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

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Bunuel
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If x >= 8 and y <= 3, then it must be true that [#permalink] New post  08 Oct 2019, 21:15
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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) \(x - y \leq 11\)
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chetan2u
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If x >= 8 and y <= 3, then it must be true that [#permalink] New post  08 Oct 2019, 21:47
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Bunuel wrote:
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) \(x - y \leq 11\)


\(x \geq 8\) 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
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bM22
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  11 Apr 2020, 08:54
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.
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chetan2u
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  11 Apr 2020, 08:59
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bm2201 wrote:
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.



The inequality signs have been reversed in both questions.
One says x<=8 & c>=3 and other Says x>=8 & x<=3
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preetamsaha
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  11 Apr 2020, 09:32
if a>b and c<d (signs in opposite direction: > 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
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bM22
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  11 Apr 2020, 10:08
Hi Bunuel,
Thank you so much, I overlooked. Apologies.
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Great1stan
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  11 Apr 2020, 10:44
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
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gurmukh
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  11 Apr 2020, 11:06
x>=8 ----(1)
y<=3
-y>=-3 -----(2)
Adding (1) and (2)
x-y>=5
Option C is the answer

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js17
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink] New post  01 May 2020, 09:13
x≥8 and y≤3
Add the same sides of inequalities
x+3≥8+y
x−y≥5
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Re: If x >= 8 and y <= 3, then it must be true that [#permalink]
01 May 2020, 09:13
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