If n is an integer, is n|n| 3^n? (1) n

Question

If n is an integer, is n|n| > 3^n?

(1) n < -1
(2) n = -11

Archit3110 · Answer

#1
n<-1
n=-2,-3 so on
-4>1/9 ; no sufficient for all values
#2
n=-11
yes sufficeint
IMO D

navderm · Answer

1. 
If we know n < -1, that means all the values n can take will be negative and greater than absolute 1.
It also means, all the values |n| can take will be positive and greater than absolute 1.
Hence, n|n| is > 1 (abs value) and negative. 
But, 3^(any positive or negative integer) is positive. Hence 1 is sufficient to answer the aforementioned question. (The ans is no)

2. if n = -11, n|n| = -121. 
But, 3^(any positive or negative integer) is positive. Hence 2 is sufficient to answer the aforementioned question. (The ans is no)

Hence D

shaliny · Answer

please experts, provide solution for this

Bunuel · Answer

If n is an integer, is n|n| > 3^n?

(1) n < -1

If n is negative, |n| is positive. So n|n| = (negative) * (positive) = negative. Meanwhile, 3^n is always positive. So negative > positive is never true. The answer is always NO. Sufficient.

(2) n = -11

Same logic: n|n| = (-11)(11) = -121, which is negative, while 3^n > 0. Again, the answer is NO. Sufficient.

Answer: D.

P.S. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

shaliny · Answer

Thanks, it helped a lot, but how would i select specific chapter questions to practice for gmat focus of different level q. gmat questions bank?

Bunuel · Answer

You should practice questions with exactly those tags. Either use the forum’s filter tool to select them, or simply watch for the tags under each question and choose the ones labeled:

Word Problems   
   Work Problems   
   Distance Problems   
   Mixture Problems   
   Percent and Interest Problems   
   Overlapping Sets Problems   
   Statistics Problems   
   Combination and Probability Problems

If n is an integer, is n|n| > 3^n? (1) n < -1 (2) n = -11

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