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

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

GMATinsight · 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

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards