BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

OG 2016 DS 170

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Mon Mar 14, 2016 6:17 pm
Thanked: 1 times
by nsuen » Fri Apr 29, 2016 6:20 am
If n is a positive integer, is ( 1/10) ^n <0.01
1) n>2
2) (1/10)^(n-1) <0.1

I got the answer correct, which is D, but my way is different and the greater than or less than sign is opposite of the official way ( underlined) so I want to make sure my logic is correct in order to master other similar questions. Thank you.

My way:
1) (1/10)^n < 1/100
(1/10)^n <(1/10)^2
n<2

2) (1/10)^(n-1) <(1/10)^1
n-1<1
n<2

Official answer:
1) (10^-1)^n <10^(-2)
-n<-2
n>2

2)(1/10)^(n-1) <0.1
(10^-1) ^(n-1)<10^(-1)
10^(-n+1)<10(-1)
-n+1<-1
n>2
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members
Location: Boston, MA
Thanked: 1153 times
GMAT Score:770

by DavidG@VeritasPrep » Fri Apr 29, 2016 7:05 am
(1/10)^n <(1/10)^2
n<2
This move isn't valid. To see why, take a simple example: we know that (1/2)^3 < (1/2)^2, right? But obviously 3 < 2 isn't true! So we need to be careful with exponents in inequalities in a way we don't have to be careful with exponents in equations.
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Fri Apr 29, 2016 9:11 am
Hi nsuen,

Sometimes the best way to tackle a Quant question (whether it's PS or DS) is to just write down all of the possibilities so that you can see the entire situation (and deduce whatever pattern might be hidden within the "math").

Here, we're asked "is (1/10)^N < .01?" This is YES/NO question. We're told that N is a POSITIVE INTEGER

Before dealing with the information in Fact 1, I'm going to do a quick series of minor calculations to see what pattern exists in this situation:

If N = 1, then (1/10)^1 = .1
If N = 2, then (1/10)^2 = 1/100 = .01
If N = 3, then (1/10)^3 = 1/1000 = .001
Etc.

So, the pattern is that as N gets bigger, more zeros appear between the decimal point and the 1.

In reference to the original question, we're essentially asked if N is less than, equal to, or greater than 2.

Fact 1: N > 2
So, N must be greater than 2 (it could be 3, 4, 5, etc.)

Each of those values would create more zeroes between the decimal point and the 1.
N = 3 gives us .001
N = 4 would be smaller and so on.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: (1/10)^(N-1) < 0.1

While this might be "scary looking", it's based on the same pattern as before (we just need to adjust the math a bit)
N = 1 gives us 1
N = 2 gives us .1
N = 3 gives us .01
N = 4 gives us .001
Etc.

The information in Fact 2 tells us that N MUST be 3 or greater. This is the SAME information as what we had in Fact 1.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Apr 29, 2016 2:17 pm
If we have

Is (1/10)� < (1/10)² ?

we could approach it algebraically or conceptually.

Algebraically, I'd start with

Is 1/10� < 1/10² ?

Then, since you know both sides are positive, cross multiply

Is 10² < 10� ?

So the question becomes "Is n greater than 2?"

Conceptually, we could think of what happens with fractions between 0 and 1. Every time we multiply such fractions by themselves, they shrink! 1/10 > 1/100 > 1/1000 > ...

For 1/10� < 1/10² to hold, we'd need to multiply 1/10 by itself MORE than once, so we'd need n > 2.

Either way, same idea :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Mon Mar 14, 2016 6:17 pm
Thanked: 1 times

by nsuen » Fri Apr 29, 2016 11:15 pm
Thank you!

DavidG: Noticed, but then how come the official answer can get to n>2?

1) (10^-1)^n <10^(-2)
-n<-2
n>2
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members
Location: Boston, MA
Thanked: 1153 times
GMAT Score:770

by DavidG@VeritasPrep » Sun May 01, 2016 9:56 am
nsuen wrote:Thank you!

DavidG: Noticed, but then how come the official answer can get to n>2?

1) (10^-1)^n <10^(-2)
-n<-2
n>2
That's a valid move because the base, in this instance, is greater than 1. This is what makes inequalities with exponents tricky. If we have 2^x < 2^y, for example, we can say that x < y, but if we have (1/2)^x < (1/2)^y, then x > y. (This is the difference between the operation you performed and the Official Guide's solution.)
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1