GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 May 2020, 02:54

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the remainder when (a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)

Author Message
TAGS:

### Hide Tags

SVP
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
What is the remainder when (a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)  [#permalink]

### Show Tags

02 Apr 2020, 04:03
4
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:47) correct 50% (01:53) wrong based on 24 sessions

### HideShow timer Statistics

What is the remainder when $$(a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)^2 + (a + 6)$$ is divided by $$(a + 3)$$, for any 2 digit number $$a$$?

A. 0
B. 1
C. 3
D. 5
E. 7
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3990
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
What is the remainder when (a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)  [#permalink]

### Show Tags

02 Apr 2020, 04:23
2
Dillesh4096 wrote:
What is the remainder when $$(a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)^2 + (a + 6)$$ is divided by $$(a + 3)$$, for any 2 digit number $$a$$?

A. 0
B. 1
C. 3
D. 5
E. 7

When (a + 2) is divided by (a+3) then remainder is -1

i.e. When $$(a + 2)^5$$ is divided by (a+3) then remainder is $$(-1)^5 = -1$$

i.e. When $$(a + 3)^4$$ is divided by (a+3) then remainder is $$0$$

i.e. When $$(a + 4)^3$$ is divided by (a+3) then remainder is $$(1)^3 = 1$$

i.e. When $$(a + 5)^2$$ is divided by (a+3) then remainder is $$(2)^2 = 4$$

i.e. When $$(a + 6)$$ is divided by (a+3) then remainder is $$3$$

Final Remainder = -1+0+1+4+3 = 7

The concept video of remainder theorem is as follows:

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes l Classroom Coaching l On-demand Quant course
Check website for most affordable Quant on-Demand course 2000+ Qns (with Video explanations)
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
GMATWhiz Representative
Joined: 07 May 2019
Posts: 700
Location: India
Re: What is the remainder when (a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)  [#permalink]

### Show Tags

02 Apr 2020, 05:09
2
Dillesh4096 wrote:
What is the remainder when $$(a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)^2 + (a + 6)$$ is divided by $$(a + 3)$$, for any 2 digit number $$a$$?

A. 0
B. 1
C. 3
D. 5
E. 7

Solution:

Since, we can see that there are no options such as "Cannot be determined", it would be safe to assume that the answer will be same for any 2-digit number "a"
o So, let's assume a as 17. (Since a + 3 = 20 and it may make our calculation easy).
o Now, $$a + 2 = 19$$
 Remainder when $$19^5$$ is divided by $$20 = -1^5 = -1$$
o Now, $$a+ 3 = 20$$
 Remainder when $$20^4$$ is divided by $$20 = 0$$
o Now, $$a + 4 = 21$$
 Remainder when $$21^3$$ is divided by $$20 = 1^3 = 1$$
o Now, $$a + 5 = 22$$
 Remainder when $$22^2$$ is divided $$20 = 2^2 = 4$$
o Now, $$a + 6 = 23$$
 Remainder when 23 is divided $$20 = 3$$
o Remainder when given expression is divided by $$a + 3 = -1 + 0 +1 +4+3 = 7$$.
Hence, the correct answer is Option E.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Senior Manager
Joined: 14 Oct 2019
Posts: 404
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: What is the remainder when (a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)  [#permalink]

### Show Tags

02 Apr 2020, 05:55
[(a+2)^5+(a+3)^4+(a+4)^3+(a+5)^2+(a+6)]/ (a+3)
or, (a+2)^5/ (a+3) +(a+3)^4/ (a+3)+(a+4)^3/ (a+3)+(a+5)^2/ (a+3)+(a+6)/ (a+3)
now, 1st term will give -1 rem
2nd term will give 0 rem
3rd term will give +1 rem
4th term will give (+2)^2 rem
5th term will give +3 rem

so the actual remainder will be 4+3 =7

Re: What is the remainder when (a + 2)^5 + (a + 3)^4 + (a + 4)^3 + (a + 5)   [#permalink] 02 Apr 2020, 05:55