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If n is an integer between 2 and 100 and if n is also the square of an
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23 Feb 2014, 07:51
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If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n? (1) n is even. (2) The cube root of n is an integer.
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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23 Feb 2014, 07:51
SOLUTIONIf n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?Given: n is a perfect square between 2 and 100 (a perfect square is an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square). (1) n is even > n can be any even perfect square in the given range: 4, 16, 36, ... Not sufficient. (2) The cube root of n is an integer > so n is also a perfect cube between 2 and 100. There are 4 perfect cubes in this range: 2^3=8, 3^3=27 and 4^3=64 but only one of them namely 64 is also a perfect square, so n=64=8^2=4^3. Sufficient. Answer: B.
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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24 Feb 2014, 00:23
If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is even. (2) The cube root of n is an integer.Sol: Given n= I^2 where I some integer and 2<n<100 or 2<I^2<100 St 1: n is even and only possible squares in the given range are for 4,6,8 which are 16,36, 64 respectively...So n can be 4,6 or 8. A and D ruled out St2: Cube root of n= a where " a " is an integer So Taking cube we get n=a^3.So n is a cube of an integer "a" but " a^3" should be between 2 and 100 so a^3=27 or 64. Since 2 (n=3 or 4) answers are there so not possible. Combining we get, n is even and cube root of n is an integer so only possible value of n=64 Ans is C
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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24 Feb 2014, 03:09
Option B From S1:2<n<100 and n is a square. =>n=4,9,16,25,36,49,64,81 According to S1:n=4,16,36,64.Not suff.
From S2:2<n<100 n=4,9,16,25,36,49,64,81 AND Cube root of n=integer Only possible for 64.Hence,Sufficient.



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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24 Feb 2014, 04:28
From the statement it states that 'n' is a square (of an integer) between 2 and 100. Thus the possible values of n are: 4,9,16,25,36,49,64,81.
Statement 1: n is even This leaves us with 4,16,36 and 64  Four values for n hence this statement is not sufficient
Statement 2: The cube root of n is an integer. Of all the values of n possible above only 64 has an integer cuberoot. Thus there is only 1 value of n. Hence it is sufficient
Thus answer is Option (B)



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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24 Feb 2014, 04:29
WoundedTiger wrote: If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is even. (2) The cube root of n is an integer.
Sol: Given n= I^2 where I some integer and 2<n<100 or 2<I^2<100
St 1: n is even and only possible squares in the given range are for 4,6,8 which are 16,36,64 respectively...So n can be 4,6 or 8. A and D ruled out
St2: Cube root of n= a where " a " is an integer So Taking cube we get n=a^3.So n is a cube of an integer "a" but " a^3" should be between 2 and 100 so a^3=27 or 64. Since 2 (n=3 or 4) answers are there so not possible.
Combining we get,
n is even and cube root of n is an integer so only possible value of n=64
Ans is C Bro 27 is not a square of an integer hence you cannot consider that



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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26 Feb 2014, 07:07
n is an integer between 2 and 100, n is also a square,what is n? 1) n is even  So n = 4,16,36,64 Not sufficient 2)Cube root of n is an integer. n =8,27,64 out of these only 64 is a square also. hence B is sufficient.
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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27 Feb 2014, 22:02
Best part of this question is the piece of sentence n is also the square of an integer It narrow downs the answer to 4,9,16,25,36,49,64,81 (between 2 and 100)
A.) n is even. As seen in the above list there are more than one even no. INSUFFICIENT B.) cube root of n is integer. Find the cube root of all above no. Only 64 yields an integer SUFFICIENT
Answer  B Difficulty  650



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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18 May 2014, 10:07
lets note down all the square numbers between 2 to 100. It won't be a pretty long list: 4, 9, 16, 25, 49, 64, 81, 100 1. N is even > We have several even values in our list. So definitely not A or D. It should be either B, D or E now 2. cube root f n is an integer > It indirectly says that the number in our list is also a cube of another integer. I can see just 64 as cube of 4 over here. Rest all numbers are not cube of any integer. Hence, B is sufficient.



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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20 Jul 2014, 03:38
Statement 1) n is even > could be 4, 16, 25 ... etc. not sufficient Statement 2) 3 variants: 8, 27 , 64 > cube root of 8 = 2 is not an square of an integer, same for 27; 64 is the only possible number.



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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13 Aug 2014, 09:05
What does cube root mean here?? For e.g if n is 16, does it mean that "sqroot(16^3)" is an integer, then its an integer. root of 64^3 is also an integer, and how are we assuming that cube root should also be in the range 2100. HELP!!!!!!



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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13 Aug 2014, 10:49
sunaimshadmani wrote: What does cube root mean here?? For e.g if n is 16, does it mean that "sqroot(16^3)" is an integer, then its an integer. root of 64^3 is also an integer, and how are we assuming that cube root should also be in the range 2100. HELP!!!!!! The cube root of n is an integer means \(\sqrt[3]{n}=integer\) > raise to the third power: \(n=integer^3\), so n is the cube of some integer: ..., 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, ... Since n is between 2 and 100 and it's also the square of an integer, then it can only be 64. Hope it's clear.
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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07 Dec 2017, 02:49
n: lies between 2 and 100, inclusive & is a perfect square.
So, the power of primes that n is made up of must be divisible by 2.
St.1: n is even : Insufficient n can be 4, 9, 16 and so on
St.2: cube root of n is an interger. This means that the power of primes that n is made up of must be divisible by 3.
So, the power of primes that n is made up of must be divisible by both 2 & 3 i.e. 6.
2 is the only prime number that has a value below 100 when raised to a power of 6.
Therefore, n= 2^6= 64.
So, Statement 2 is sufficient.
Hence, Ans B
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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07 Dec 2017, 03:25
Option B Already it has been given that n is the square of an integer or the square root of n is an integer. As per the second statement, n is also the cube root of an integer. Combining the info given in the question, we can conclude that the sixth root of n will also be an integer. Or n = sixth power of an integer. Only one such number , 64, exists within 2 to 100 range. Sent from my A1601 using GMAT Club Forum mobile app



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Re: If n is an integer between 2 and 100 and if n is also the square of an
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18 Jun 2019, 02:06
Bunuel wrote: SOLUTION
If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
Given: n is a perfect square between 2 and 100 (a perfect square is an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square).
(1) n is even > n can be any even perfect square in the given range: 4, 16, 36, ... Not sufficient.
(2) The cube root of n is an integer > so n is also a perfect cube between 2 and 100. There are 4 perfect cubes in this range: 2^3=8, 3^3=27 and 4^3=64 but only one of them namely 64 is also a perfect square, so n=64=8^2=4^3. Sufficient.
Answer: B. Bunuelbetween 2 and 100 should we include 2^3=8? They did not say inclusive.
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Re: If n is an integer between 2 and 100 and if n is also the square of an
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18 Jun 2019, 11:37
Bunuel wrote: SOLUTION
If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
Given: n is a perfect square between 2 and 100 (a perfect square is an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square).
(1) n is even > n can be any even perfect square in the given range: 4, 16, 36, ... Not sufficient.
(2) The cube root of n is an integer > so n is also a perfect cube between 2 and 100. There are 4 perfect cubes in this range: 2^3=8, 3^3=27 and 4^3=64 but only one of them namely 64 is also a perfect square, so n=64=8^2=4^3. Sufficient.
Answer: B. Hi BunuelShouldn't it be just 3 perfect cubes in this range? Thanks__
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