If n is an integer, is (0.1)^n greater than (10)^n?

Question

If n is an integer, is  (0.1)^n  greater than  (10)^n ?

(1)  n > -10

(2)  n < 10

GMATinsight · Accepted Answer

Question : is (0.1)^n > (10)^n? Question : is (1/10)^n > (10)^n? Question : is (10)^{-n} > (10)^n? Question : is (-n) > n? Question : is (2n) < 0? Question : is n < 0? Statement 1 : n > −10 n may be Negative or Positive. Hence NOT SUFFICIENT Statement 2 : n < 10 n may be Negative or Positive. Hence NOT SUFFICIENT Combining the two statements even after combining the two -10 < n < 10 i.e. n may be Negative or Positive. Hence NOT SUFFICIENT Answer: Option E

ENGRTOMBA2018 · Answer

Is (0.1)^n > (10)^n ---> 10^{-n} > 10^n ---> 10^{2n} < 1 ---> 10^{2n} < 10^0 ---> 2n < 0 ---> is n<0? Per statement 1, n>-10, yes for n=-5 but no for n=5. Not sufficient. Per statement 2, n<10, yes for n=-5 but no for n=5. Not sufficient. Combining, the above 2 cases still apply giving you an ambiguous answer. Thus, E is the correct answer.

BrentGMATPrepNow · Answer

Target question : Is (0.1)^n greater than (10)^n? REPHRASED target question : Is (1/10)^n greater than (10)^n? Statement 1 : n > −10 This statement doesn't FEEL sufficient, so I'll TEST some values. There are several values of n that satisfy statement 1. Here are two: Case a: n = 1, in which case (1/10)^n is NOT greater than (10)^n Case b: n = -1, in which case (1/10)^-1 = 10 and 10^-1 = 1/10. Here, (1/10)^n IS greater than (10)^n Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2 : n < 10 There are several values of n that satisfy statement 2. Here are two: Case a: n = 1, in which case (1/10)^n is NOT greater than (10)^n Case b: n = -1, in which case (1/10)^-1 = 10 and 10^-1 = 1/10. Here, (1/10)^n IS greater than (10)^n Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT IMPORTANT - Notice that I tested the SAME VALUES for both statements. This means that, the STATEMENTS COMBINED are also NOT SUFFICIENT Answer = E Cheers, Brent

cutegirlsimran · Answer

If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Sol. (10)^-n > (10)^n or -n>n or n<0 ?
1) n > -10 Not sufficient
2) n < 10 Not sufficient

1) + 2) -10 < n <10 Not sufficient

Hence E

ganand · Answer

Please note that for n=0, both the expressions will be equal to 1.

Hence, Answer: E.

BrentGMATPrepNow · Answer

Here's another approach: Target question : Is (0.1)^n > (10)^n? This is a good candidate for rephrasing the target question. Since (0.1)^n is always POSITIVE, we can safely divide both sides of the inequality by (0.1)^n to get: 1 > / There's a nice rule that says (a^n)/(b^n) = (a/b)^n When we apply this rule to the right side of the inequality, we get: 1 > (10/0.1)^n Simplify to get: Is 1 > 100^n? Notice that, when n = 0, then 100^n = 100^0 = 1 So, when n > 0, then 100^n > 1, and when n < 0, then 100^n < 1 So, we can REPHRASE the target question as.... REPHRASED target question : Is n < 0? Statement 1 : n > -10 There are several values of n that satisfy statement 1. Here are two: Case a: n = -9, in which case n < 0 Case b: n = 2, in which case n > 0 Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT Statement 2 : n < 10 There are several values of n that satisfy statement 1. Here are two: Case a: n = -9, in which case n < 0 Case b: n = 2, in which case n > 0 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED. Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT Answer: E RELATED VIDEOS https://www.youtube.com/watch?v=MyG1K3ee69w https://www.youtube.com/watch?v=EVUOYdRgt30

Shiv2016 · Answer

Bunuel  can we play around with the statement in question like this?
I mean to say:

Its given that is 10^-n>10^n

So can we divide/subtract/multiple/add on both sides of an expression that is to be proved?

When should we not do it?

Thanks

Bunuel · Answer

How to manipulate inequalities  (adding, subtracting, squaring etc.).

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=j0ulvH21dyc

ScottTargetTestPrep · Answer

Solution: Question Stem Analysis: We need to determine whether 0.1^n is greater than 10^n, given that n is an integer. Notice that 0.1 = 10^(-1); therefore, 0.1^n = 10^(-n) and 10^(-n) is greater than 10^n if -n > n. We see that -n > n if and only if n is negative. In other words, we need to determine whether n is negative. Statement One Alone: Even though we know n > -10, n could be either positive or negative. So we cannot definitely say n is negative. Statement alone is not sufficient. Statement Two Alone: Even though we know n < 10, n could be either positive or negative. So we cannot definitely say n is negative. Statement two is not sufficient. Statements One and Two Together: With the two statements, we see that -10 < n < 10. Thus, n could still be either positive or negative. Both statements together are not sufficient. Answer: E

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=dnJWI0EQvsY

varshas044 · Answer

IMO here is the simplest explanation: Let’s analyze the question --------- the only case when 0.1^n > 10^n is if n is negative So basically, we are trying to find if n < 0 Statement 1: N > -10 Here n can be ------- n < 0 or if the value goes beyond 0 then n > 0 NOT SUFFICIENT Statement 2: N < 10 Here n can be --------- n > 0 or n < 0 NOT SUFFICIENT Statement 1+2 -10 < n < 10 Again n can be ------- n < 0 or n > 0 NOT SUFFICIENT Answer – E

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If n is an integer, is (0.1)^n greater than (10)^n?

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If n is an integer, is (0.1)^n greater than (10)^n?

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