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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

tricky exponent question - N = 10^40 + 2^40

Expert replies
Post new topic Post Reply
Previous Topic Next Topic

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770
by Brent@GMATPrepNow » Sat Apr 01, 2017 7:08 am
N = 10^40 + 2^40. 2^k is a divisor of N, but 2^(k+1) is not a divisor of N. If k is a positive integer, what is the value of k-2?

A) 38
B) 39
C) 40
D) 41
E) 42

Answer: B

Source: www.gmatprepnow.com
Difficulty level: 700+
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members
Thanked: 14 times

by Mo2men » Sat Apr 01, 2017 2:37 pm
Brent@GMATPrepNow wrote:N = 10^40 + 2^40. 2^k is a divisor of N, but 2^(k+1) is not a divisor of N. If k is a positive integer, what is the value of k-2?

A) 38
B) 39
C) 40
D) 41
E) 42

Answer: B

Source: www.gmatprepnow.com
Difficulty level: 700+
Really Tricky question, Brent!!

N = 10^40 + 2^40 = (2^40)(5^40) + (2^40)= (2^40) (5^40 + 1)

2^k is divisor of N

(2^40) (5^40 + 1)/(2^k).....it means that 2^40........k= 40. However, when apply k=40 in 2^(k+1, it is still advisable because the term (5^40 + 1) hides another 2 as (5^40 + 1)= (number with unit digit 5+ 1) = number with unit digit of 6.

Therefore k=41 So make all conditions above works.

k-2 = 41-2 =39

Answer:B

Great question
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 02, 2017 6:16 am
Brent@GMATPrepNow wrote:N = 10^40 + 2^40. 2^k is a divisor of N, but 2^(k+1) is not a divisor of N. If k is a positive integer, what is the value of k-2?

A) 38
B) 39
C) 40
D) 41
E) 42
IMPORTANT: we need to recognize that 5^b will end in 25 for all integer values of b greater than 1.
For example, 5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3125
5^6 = XXX25etc....

So......
N = 10^40 + 2^40
= 2^40(5^40 + 1)
= 2^40(XXXX25 + 1) [aside: XXXX25 denotes some number ending in 25]
= 2^40(XXXX26)
= 2^40[2(XXXX3)] [Since XXX26 is EVEN, we can factor out a 2]
= 2^41[XXXX3]

Since XXXX3 is an ODD number, we cannot factor any more 2's out of it.
This means that 2^41 IS a factor of N, but 2^42 is NOT a factor of N.
In other words, k = 41

What is the value of k-2?
Since k = 41, we can conclude that k - 2 = 41 - 2 = 39

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1