If x = 8 and y

Question

If  x \geq 8  and  y \leq 3 , then it must be true that

(A)  x + y \geq 5

(B)  x + y \leq 11

(C)  x - y \geq 5

(D)  x - y \leq 5

(E)  x - y \leq 11

chetan2u · Answer

x \geq 8  and  y \leq 3 
Multiply the same sides of inequalities..
 x+3 \geq 8+y ..... x - y \geq 5

OR

(I) x \geq 8  and 
(II)  y \leq 3 .. Multiply by '-' and change the INEQUALITY sign, so  -y \geq -3

Now we can add same sides of inequality..  x +(-y)\geq 8+(-3)........x -y\geq 8-3.........x -y\geq 5

C

bM22 · Answer

Hi Bunuel,

Could you explain the solution and the correct answer to this question as I found this question in 2 different posts and with different answers. It would be of great help. I am posting the link to the same other in a different thread, with OA as D and for one the OA is C.

https://gmatclub.com/forum/if-x-8-and-y ... fl=similar

Please explain.
Thanks.

chetan2u · Answer

The inequality signs have been reversed in both questions. One says x<=8 & c>=3 and other Says x>=8 & x<=3

preetamsaha · Answer

if a>b and c and <) --> a−c>b−d (take the sign of the inequality you subtract from). Example: 3<4 and 5>1 --> 3−5<4−1 here, x≥8 and y≤3 or,x−y≥5 (subtracting ) correct answer C

bM22 · Answer

Hi Bunuel,
 Thank you so much, I overlooked. Apologies.

Great1stan · Answer

My approach was as followed...
Rewrite exactions as
8≤x
y≤3

Then add the exactions (top-down approach)
thus..
8+y≤x+3
subtract y and 3 from both sides 
thus
5≤x-y

answer C

Is this an acceptable approach? if Not please explain why this can be an issue in the future

gurmukh · Answer

x>=8 ----(1)
y<=3
-y>=-3 -----(2)
Adding (1) and (2)
x-y>=5
Option C is the answer

Posted from my mobile device

js17 · Answer

x≥8 and y≤3
Add the same sides of inequalities
x+3≥8+y
x−y≥5

If x >= 8 and y <= 3, then it must be true that

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