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# If r(r-4)=12 where r represents a positive integer, then

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If r(r-4)=12 where r represents a positive integer, then  [#permalink]

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05 Feb 2020, 07:17
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If $$r(r-4)=12$$ where r represents a positive integer, then $$(r-2)^2 +10=$$

A 18
B 26
C 36
D 40
E 52

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GMAT 1: 570 Q41 V27
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Re: If r(r-4)=12 where r represents a positive integer, then  [#permalink]

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05 Feb 2020, 07:26
1
If $$r(r−4)=12$$ where r represents a positive integer, then $$(r−2)^2+10$$=?

A 18
B 26
C 36
D 40
E 52

$$r(r−4)=12$$ -> $$r^2−4r-12=0$$ -> $$(r-6)(r+2) = 0$$ -> r=6, r=-2 -> Since r is positive only r=6 is valid

$$(r−2)^2+10$$= $$r^2-4r+14$$ = $$36-24+14 = 26$$ -> Answer - B
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Re: If r(r-4)=12 where r represents a positive integer, then  [#permalink]

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05 Feb 2020, 07:53
1
B.26
r(r-4)=12
r²-4r=12
r²-4r-12=0
we will maje factorize
r_____-6
r_____2
so,r=6

(r-2)²=-10
r²-4r+4=-10
r²-4r=-14
r=6,so, 36-24=-14
12+14=26

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Re: If r(r-4)=12 where r represents a positive integer, then  [#permalink]

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09 Feb 2020, 04:20
If $$r(r-4)=12$$ where r represents a positive integer, then $$(r-2)^2 +10=$$

A 18
B 26
C 36
D 40
E 52

Simplifying the given equation, we have:

r^2 - 4r = 12

Foiling the final expression, we have:

r^2 - 4r + 4 + 10 = ?

Since r^2 - 4r = 12, we have:

12 + 4 + 10 = 26

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Re: If r(r-4)=12 where r represents a positive integer, then   [#permalink] 09 Feb 2020, 04:20
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