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If x-y= R and xy=S, then (x-2)(y+2)=

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carcass
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If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   23 Jul 2017, 10:21
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If x-y= R and xy=S, then (x-2)(y+2)=

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S
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Bunuel
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Re: If x-y= R and xy=S, then (x-2)(y-2)= [#permalink] New post   23 Jul 2017, 10:36
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If x-y= R and xy=S, then (x-2)(y+2)=

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S


\((x-2)(y+2)=xy +2x-2y-4=xy+2(x-y)-4=S+2R-4\).

Answer: D.
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BrentGMATPrepNow
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If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   Updated on: 19 Jan 2020, 13:48
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carcass wrote:
If x-y= R and xy=S, then (x-2)(y+2) =

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S


Another approach is to assign some values for x and y.

Let's say that x = 5 and y = 2
This means R = 3 and S = 10

We must determine the value of (x - 2)(y + 2)
Plug in x = 5 and y = 2 to get: (x - 2)(y + 2) = (5 - 2)(2 + 2) = (3)(4) = 12

Now take each answer choices to see which one gives us an OUTPUT of 12.

A. R + S - 4 = 3 + 10 - 4 = 9. ELIMINATE

B. R + 2S - 4 = 3 + 2(10) - 4 =19. ELIMINATE

C. 2R - S - 4 = 2(3) - 10 - 4 = -8. ELIMINATE

D. 2R + S - 4 = 2(3) + 10 - 4 = 12 KEEP

E. R + S = 3 + 10 = 13. ELIMINATE

Answer: D

Originally posted by BrentGMATPrepNow on 18 Mar 2018, 12:15.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:48, edited 1 time in total.
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   24 Jul 2017, 21:47
carcass wrote:
If x-y= R and xy=S, then (x-2)(y+2)=

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S

(x-2)(y+2) = xy +2x - 2y -4
=xy +2(x-y) -4
=S + 2R - 4

Answer D
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   24 Jul 2017, 22:19
(x-2) (y+2) = xy - 2y + 2x - 4

x-y = R, xy = S

xy - 2y + 2x - 4 = S + 2(x-y) - 4 = S + 2R - 4. Ans - D.
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   24 Jul 2017, 22:58
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carcass wrote:
If x-y= R and xy=S, then (x-2)(y+2)=

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S


x-y = R
xy = S
(x-2)(y+2) = xy - 2y + 2x -4 = xy + 2(x-y) - 4
= S + 2R - 4

Answer D
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   26 Jul 2017, 16:16
Expert Reply
carcass wrote:
If x-y= R and xy=S, then (x-2)(y+2)=

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S


(x-2)(y+2)

= xy + 2x - 2y - 4

= xy + 2(x - y) - 4

= S + 2R - 4

Answer: D
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   28 Aug 2017, 00:14
I made a frivulous mistake in hurry and picked B.

I solved xy+2(x-y)-4
But in hurry picked R+2S-4 Instead of S+2R-4.
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   05 Sep 2017, 06:05
1. (x-2)(y+2)
2. xy + 2x -2y - 4 (order of operations/multiplication/parenthesis)

3. xy = S; 2x - 2y = 2R, for R = x - y; and - 4 stays the same
4. xy + 2x - 2y - 4 ----> S + 2R - 4

Ans = (D) 2R + S - 4
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   06 Sep 2018, 09:32
\((x-2)(y+2)=xy+2x-2y-4\)
\(xy+2(x-y)-4\)
\(S+2R-4\)
\(2R+S-4\)

Answer D
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If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   08 Sep 2018, 17:19
Let x=2 and y=1. Then: 2-1=1 (R) and 2*1=2 (S).

(x−2)(y+2) = (2−2)(1+2) = 0.

So we know that when 1 = (R) and 2 = (S), the equation = 0. Option D: 2R+S−4 = 2*1+2-4 = 0.
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   10 May 2020, 22:17
Why are (y=2 and x=1) not working?
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   11 May 2020, 06:23
carcass wrote:
If x-y= R and xy=S, then (x-2)(y+2)=

A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S


Plug in and solve

Let x = 3 & y = 1 , So R = 2 & S = 3

Thus, (x-2)(y+2) = 1*3 => 3

Now, check the options -

(A) R+S-4 = 1
(B) R+2S -4 = 4
(C) 2R - S -4 = -3
(D) 2R + S - 4 = 3
(E) R + S = 5

Thus, Answer must be (D) 3
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   04 Aug 2020, 23:47
carcass wrote:


A. R+S-4

B. R+2S -4

C. 2R - S -4

D. 2R + S - 4

E. R + S


Asked: If x-y= R and xy=S, then (x-2)(y+2)=

(x-2)(y+2)= xy + 2x - 2y - 4 = S + 2R - 4

IMO D
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Re: If x-y= R and xy=S, then (x-2)(y+2)= [#permalink] New post   31 Mar 2023, 12:00
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