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

Redeem

number properties (720+ level question)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Mon Dec 13, 2010 9:09 pm
IMO A.

This might be a 720+ problem if we need to solve it arithmetically. If we plugin, it should be simple.

if k^2 has to end in 4, k has to end in either 2 or 8
if (k+1)^2 has to end in 1, k+1 has to end in 1 or 9

Let us say k=2,
k+1 =3 will not end in 1 or 9
hence k cant be 2

Let us say k=8,
k+1 = 9 ends in 9

Hence k+2 = 10
(k+2)^2 = 100 will end in 0

pick A.
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Master | Next Rank: 500 Posts
Posts: 437
Joined: Sat Nov 22, 2008 5:06 am
Location: India
Thanked: 50 times
Followed by:1 members
GMAT Score:580

by beat_gmat_09 » Mon Dec 13, 2010 9:10 pm
Numbers that satisfy the conditions have 8 as their units digit, Number+1 has 9 as its units digit which when squared gives 1 at the units digit. Numbers can be - 8 : 8^2 = 64, (8+1)^2 81 units digit 1 (8+2)^2 100 units digit 0.
Other number that satisfies:18, (18+2)^2 = 400 units digit 0.
Option A.
Hope is the dream of a man awake
Top
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Mon Dec 13, 2010 9:15 pm
arithmetically:

(k+1)^2 = k^2 + 2k +1
if k^2 ends in 4, k will end in 2 or 8
hence 2k will end in 4 or 6

representing last digit as LD
LD(k+1)^2 = LD(4)+LD(4)+1 = LD(9)
9 cannot equal 1.

LD(k+1)^2 = LD(4)+LD(6)+1 = LD(1)
Hence satisfied.
Hence k will end in 8.

(K+2)^2 = k^2 + 4k + 4
LD(k+2)^2 = LD(4)+2*LD(6)+4 = LD(4)+LD(2)+4 = LD(0)

Hence last digit is 0.

Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Dec 13, 2010 9:40 pm
thank you guys, below is my solution took around 60 sec
k^2=... 4
(k+1)^2= ... 1 <=> k^2+2k+1= ... 1 <=> 2(k^2+2k+1)= ... 2
(k+2)^2= ... ? <=> k^2+4k+4= ... ? <=> ...2+2-...4= ...0
Top
Legendary Member
Posts: 537
Joined: Fri Jan 22, 2010 10:06 pm
Thanked: 14 times
Followed by:1 members

by frank1 » Tue Dec 14, 2010 12:47 am
It should be A

initially i thought there was some trap as it was labelled 720+

any way is it?
GMAT score is equally counted as your GPA and 78 clicks can change you life.
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Tue Dec 14, 2010 1:56 am
frank1 wrote:It should be A

initially i thought there was some trap as it was labelled 720+

any way is it?
yes Frank, this comes to be 720+ or level 7 question in Gmat Hacks challenge set for number properties;

as you, I am also discouraged with many problems in this set- I simply find them easy...
may be test has trained us to be monsters
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 181
Joined: Fri Sep 04, 2009 12:06 pm
Thanked: 17 times
Followed by:1 members

by ikaplan » Tue Dec 14, 2010 7:16 am
I listed all digits from 1-9 and squared them- it turned out that both 2 and 8 satisfy the first condition (k^2=4).

Then I plugged in 2 and 8 into the second condition- (k+1)^2=1 and only 8 satisfied the condition (so 2 is out).

Lastly, I plugged in 8 into (k+2)^2 ---> (8+2)^2=100 so

IMO- A is the correct choice
"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."
Top
Legendary Member
Posts: 537
Joined: Fri Jan 22, 2010 10:06 pm
Thanked: 14 times
Followed by:1 members

by frank1 » Tue Dec 14, 2010 7:59 am
Night reader wrote:
yes Frank, this comes to be 720+ or level 7 question in Gmat Hacks challenge set for number properties;

as you, I am also discouraged with many problems in this set- I simply find them easy...
may be test has trained us to be monsters
yup i agree
and may be another thing is in exam scenario or under timed condition,the difficulty of the question depends upon several factors..
i have experience of making error in even simple question when i was running for time or i have very limited time to finish test
or when i was not confident of earlier question....
so i think these are all reasons which makes gmat difficult
otherwise if they allow 4-5 hours to solve thing i feel there will be many 770+ people...
just what i feel

best of luck with you preparation

i agree when i first look at the things question stem seems intimidating as we feel it may require lot of calculations
GMAT score is equally counted as your GPA and 78 clicks can change you life.
Top
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Sat Nov 06, 2010 12:04 pm

by Woozler » Tue Dec 14, 2010 9:22 am
I am mediocre at quant and horrid at number properties, yet I solved it by just plugging in all even numbers (2, 4, 6, 8) and then added one to them. 8 is the only one that worked, therefore (A)

Is this really a 720+ level problem? I wouldn't have been able to solve it if it really were. I score 46-49 on quant sections.
Top
Post new topic Post Reply
• Page 1 of 1