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# If n is an integer between 2 and 100 and if n is also the

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Joined: 29 Jan 2011
Posts: 2
Location: New York City
Schools: Harvard, Stanford, Wharton, NYU, Columbia
If n is an integer between 2 and 100 and if n is also the  [#permalink]

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08 Mar 2011, 14:26
7
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:36) correct 43% (01:31) wrong based on 457 sessions

### HideShow timer Statistics

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

My thoughts
n is an integer between 2 and 100... (keep reading von, don't make a careless error because you prematurely solved the problem without reading the question) ... and n is the square of an integer so let's make a chart and test values:

integer.....n.........2<n<100?
1.............1.........NO
2.............4.........YES
3.............9.........YES
4.............16.......YES
5.............25.......YES
6.............36.......YES
7.............49.......YES
8.............64.......YES
9.............81.......YES
10...........100.......NO

So n could be 4, 9, 16, 25, 36, 49, 64, or 81 since each of these values represent the square of an integer between 2 and 100 exclusive.

(1)n is even
Well from my above chart, we can see at least two unique values for n when n is even, (For example: 16 and 36); therefore, this statement is insufficient to answer the question because it can have more than one value. In my answer grid I eliminated ADBCE
(2)the cube root of n is an integer
Make a chart again:

n..............$$\sqrt[3]{n}$$
8................2
27..............3

So $$\sqrt[3]{n}$$ could give you different values depending on the value of n; therefore, this statement is insuffcient as well because it yields more than one answer for n. ADBCE
Combining statements (1) and (2) together I got the following table:

n..............$$\sqrt[3]{n}$$
8................2
27...............3
64...............4

So we see that n is even per statement (1) and the cube root of n is an integer for 8, 27, and 64; thus there three possible values for n; thus statements (1) and (2) together are not sufficent to answer the question. ADBCE; therefore, the answer must be E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-n-is-an-i ... 67846.html
Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: If n is an integer between 2 and 100 and if n is also the  [#permalink]

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08 Mar 2011, 14:37
2
2
von wrote:
110 Quant2nd Edition

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

My thoughts
n is an integer between 2 and 100... (keep reading von, don't make a careless error because you prematurely solved the problem without reading the question) ... and n is the square of an integer so let's make a chart and test values:

integer.....n.........2<n<100?
1.............1.........NO
2.............4.........YES
3.............9.........YES
4.............16.......YES
5.............25.......YES
6.............36.......YES
7.............49.......YES
8.............64.......YES
9.............81.......YES
10...........100.......NO

So n could be 4, 9, 16, 25, 36, 49, 64, or 81 since each of these values represent the square of an integer between 2 and 100 exclusive.

(1)n is even
Well from my above chart, we can see at least two unique values for n when n is even, (For example: 16 and 36); therefore, this statement is insufficient to answer the question because it can have more than one value. In my answer grid I eliminated [strike]AD[/strike]BCE
(2)the cube root of n is an integer
Make a chart again:

n..............$$\sqrt[3]{n}$$
8................2
27..............3

So $$\sqrt[3]{n}$$ could give you different values depending on the value of n; therefore, this statement is insuffcient as well because it yields more than one answer for n. [strike]ADB[/strike]CE
Combining statements (1) and (2) together I got the following table:

n..............$$\sqrt[3]{n}$$
8................2
27...............3
64...............4

So we see that n is even per statement (1) and the cube root of n is an integer for 8, 27, and 64; thus there three possible values for n; thus statements (1) and (2) together are not sufficent to answer the question. [strike]ADBC[/strike]E; therefore, the answer must be .

When considering the second statement you forgot that n must also be a perfects square.

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.

_________________
Director
Joined: 01 Feb 2011
Posts: 658
Re: If n is an integer between 2 and 100 and if n is also the  [#permalink]

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08 Mar 2011, 17:44
1

squares between 2 and 100 -

4 9 16 25 36 49 64 81

1. is not sufficient
as n could be 4,16,36...
2. n is also a cube, only cube we have here is 64 which is 4 ^3. Sufficient
Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: If n is an integer between 2 and 100 and if n is also the  [#permalink]

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25 Mar 2018, 09:25
von 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

My thoughts
n is an integer between 2 and 100... (keep reading von, don't make a careless error because you prematurely solved the problem without reading the question) ... and n is the square of an integer so let's make a chart and test values:

integer.....n.........2<n<100?
1.............1.........NO
2.............4.........YES
3.............9.........YES
4.............16.......YES
5.............25.......YES
6.............36.......YES
7.............49.......YES
8.............64.......YES
9.............81.......YES
10...........100.......NO

So n could be 4, 9, 16, 25, 36, 49, 64, or 81 since each of these values represent the square of an integer between 2 and 100 exclusive.

(1)n is even
Well from my above chart, we can see at least two unique values for n when n is even, (For example: 16 and 36); therefore, this statement is insufficient to answer the question because it can have more than one value. In my answer grid I eliminated ADBCE
(2)the cube root of n is an integer
Make a chart again:

n..............$$\sqrt[3]{n}$$
8................2
27..............3

So $$\sqrt[3]{n}$$ could give you different values depending on the value of n; therefore, this statement is insuffcient as well because it yields more than one answer for n. ADBCE
Combining statements (1) and (2) together I got the following table:

n..............$$\sqrt[3]{n}$$
8................2
27...............3
64...............4

So we see that n is even per statement (1) and the cube root of n is an integer for 8, 27, and 64; thus there three possible values for n; thus statements (1) and (2) together are not sufficent to answer the question. ADBCE; therefore, the answer must be E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-n-is-an-i ... 67846.html
_________________
Re: If n is an integer between 2 and 100 and if n is also the &nbs [#permalink] 25 Mar 2018, 09:25
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