Number Properties

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raju232007: Master | Next Rank: 500 Posts; Posts: 133; Joined: Sat Dec 29, 2007 2:43 am; Thanked: 12 times

by raju232007 » Mon Jan 25, 2010 2:10 am

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?

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Source: Beat The GMAT — Data Sufficiency | Mon Jan 25, 2010 2:10 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Jan 25, 2010 2:24 am

raju232007 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?

You cannot deduct one inequality from another. You can only add them as long as they have similar signs in the middle

-(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.

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raju232007: Master | Next Rank: 500 Posts; Posts: 133; Joined: Sat Dec 29, 2007 2:43 am; Thanked: 12 times

by raju232007 » Mon Jan 25, 2010 2:56 am

Thanks for your prompt response....But why can't -7x-7y<0 be multiplied by -1 on both sides to give 7x+7y>0?

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Jan 25, 2010 3:16 am

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?

You can do that and it is perfectly valid.

Always borrow money from a pessimist, he doesn't expect to be paid back.

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raju232007: Master | Next Rank: 500 Posts; Posts: 133; Joined: Sat Dec 29, 2007 2:43 am; Thanked: 12 times

by raju232007 » Mon Jan 25, 2010 3:25 am

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?

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Jan 25, 2010 3:31 am

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?

Only add operation is valid for inequalities ( Signs have to match)

(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.

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