regardless of x and y values we have a true statement - Yes the expression can be divided by 8. Statement (2) -Sufficient.
Answer B.
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
-
- GMAT Instructor
- Posts: 1302
- Joined: Mon Oct 19, 2009 2:13 pm
- Location: Toronto
- Thanked: 539 times
- Followed by:164 members
- GMAT Score:800
As shovan85 above points out, we don't know whether x and y are integers. x can be 5.2 while y is 2.8. Then, x + y is 8 but x - y is a non-integer.
If we muliply a non-integer by 8, is the result a multiple of 8?
If we muliply a non-integer by 8, is the result a multiple of 8?
Kaplan Teacher in Toronto