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# If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative

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Senior Manager
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If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

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19 Nov 2017, 10:17
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40% (00:41) correct 60% (00:30) wrong based on 35 sessions

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If $$R^a*R^b*R^c=R^{-9}$$ and if R>0 and a,b and c are each different negative integers, what is the smallest that c could be?
A) -1
B) -2
C) -6
D) -7
E) Cannot be determined
[Reveal] Spoiler: OA

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If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

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19 Nov 2017, 11:03
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souvonik2k wrote:
If $$R^a*R^b*R^c=R^{-9}$$ and if R>0 and a,b and c are each different negative integers, what is the smallest that c could be?
A) -1
B) -2
C) -6
D) -7
E) Cannot be determined

$$R^{a+b+c}=R^{-9}$$

$$=>a+b+c=-9$$

so $$c=-9-a-b$$. for $$c$$ to be smallest either of $$a$$ or $$b$$ has to be $$-1$$ and the other $$-2$$

hence $$c=-9+1+2=-6$$

Option C

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If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

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19 Nov 2017, 11:28
souvonik2k wrote:
If and if R>0 and a,b and c are each different negative integers, what is the smallest that c could be?
A) -1
B) -2
C) -6
D) -7
E) Cannot be determined

$$R^a*R^b*R^c=R^{-9}$$
$$R^{a+b+c} = R^{-9}$$
From the above equation, a+b+c = -9

It has been given that a,b,and c are all negative integers(different)

The largest negative integer is -1, second largest is -2
Hence, the third largest/smallest integer(c) must be -1 + (-2) + c = -9

Therefore, c = -9 + 3 = -6(Option C)
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If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

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19 Nov 2017, 11:30
souvonik2k wrote:
If $$R^a*R^b*R^c=R^{-9}$$ and if R>0 and a,b and c are each different negative integers, what is the smallest that c could be?
A) -1
B) -2
C) -6
D) -7
E) Cannot be determined

The trap in this question is "smallest."

It almost got me; I decided that "-1" was too obvious. The smallest negative variable/ number is the one most to the left on the number line.

When bases are the same (here, R), add exponents. Sum = -9

a + b + c = -9
c = 9 - a - b

a and b are different negative integers. To minimize c, to make it farthest to the left of 0, maximize a and b -- make them, going left from zero, as close to 0 as possible.
a = -1
b = -2

c = 9 - a - b
c = 9 - (-1) - (-2) = (-9 + 1 + 2) = -6

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If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative   [#permalink] 19 Nov 2017, 11:30
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