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Is r^x < 100?

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Is r^x < 100? [#permalink]

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New post 03 Oct 2017, 00:05
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E

Difficulty:

  45% (medium)

Question Stats:

31% (01:23) correct 69% (00:53) wrong based on 49 sessions

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Is r^x < 100? [#permalink]

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New post 03 Oct 2017, 00:22
Is \(r^x<100\) ?


(1) \(r∗\sqrt[3]{x}>100\)

if x = 1/8
=> \(r∗\sqrt[3]{\frac{1}{8}}>100\)
=> \(r*\frac{1}{2} > 100\)
=> r > 200
\(r^x<100\)
=>\(300^{\frac{1}{8}}<100\) True

if x = 8
=> r > 50
\(r^x<100\)
=>\(51^{8}<100\) False
So here we don't have max and min of x and r, so we cannot calculate value of \(r^x<100\)
Insufficient

(2) x>1
Here we dont know value of r
Insufficient

1+2
\(r∗\sqrt[3]{x}>100\) and x>1

for x =8>1 => \(r∗\sqrt[3]{x}>100\)
=> \(r∗\sqrt[3]{8}>100\)
=> r >50
so \(r^x<100\)
=> \(51^8<100\) False

for x=100000000
\(r∗\sqrt[3]{x}>100\)
=> \(r∗\sqrt[3]{100000000}>100\)
=> r* 1000>100
=> r >1/10
so \(r^x<100\)
=> \(1^{1000000000}<100\) True

So here there is no max limit on x. Hence insufficient

Answer: E

Last edited by Nikkb on 03 Oct 2017, 04:26, edited 4 times in total.

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Re: Is r^x < 100? [#permalink]

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New post 03 Oct 2017, 03:20
Ans : c

1. r * x^1/3 > 100

consider x= positive (eg x= 27 and r =50)

Putting the values 125>100

Substituting x and r values in the given equation , r^x>100

Consider x= negative (eg x= -1 and r = -101)

Putting the values 101>100

Substituting x and r values in the given equation ,
r^x<100

NOt sufficient .

1.x > 1.

Statement alone is not sufficient as r can be any value.

Combining the two and subsituting anyvalue of x>1 and r that satisfies equation 1 ,

r^x is not less than 100 anytime.

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Is r^x < 100? [#permalink]

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New post 03 Oct 2017, 03:50
Bunuel wrote:
Is \(r^x < 100\)?


(1) \(r*\sqrt[3]{x}>100\)

(2) \(x> 1\)


Statement 1: if \(r<0\), then \(x<0\) and if \(r>0\) then \(x>0\)

\(r=-200\) & \(x=-8\), then \(r*\sqrt[3]{x}\) \(=-200*-2=400>100\)

but \(r^x\) \(= (-200)^{-8} = \frac{1}{(-200)^8}\)\(<100\)

if \(r=200\) and \(x=8\), then \(r*\sqrt[3]{x}>100\) \(=200*2=400>100\)

but \(r^x=200^8>100\). Hence insufficient

Statement 2: \(x>\)1 but nothing given about \(r\). hence insufficient

Combining 1 & 2 if \(r=200\) and \(x=8\), then \(r*\sqrt[3]{x}>100\) \(=200*2=400>100\), then the answer to our question Stem is NO.

but if \(x=0.5\) and \(r=10^9\), then \(r*\sqrt[3]{x}>100\) \(=0.5*10^3=500>100\) but \(r^x=(0.5)^{10^9}<100\). So we get a Yes for our question stem.

Hence Insufficient

Option E

Last edited by niks18 on 04 Oct 2017, 07:39, edited 1 time in total.

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Is r^x < 100? [#permalink]

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New post 04 Oct 2017, 07:23
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niks18 wrote:
Bunuel wrote:
Is \(r^x < 100\)?


(1) \(r*\sqrt[3]{x}>100\)

(2) \(x> 1\)


Statement 1: if \(r<0\), then \(x<0\) and if \(r>0\) then \(x>0\)

\(r=-200\) & \(x=-8\), then \(r*\sqrt[3]{x}\) \(=-200*-2=400>100\)

but \(r^x\) \(= (-200)^{-8} = \frac{1}{(-200)^8}\)\(<100\)

if \(r=200\) and \(x=8\), then \(r*\sqrt[3]{x}>100\) \(=200*2=400>100\)

but \(r^x=200^8>100\). Hence insufficient

Statement 2: \(x>\)1 but nothing given about \(r\). hence insufficient

Combining 1 & 2 we know that \(x>0\), hence \(r>0\) so \(r^x>100\). Hence we get a NO for our question stem. Sufficient

Option C


Hi niks18,

When you combine 1 & 2

beside your example, you neglected when x is huge number and 0<r<1

if \(r=200\) and \(x=8\), then \(r*\sqrt[3]{x}>100\) \(=200*2=400>100\).......Is 200^8 < 100........Answer No

if \(r=0.2\) and \(x=10^9\), then \(r*\sqrt[3]{x}>100\) \(=0.2 *1000=200>100\).....Is (0.2)^1000000000 < 100...Answer Yes

It should be E

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Re: Is r^x < 100? [#permalink]

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New post 04 Oct 2017, 07:31
Mo2men wrote:
niks18 wrote:
Bunuel wrote:
Is \(r^x < 100\)?


(1) \(r*\sqrt[3]{x}>100\)

(2) \(x> 1\)


Statement 1: if \(r<0\), then \(x<0\) and if \(r>0\) then \(x>0\)

\(r=-200\) & \(x=-8\), then \(r*\sqrt[3]{x}\) \(=-200*-2=400>100\)

but \(r^x\) \(= (-200)^{-8} = \frac{1}{(-200)^8}\)\(<100\)

if \(r=200\) and \(x=8\), then \(r*\sqrt[3]{x}>100\) \(=200*2=400>100\)

but \(r^x=200^8>100\). Hence insufficient

Statement 2: \(x>\)1 but nothing given about \(r\). hence insufficient

Combining 1 & 2 we know that \(x>0\), hence \(r>0\) so \(r^x>100\). Hence we get a NO for our question stem. Sufficient

Option C


Hi niks18,

When you combine 1 & 2

beside your example, you neglected when x is huge number and 0<r<1

if \(r=200\) and \(x=8\), then \(r*\sqrt[3]{x}>100\) \(=200*2=400>100\).......Is 200^8 < 100........Answer No

if \(r=0.2\) and \(x=10^9\), then \(r*\sqrt[3]{x}>100\) \(=0.2 *1000=200>100\).....Is (0.2)^1000000000 < 100...Answer Yes

It should be E


Hi Mo2men

Yup agreed :thumbup: . Thanks for highlighting, will edit the solution

Kudos [?]: 174 [0], given: 31

Re: Is r^x < 100?   [#permalink] 04 Oct 2017, 07:31
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