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
TRUE?
This topic has expert replies
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
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
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- fibbonnaci
- MBA Student
- Posts: 403
- Joined: Tue Dec 22, 2009 7:32 pm
- Thanked: 98 times
- Followed by:22 members
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
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
-
- Senior | Next Rank: 100 Posts
- Posts: 35
- Joined: Tue Dec 22, 2009 9:26 am
- Thanked: 1 times
I'm not sure if I did something wrong.. but I tested with 5 and II and III were proven incorrect.
- fibbonnaci
- MBA Student
- Posts: 403
- Joined: Tue Dec 22, 2009 7:32 pm
- Thanked: 98 times
- Followed by:22 members
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!
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!
-
- Senior | Next Rank: 100 Posts
- Posts: 35
- Joined: Tue Dec 22, 2009 9:26 am
- Thanked: 1 times
- kevincanspain
- GMAT Instructor
- Posts: 613
- Joined: Thu Mar 22, 2007 6:17 am
- Location: madrid
- Thanked: 171 times
- Followed by:64 members
- GMAT Score:790
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
Also, each integer can be written as 3k - 1 , 3k, or 3k + 1
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
GMAT Instructor
Gmatclasses
Madrid