inequality 2

[artstudent]

For the integers m,n,r, and s if m+n=250 and m>n is m-r>s-n?
1)250>r-s
2) m+r+s=375

Lets see multiple ways to do this.

[dodgeforgmat]

M+N = 250
M>N implies M is positive
When N is negative or zero, M >= 250 and N <= 0

When N is positive then M >= 126 0<N<=124 (since M greater than N, N cannot be greater than (250/2)-1)

Hence Range of M is any positive integer greater than 126


Is M-R > S-N
=> M+N > R+S
=> R+S < 250 (since M+N = 250:given)

Statement 1:
R-S > 250
Does not say anything about R+S
INSUFFICIENT

Statement 2:
M+R+S = 375
R+S = 375 - M
R+S = 375 - 126 = 249 (This is the Maximum value of R+S) => R+S is always less than 250

SUFFICIENT

IMO: B

[pemdas]

m=250-n and 250-n>n or 250>2n, 125>n
....m+n=250
Is m-r>s-n can be rephrased as m+n>s+r or 250>s+r?

st(1) 250>r-s is Not Sufficient as 250>s+r and we need to know s and r
st(2) m+r+s=375
m+n=250 and m>n is translated into m>250-m, 2m>250, m>125; m=375-r-s ... 375-r-s>125 ... 250>s+r
our question Is 250>s+r?, Sufficient


b

For the integers m,n,r, and s if m+n=250 and m>n is m-r>s-n?
1)250>r-s
2) m+r+s=375

Lets see multiple ways to do this.

[amit2k9]

question is asking if r+s < 250 ?

a not sufficient.

b r+s = k hence,

m+k = 375
also , adding n to both sides

250+k = 375 +n
thus, k-n = 125.

now m (min value) = 126 and n (max value) = 124 for m+n = 250.

thus 126+k = 375 meaning k= 249 thus < 250.

hence B is true.

[mirantdon]

+1 for B.
Considering the minimum value for m --> 126

Hence r+s < 250