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OG C DS 144 If n is a positive integer, is (1/10)^n < .01? a. n>2 b. (1/10)^(n-1) <0.1
First lets make the question simpler... n is a postive integer....so n can be 1, 2, 3..... (1/10)^n < .01 ? ===> 10^-n < .01? ===== > 10^-n < 10^-2 ? so the question now becomes ----- > is 10 raised to -n less than 10 raised to -2
a. n > 2====> since n can only be an integer, lets take the value of n as 3. so, substitiuting n = 3,
10^-3 < 10^-2 i.e. 10^-3 IS less than 10^-2 .... so statement 1 is sufficient...
b. (1/10)^(n-1) <0.1 simplying statement 2 goes like this..:
(1/10)^(n-1) <0.1 =====> (10)^-(n-1) <0.1 ====>
(10)^-n+1 <0.1 =====> (10)^-n <0.01 ..ie. this is what the question was asking for...
Hoping someone can please shed some light on this as I'm seeing conflicting answers in different threads.
OG C DS 144 If n is a positive integer, is \(\frac{1}{10}^n < 0.01\)? a. \(n>2\) b. \(\frac{1}{10}^{n-1} < 0.1\)
Taking the stem, I change it to \(\frac{1}{10}^n < \frac{1}{100}\). For this to be true, n > 2. So the question is asking... is n > 2?
A. n > 2 Sufficient based on manipulation of stem.
B. \(\frac{1}{10}^{n-1} < 0.1\) This is where it gets really confusing. There are two ways I can go about doing this resulting in different answers...
Method 1 \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into decimals. \(0.1^{n-1} < 0.1^1\) The bases on both sides of the inequality match, so I focus on the exponents: \(n-1 < 1\) \(n < 2\) This is sufficient, but this answer conflicts with A. From what I understand, this should never happen on the GMAT.
Method 2 \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into whole numbers: \((10^{-1})^{n-1} < 10^{-1}\) Now that the bases are the same on both sides, I focus on the exponents: \(-1(n-1) < -1\) \(-n+1 < -1\) \(-n < -2\) \(n > 2\) This is sufficient and this answer agrees with A.
Method 2 is the explanation given in the OG. But why does Method 1 (my approach) give a different answer? What am I doing wrong?
Hoping someone can please shed some light on this as I'm seeing conflicting answers in different threads.
OG C DS 144 If n is a positive integer, is \(\frac{1}{10}^n < 0.01\)? a. \(n>2\) b. \(\frac{1}{10}^{n-1} < 0.1\)
Taking the stem, I change it to \(\frac{1}{10}^n < \frac{1}{100}\). For this to be true, n > 2. So the question is asking... is n > 2?
A. n > 2 Sufficient based on manipulation of stem.
B. \(\frac{1}{10}^{n-1} < 0.1\) This is where it gets really confusing. There are two ways I can go about doing this resulting in different answers...
Method 1 \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into decimals. \(0.1^{n-1} < 0.1^1\) The bases on both sides of the inequality match, so I focus on the exponents: \(n-1 < 1\) \(n < 2\) This is sufficient, but this answer conflicts with A. From what I understand, this should never happen on the GMAT.
Method 2 \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into whole numbers: \((10^{-1})^{n-1} < 10^{-1}\) Now that the bases are the same on both sides, I focus on the exponents: \(-1(n-1) < -1\) \(-n+1 < -1\) \(-n < -2\) \(n > 2\) This is sufficient and this answer agrees with A.
Method 2 is the explanation given in the OG. But why does Method 1 (my approach) give a different answer? What am I doing wrong?
Anyone? I'd really appreciate an explanation because clearly something is wrong with my logic.
Hoping someone can please shed some light on this as I'm seeing conflicting answers in different threads.
OG C DS 144 If n is a positive integer, is \(\frac{1}{10}^n < 0.01\)? a. \(n>2\) b. \(\frac{1}{10}^{n-1} < 0.1\)
Taking the stem, I change it to \(\frac{1}{10}^n < \frac{1}{100}\). For this to be true, n > 2. So the question is asking... is n > 2?
A. n > 2 Sufficient based on manipulation of stem.
B. \(\frac{1}{10}^{n-1} < 0.1\) This is where it gets really confusing. There are two ways I can go about doing this resulting in different answers...
Method 1 \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into decimals. \(0.1^{n-1} < 0.1^1\) The bases on both sides of the inequality match, so I focus on the exponents: \(n-1 < 1\) \(n < 2\) This is sufficient, but this answer conflicts with A. From what I understand, this should never happen on the GMAT.
Method 2 \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into whole numbers: \((10^{-1})^{n-1} < 10^{-1}\) Now that the bases are the same on both sides, I focus on the exponents: \(-1(n-1) < -1\) \(-n+1 < -1\) \(-n < -2\) \(n > 2\) This is sufficient and this answer agrees with A.
Method 2 is the explanation given in the OG. But why does Method 1 (my approach) give a different answer? What am I doing wrong?
Anyone? I'd really appreciate an explanation because clearly something is wrong with my logic.
GSD, the Method 2 deals with whole numbers, Method 1 is deals with decimals/fractions. A fraction raised to the (n+1) power is smaller than that same fraction raised to the n power (assuming n is positive), whereas a whole number raised to the (n+1) power is larger than that same number raised to the n power. That's why you're seeing the conflicting answers.
GSD, the Method 2 deals with whole numbers, Method 1 is deals with decimals/fractions. A fraction raised to the (n+1) power is smaller than that same fraction raised to the n power (assuming n is positive), whereas a whole number raised to the (n+1) power is larger than that same number raised to the n power. That's why you're seeing the conflicting answers.
Thank you for the response. Do you mind elaborating on this? I understand the concept that when you take any number between 0 and 1 and raise it to a power, the value will decrease. But I still don't understand how it matters in this particular context. The stem was not manipulated to use whole numbers as the base, so why does Method 2 (using whole numbers) arrive at the correct conflusion? Are there any general rules about flipping inequalities when dealing with numbers between 0 and 1?
(1) \(\frac{1}{10}^{n-1} < 0.1\) Change the bases into decimals. (2) \(0.1^{n-1} < 0.1^1\)
The bases on both sides of the inequality match, so I focus on the exponents: (3) \(n-1 < 1\)
Going from step (2) to step (3) is not logically or mathematically correct.
If: \(0.1^{n-1} < 0.1^1\) Then: n-1 > 1, since the higher the exponent of 0.1, the lower the resulting decimal.
For example, if n-1 WAS less than 1, you can see that \(0.1^{n-1} > 0.1^1\) If n-1 = 0, which is less than 1, then \(0.1^{0} = 1 > 0.1^1\) If n-1 = -1, which is less than 1, then \(0.1^{-1} = 10 > 0.1^1\) If n-1 = 1, which is greater than 1, then \(0.1^{-1} = .01 < 0.1^1\)
OG C DS 144 If n is a positive integer, is (1/10)^n < .01? a. n>2 b. (1/10)^(n-1) <0.1
(1) n is greater than 2 that is at least 3 so 1 is divided by 1000 (1/1000=.001) less than 0.01 suff. (2) if n=2 then left=right part, if n=3 then left part (.01) <0.1, n>2 suff.
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