GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 06:53

### 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

# For some integer q, q^2 - 5 is divisible by all of the follo

Author Message
TAGS:

### Hide Tags

GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8124
Location: Pune, India

### Show Tags

Updated on: 08 Jan 2011, 21:17
4
3
dimitri92 wrote:
For some integer q, q^2 - 5 is divisible by all of the following EXCEPT
(A) 29
(B) 30
(C) 31
(D) 38
(E) 41

The way I would approach this question:

So q^2 - 5 is divisible by all of the following except:
29, 31, 41 - big prime numbers, don't know any divisibility rules for these, forget them for the time being.. 38 = 19*2. (q^2 - 5) can be divisible by 2 (e.g. when q^2 ends with a 5, q^2 - 5 ends with a 0). As for 19, again a big prime number. Leave it for the time being.

(If the question is anywhere close to an actual GMAT question, they will not expect you to do many calculations with 29, 31, 41 etc. I see these big prime numbers and am quite convinced that they are just a smokescreen.Try and focus on what they could ask you like divisibility by 2, 3 etc. )

As for 30, q^2 - 5 is divisible by 10 (using the logic shown above). What about 3?
$$q^2 - 5 = q^2 - 1 - 4 = (q - 1)(q + 1) - 4$$
In any 3 consecutive numbers, (e.g. $$(q - 1), q, (q + 1)$$), one and only one number will be divisible by 3.
If either (q - 1) or (q + 1) is divisible by 3, (q - 1)(q + 1) is divisible by 3, which means $$(q - 1)(q + 1) - 4$$ cannot be divisible by 3. If q is divisible by 3, then q^2 will be divisible by 3 and q^2 - 5[/m] will not be divisible by 3.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Originally posted by KarishmaB on 08 Jan 2011, 21:10.
Last edited by KarishmaB on 08 Jan 2011, 21:17, edited 1 time in total.
Director
Joined: 04 Jun 2016
Posts: 607
GMAT 1: 750 Q49 V43
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink]

### Show Tags

26 Jul 2016, 05:10
dimitri92 wrote:
$$q^2-5=( q^2-1) +4$$
= ( q+1) (q-1) +4

ummmm.. shouldn't $$q^2-5=( q^2-1)$$-4 ?????
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8124
Location: Pune, India
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink]

### Show Tags

26 Jul 2016, 23:32
LogicGuru1 wrote:
dimitri92 wrote:
$$q^2-5=( q^2-1) +4$$
= ( q+1) (q-1) +4

ummmm.. shouldn't $$q^2-5=( q^2-1)$$-4 ?????

Yes, it should be.
Check: for-some-integer-q-q-2-5-is-divisible-by-all-of-the-follo-94414-20.html#p848986
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Manager
Joined: 04 Aug 2015
Posts: 82
Location: India
GMAT 1: 700 Q50 V35
GPA: 3.39
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink]

### Show Tags

04 Sep 2017, 17:18
Bunuel wrote:
dimitri92 wrote:
For some integer q, q^2 - 5 is divisible by all of the following EXCEPT
(A) 29
(B) 30
(C) 31
(D) 38
(E) 41

Hint: q^2-5 (q is an integer) is never multiple of 3 (try to prove this), hence 30 is out.

A) 29 - Prime
B) 30 - 2 * 3 * 5
C) 31 - Prime
D) 38 - 2 * 19
E) 41 - Prime

1) 2

Remainder when 5/2 is 1. And, perfect squares such as 81 produce remainder 1 when divided by 2. Thus, the overall remainder (1-1) is 0. 2 might divide. Park aside.

2) 3

Remainder when 5/3 is 2. The perfect squares when divided by 3, produce either 0 or 1 remainder.
Case 1) When the remainder is 0
The remainder value of the expression is 0-2 = -2. Not divisible by 3

Case 2) When the remainder is 1
The remainder value of the expression is 1-2 = -1. Not divisible by 3

Thus, the expression will not be divisible by 3 or any multiple of it. Thus, option B.
Manager
Joined: 04 May 2014
Posts: 162
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink]

### Show Tags

10 Sep 2017, 20:43
Since could not think of any other way used brute force to solve the question. it can be done in 2 mins.

The Min no is 29 hence we can start squaring from 6 onwards.
6²=36-5=31-C is out.
7²=49-5=44
8²=64-5=59
9²=81-5=76-D is out(38*2=76)
10²=100-5=95
11²=121-5=116-A is out (units digit is 6 try 29*4=116)
12²=144-5=139
13²=169-5=164-E is out(41*4=164)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2669
Re: For some integer q, q^2 - 5 is divisible by all of the follo [#permalink]

### Show Tags

14 Sep 2017, 10:42
dimitri92 wrote:
For some integer q, q^2 - 5 is divisible by all of the following EXCEPT

(A) 29
(B) 30
(C) 31
(D) 38
(E) 41

We need to find the answer choice that does not divide 5 less than a perfect square. Let’s analyze each answer choice:

A) 29

Since 11^2 - 5 = 116, which is divisible by 29, answer A is not correct.

B) 30

It doesn’t seem that we can find an integer q such that q^2 - 5 is divisible by 30. However, let’s make sure we can find an integer q such that q^2 - 5 is divisible by 31, 38, and 41.

C) 31

Since 6^2 - 5 = 31, which is divisible by 31, answer C is not correct.

D) 38

Since 9^2 - 5 = 76, which is divisible by 38, answer D is not correct.

E) 41

Since 13^2 - 5 = 164, which is divisible by 41, answer E is not correct.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: For some integer q, q^2 - 5 is divisible by all of the follo   [#permalink] 14 Sep 2017, 10:42

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.