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Source: — Data Sufficiency |
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by amit2k9 » Fri Jun 17, 2011 3:27 am
(1/10)^n < 1/100

meaning n > 2 as 1/1000 < 1/100 or so.

a sufficient.

b 10 * (1/10)^n < 0.1
means

(1/10)^n < 0.1/10

sufficient.

D it is.
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by Geva@EconomistGMAT » Fri Jun 17, 2011 3:49 am
sunilrawat wrote:If n is a positive integer, is (1/10)^n < 0.01 ?

(1) n > 2
(2) (1/10)^(n-1) < 0.1[/img]
Do some work on the question stem first. Turn (1/10)^n into 1^n / 10^n, which is basically 1/10^n
Turn 0.01 into 1/100, which is the equivalent of 1/10^2.

So now the question stem says "is 1/10^n < 1/10^2 ?

For the fraction on the left to be smaller than the fraction on the right, the denominator needs to be greater on the left than on the right; the question stem is really asking "is 10^n > 10^2?, or in other words, "is n greater than 2?"

Stat. (1) is therefore a clean "yes" answer, and is sufficient.

Stat. (2) a minus in the exponent means translates into a division: 10^n-1 is equal to 10^n/10^1, which in turn is equal to 10^n/10.

So (1/10)^n-1 is equal to 1/10^(n-1) = 1/ 10^n/10. Multiply the numerator 1 by the reciprocal of the denominator to get 1/1 * 10/10^n.

So stat. (2) says
10/10^n < 1/10.
Divide by 10 on both sides to get

10/10*10^n < 1/100

Reduce the 10s on the left side to get
1/10^n < 1/100 - which is the same as the question stem, privng that the answer is yes.
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by HSPA » Fri Jun 17, 2011 5:41 am
sunilrawat wrote:If n is a positive integer, is (1/10)^n < 0.01 ?

(1) n > 2
(2) (1/10)^(n-1) < 0.1[/img]
1) is straight forward
2) same as is requested just a small resemblence change in power.
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by sunilrawat » Sat Jun 18, 2011 6:57 am
in (2), why 0.1 cant be read as (1/10)^1 instead of (1/10)^-1
tht way we get n<2
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by magicalhat » Sat Jun 18, 2011 8:25 am
awesome! thank you!
Geva@MasterGMAT wrote:
sunilrawat wrote:If n is a positive integer, is (1/10)^n < 0.01 ?

(1) n > 2
(2) (1/10)^(n-1) < 0.1[/img]
Do some work on the question stem first. Turn (1/10)^n into 1^n / 10^n, which is basically 1/10^n
Turn 0.01 into 1/100, which is the equivalent of 1/10^2.

So now the question stem says "is 1/10^n < 1/10^2 ?

For the fraction on the left to be smaller than the fraction on the right, the denominator needs to be greater on the left than on the right; the question stem is really asking "is 10^n > 10^2?, or in other words, "is n greater than 2?"

Stat. (1) is therefore a clean "yes" answer, and is sufficient.

Stat. (2) a minus in the exponent means translates into a division: 10^n-1 is equal to 10^n/10^1, which in turn is equal to 10^n/10.

So (1/10)^n-1 is equal to 1/10^(n-1) = 1/ 10^n/10. Multiply the numerator 1 by the reciprocal of the denominator to get 1/1 * 10/10^n.

So stat. (2) says
10/10^n < 1/10.
Divide by 10 on both sides to get

10/10*10^n < 1/100

Reduce the 10s on the left side to get
1/10^n < 1/100 - which is the same as the question stem, privng that the answer is yes.
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by Geva@EconomistGMAT » Sat Jun 18, 2011 12:18 pm
sunilrawat wrote:in (2), why 0.1 cant be read as (1/10)^1 instead of (1/10)^-1
tht way we get n<2
You're right in your translation into 1/10^1, but wrong about the interpretation. Read my post - for a fraction to be smaller than another fraction, the denominator of the left hand side must be GREATER than the denominator on the right hand side. you get that (n-1) must be >1, so n is >2.
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by edvhou812 » Sat Jun 18, 2011 7:26 pm
.01 = 1/100

1) 1/10^2 = 1/100. 1/10^3 = 1/1000 1/1000<1/100. (Sufficient)

2) 1/10^4 = 1/10000<1/100, 1/10^4-1=>1/10^3<1/100. (Sufficient)

Answer is D.
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