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# If n is an integer, what is the greatest possible value for n that wou

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Math Expert
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If n is an integer, what is the greatest possible value for n that wou [#permalink]

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11 Jan 2015, 12:27
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35% (medium)

Question Stats:

64% (00:49) correct 36% (00:51) wrong based on 228 sessions

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If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?

(A) –4
(B) –3
(C) –2
(D) –1
(E) 0

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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11 Jan 2015, 19:06
1
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Tested the answers - I believe the answer is B - "-3" - took 1:10

Started with E - 0

11/10^0 = 11 - does not work
11/10^1 = 11/10 - does not work
11/10^2 = 11/100 > 10/100 - does not work
11/10^3 = 11/1000 - works, the answer is "-3"

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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11 Jan 2015, 20:05
1
KUDOS
Just putting values, the LHS becomes
n=0 --> 11
n=-1 --> 11/10
n=-2 --> 11/100
n=-3 --> 11/1000

Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3.

Bunuel wrote:
If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?

(A) –4
(B) –3
(C) –2
(D) –1
(E) 0

Kudos for a correct solution.

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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11 Jan 2015, 23:28
2
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here we go

Simplifying the equation

11*10^n < 1/10

(10+1)*10^n <1/10

10^(n+1) + 10^n < 1/10

Multiply the equation by 10

10^(n+2) + 10^(n+1) < 1

Option A and Option B left

Option B is the winner.

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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14 Jan 2015, 03:08
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Anwer = (B) –3

$$11*10^n < \frac{1}{10}$$

$$11 * 10^{n+1} < 1$$

We require to find the greatest value. In the OA, 0 (Option E) is greatest and -4 (Option A) is the least

Starting with option E

For n = 0, -1, -2, LHS > RHS

For n = -3, $$\frac{11}{100} = 0.01 < 1$$
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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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05 May 2016, 03:42
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11*10^n < 1/10

11*10^n+1<1

try solution for n :

n= 0 => 11 x 10 ^1 = 110 >1
n=-1 => 11 x 10^0 = 11 > 1
n=-2 => 11 x 10^-1 = 11/10 > 1
n=-3 => 11 x 10^-2 = 11/100 < 1

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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17 Jul 2016, 11:01
Hi!
Can some expert help for the method to arrive at B .. which is correct option.
thanks

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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18 Jul 2016, 02:00
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11*10^n<1/10
10^n<1/(10*11)
10^n<1/110
1/(10^-n)<1/110
n=-2
100>110
1/100<1/110

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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20 Jul 2016, 04:15
Celestial09 wrote:
Hi!
Can some expert help for the method to arrive at B .. which is correct option.
thanks

11*10^n<1/10
10^n<1/(10*11)
10^n<1/110
1/(10^-n)<1/110
n=-2
100>110
1/100<1/110

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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21 Jul 2016, 09:57
Bunuel wrote:
If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?

(A) –4
(B) –3
(C) –2
(D) –1
(E) 0

Kudos for a correct solution.

Let us start by substituting the answer choice

for n = 0
LHS = 11
11*10^n < 1/10 ---does not satisfy

for n= -1
LHS = 11*10^-1
11/10 < 1/10 ---does not satisfy

for n = -2
LHS = 11/100=0.11
0.11 < 0.10 ----does not satisfy

for n = -3
LHS = 11*10^-3
11/1000 < 1/10 ---satisfies !!

Therefore n = -3

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Re: If n is an integer, what is the greatest possible value for n that wou [#permalink]

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05 Oct 2017, 08:56
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If n is an integer, what is the greatest possible value for n that wou [#permalink]

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17 Oct 2017, 22:33
Celestial09 wrote:
Hi!
Can some expert help for the method to arrive at B .. which is correct option.
thanks

11*10^n<1/10
10^n<1/(10*11)
10^n<1/110
1/(10^-n)<1/110
n=-2
100>110
1/100<1/110

Hi,

1/100<1/110 is not correct, the opposite is though, hence why -3 (B) would satisfy the condition, i.e 1/1000<1/110. Otherwise, your approach is brilliant.

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If n is an integer, what is the greatest possible value for n that wou   [#permalink] 17 Oct 2017, 22:33
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