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

Redeem

TRUE?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

TRUE?

by sanju09 » Fri Mar 05, 2010 6:21 am
Which of the following is/are TRUE?

I. If a number has n digits, then its square will have 2 n or 2 n - 1 digit(s).
II. A square number can always be written in the form 3 n or 3 n + 1, where n is any non-negative integer.
III. A square number can always be written in the form 4 n or 4 n + 1, where n is any non-negative integer.

(A) I only
(B) II & III only
(C) I & III only
(D) I & II only
(E) I, II, & III
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Tue Mar 02, 2010 4:27 am
Thanked: 2 times

by yeahdisk » Fri Mar 05, 2010 7:34 am
I would go for C although I'm not sure of an algebraic proof? Is there one?
Top
User avatar
MBA Student
Posts: 403
Joined: Tue Dec 22, 2009 7:32 pm
Thanked: 98 times
Followed by:22 members

by fibbonnaci » Fri Mar 05, 2010 7:49 am
I tried to solve this question by picking numbers.

I. lets say number - 5 (n= 1) 25 (n= 2)
- 13 (n=2) 169 (n=3) => (2n-1 digits)
Satisfies

II. lets consider the same numbers. 25 can be written as 3*8 +1
Similarly even 169 can be written in the form of 3n +1. You can check for any square number, you will see it satisfies this criteria.

III. say 25 can be written as 4*6 + 1
similarly you can check for other square numbers also. You will find it satisfies the criteria.

So my take is E
Top
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Tue Mar 02, 2010 4:27 am
Thanked: 2 times

by yeahdisk » Fri Mar 05, 2010 7:59 am
I think I agree with you
Top
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Fri Mar 05, 2010 9:02 am

by sharuvman » Fri Mar 05, 2010 9:24 am
II. would fail if n =2,
3n+1 = 7 which is not a square number

III. would fail if n = 1,
4n+1 = 5 which is again not a square number

I. Is always true
Top
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Tue Dec 22, 2009 9:26 am
Thanked: 1 times

by camilaross » Fri Mar 05, 2010 11:37 am
I'm not sure if I did something wrong.. but I tested with 5 and II and III were proven incorrect.
Top
User avatar
MBA Student
Posts: 403
Joined: Tue Dec 22, 2009 7:32 pm
Thanked: 98 times
Followed by:22 members

by fibbonnaci » Fri Mar 05, 2010 11:40 am
note the term 'n' in I is different from II and III
In I, 'n' denotes the number of digits, which is not the case in II and III.
Also in II, we are talking about squared numbers. 5 is not a square number. 25 is a square of number 5, so we can call 25 to be square number

Hope this helps!
Top
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Tue Dec 22, 2009 9:26 am
Thanked: 1 times

by camilaross » Fri Mar 05, 2010 11:57 am
yeah.. I see it.... thanks!
Top
User avatar
GMAT Instructor
Posts: 613
Joined: Thu Mar 22, 2007 6:17 am
Location: madrid
Thanked: 171 times
Followed by:64 members
GMAT Score:790

by kevincanspain » Fri Mar 05, 2010 12:33 pm
Note that each integer can be written as 2k or 2k + 1


Also, each integer can be written as 3k - 1 , 3k, or 3k + 1
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
Top
Post new topic Post Reply
• Page 1 of 1