If 1

Question

If −1 < n < 0, which of the following expressions has the greatest value?

(A) n
(B) n^2
(C) n^3
(D) (1 − n)^2
(E) (1 − n)^3

Part of the project:   GMAT DS & PS DAILY Challenge -   (2022)  -  Gain 25 Kudos   &   Get   FREE   Access to GMATClub TESTS 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 GMAT - Math Book  
 Ultimate GMAT Quantitative Megathread  
 ALL YOU NEED FOR QUANT ! ! ! 
 ALL GMAT PREP PS + DS QUESTIONS (LINKS TO ALL 825 QUESTIONS)  3

Archit3110 · Answer

for given range -1<n<0
n = -0.5
(A) n ; -0.5
(B) n^2 ; .25
(C) n^3; -.125
(D) (1 − n)^2 ; ( 2.25)
(E) (1 − n)^3 ; (3.3)
OPTION E is greatest

SaquibHGMATWhiz · Answer

Solution:      
  Apart from plugging an easy value like -0.5 or -0.2, there is a logical and faster way to approach this problem

We know n is negative, right?  
 If we look at options A, B and C, we will notice that option B has even power n thereby making is positive 
 Thus  option B is definitely bigger than A and C and we can eliminate option A and C

Anothe thing to notice here is the range of n is −1 < n < 0 which means the value of 1 - n will always be positive and greater than 1 
 This means between options D and E, the later will be bigger because or higher power 3 
 Thus,  we can eliminate option D

Now the choice is between options B and E 
  Option B is the square of numbers like -0.2, -0.5, -0.9 and so on. The value of which will only tend to touch 1  
  Whereas option E is the cube of 1 - n, which in itself is greater than 1

Hence the right answer is    Option E

av1901 · Answer

Looking at the answer choices, we can choose a value for n (plugging in purposes) which can help us remove options quickly, in this case it is:  n = -0.2

We have squares in the answer choices so yes there is going to be positive answer choices and since we are searching for the greatest value, we can safely eliminate the answer choices which give us negative values

Options A and C eliminated

Now, between options B and D: B gives us  (-0.02)^2 , and D gives us  (1.2)^2 , thus eliminate B

D v/s E
D:  1.2^2 
E:  1.2^3

We DO NOT need to calculate because for values > 1, number increases with increasing powers

Answer - E

If 1 < n < 0, which of the following expressions has the greatest val

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

GMAT Problem Solving (PS) Questions