The question is not visible completely...can u post it
?
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
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
Toughie
Source: Beat The GMAT — Problem Solving |
-
GmatMathPro
- GMAT Instructor
- Posts: 349
- Location: Austin, TX
- Thanked: 236 times
- GMAT Score:770
735^4-735^3+735^2-735 = 735^3(735-1)+735(735-1) = 735^3(734)+735(734) = 734(735^3+735) = 734(735)(735^2+1).
So p divides 734(735)(735^2+1), which means p divides one of those factors.
We also know p divides 735^3+736, which is the same as 735^3+735+1 = 735(735^2+1)+1. This tells us that p divides a number that is one more than a multiple of 735 and one more than a multiple of 735^2+1, which means p CANNOT divide 735 or 735^2+1. Thus, p must divide 734.
Therefore the remainder when 734 is divided by p must be 0
So p divides 734(735)(735^2+1), which means p divides one of those factors.
We also know p divides 735^3+736, which is the same as 735^3+735+1 = 735(735^2+1)+1. This tells us that p divides a number that is one more than a multiple of 735 and one more than a multiple of 735^2+1, which means p CANNOT divide 735 or 735^2+1. Thus, p must divide 734.
Therefore the remainder when 734 is divided by p must be 0
Let 735 = a, which means 734 = a-1 and 736 = a+1
Therefore, (a^4 - a^3 + a^2 - a) is divisible by p
which means, a^2(a^2 + 1) - a(a^2 + 1) is divisible by p
or, a(a-1)(a^2+1) is divisible by p
We also know that a(a^2+1) + 1 is divisible by p, which means that a(a^2+1) is not divisible by p
Therefore, a-1 must be divisible by p
or 734 must be divisible by p.
Remainder = 0
Therefore, (a^4 - a^3 + a^2 - a) is divisible by p
which means, a^2(a^2 + 1) - a(a^2 + 1) is divisible by p
or, a(a-1)(a^2+1) is divisible by p
We also know that a(a^2+1) + 1 is divisible by p, which means that a(a^2+1) is not divisible by p
Therefore, a-1 must be divisible by p
or 734 must be divisible by p.
Remainder = 0
knight247 wrote:OA is A
