The answer to this question has already been posted in this forum..But I am still not able to understand the explanation
If x and y are integers and x>0, is y>0?
1. 7x-2y>0
2. -y<x
The first statement says that 7x-2y>0........................(1)
The second statement can be rewritten as x+y>0..
Multiplying by 7 on both sides we get 7x+7y>0 ..........(2)
(1) - (2) gives -9y>0 .....From this equation we can clearly observe that y is negative..
So in my opinion the answer to this question should be C..
But the OA is E...Could someone point out where I am going wrong?
Number Properties
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 133
- Joined: Sat Dec 29, 2007 2:43 am
- Thanked: 12 times
- ajith
- Legendary Member
- Posts: 1275
- Joined: Thu Sep 21, 2006 11:13 pm
- Location: Arabian Sea
- Thanked: 125 times
- Followed by:2 members
You cannot deduct one inequality from another. You can only add them as long as they have similar signs in the middleraju232007 wrote:The answer to this question has already been posted in this forum..But I am still not able to understand the explanation
If x and y are integers and x>0, is y>0?
1. 7x-2y>0
2. -y<x
The first statement says that 7x-2y>0........................(1)
The second statement can be rewritten as x+y>0..
Multiplying by 7 on both sides we get 7x+7y>0 ..........(2)
(1) - (2) gives -9y>0 .....From this equation we can clearly observe that y is negative..
So in my opinion the answer to this question should be C..
But the OA is E...Could someone point out where I am going wrong?
-(2) gives -7x - 7y <0 ---(3) ( if you multiply an en equality by a negative number the sign changes)
Now the (1) and (3) cannot be added since one is a greater than and the other is a less than inequality
that's where you are going wrong
Last edited by ajith on Mon Jan 25, 2010 3:33 am, edited 1 time in total.
Always borrow money from a pessimist, he doesn't expect to be paid back.
-
- Master | Next Rank: 500 Posts
- Posts: 133
- Joined: Sat Dec 29, 2007 2:43 am
- Thanked: 12 times
Thanks for your prompt response....But why can't -7x-7y<0 be multiplied by -1 on both sides to give 7x+7y>0?
- ajith
- Legendary Member
- Posts: 1275
- Joined: Thu Sep 21, 2006 11:13 pm
- Location: Arabian Sea
- Thanked: 125 times
- Followed by:2 members
You can do that and it is perfectly valid.raju232007 wrote:Thanks for your prompt response....But why can't -7x-7y<0 be multiplied by -1 on both sides to give 7x+7y>0?
Always borrow money from a pessimist, he doesn't expect to be paid back.
-
- Master | Next Rank: 500 Posts
- Posts: 133
- Joined: Sat Dec 29, 2007 2:43 am
- Thanked: 12 times
I am sorry to if bother you again.....but then if 7x+7y>0 is fine then I can combine this equation with equation 1 (i.e 7x-2y>0) to conclude that -9y>0, so y should be negative...
That is
7x-2y>0..............(1)
7x+7y>0.............(2)
(1)-(2) => -9y>0
Can you tell me what's wrong in what I have done?
That is
7x-2y>0..............(1)
7x+7y>0.............(2)
(1)-(2) => -9y>0
Can you tell me what's wrong in what I have done?
- ajith
- Legendary Member
- Posts: 1275
- Joined: Thu Sep 21, 2006 11:13 pm
- Location: Arabian Sea
- Thanked: 125 times
- Followed by:2 members
Only add operation is valid for inequalities ( Signs have to match)raju232007 wrote:I am sorry to if bother you again.....but then if 7x+7y>0 is fine then I can combine this equation with equation 1 (i.e 7x-2y>0) to conclude that -9y>0, so y should be negative...
That is
7x-2y>0..............(1)
7x+7y>0.............(2)
(1)-(2) => -9y>0
Can you tell me what's wrong in what I have done?
(1) + (2) is valid operation since - inequalities have the same sign
(1) - (2) is not a valid operation (because it is nothing but (1) + (-(2)) and signs do not match there)
Further I will make it obvious by an example
say x = 1 and y =1
Follows (1) and (2)
since 5>0 and 14>0
Now if we follow your math
y<0 but y =1 which is greater than 0.
Always borrow money from a pessimist, he doesn't expect to be paid back.