It is currently 21 Mar 2018, 17:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Director
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 524
Location: India
GPA: 3.64
If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

### Show Tags

19 Nov 2017, 11:17
3
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

44% (00:43) correct 56% (00:29) wrong based on 55 sessions

### HideShow timer Statistics

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

_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1008
Location: India
GPA: 3.82
If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

### Show Tags

19 Nov 2017, 12:03
1
This post was
BOOKMARKED
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
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2282
Location: India
GPA: 3.12
If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

### Show Tags

19 Nov 2017, 12:28
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)
_________________

Stay hungry, Stay foolish

VP
Joined: 22 May 2016
Posts: 1432
If R^a*R^b*R^c=R^-9. if R>0 and a,b and c are each different negative [#permalink]

### Show Tags

19 Nov 2017, 12:30
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

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

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, 12:30
Display posts from previous: Sort by