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1000PS: Section 4 Question 13

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Intern
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1000PS: Section 4 Question 13 [#permalink] New post 16 Mar 2011, 09:02
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

73% (01:29) correct 27% (00:30) wrong based on 11 sessions
Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?
(A) 75
(B) 42
(C) 32
(D) 25
(E) 12



I have no clue as to how to attempt this question. Can someone help me out :(
[Reveal] Spoiler: OA
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Re: 1000PS: Section 4 Question 13 [#permalink] New post 16 Mar 2011, 09:11
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Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?
(A) 75
(B) 42
(C) 32
(D) 25
(E) 12
******************
Prime factorization
75 = 5*5*3 = 5^2*3. Includes a perfect square 25
42 = 7*6 = 7*3*2. We got our candidate. No perfect squares here.
32 = 2^5 = 4^2*2. Includes a perfect square 4
25 = 5^2. Perfect square 25
12 = 2^2*3 = Perfect square 4.

All but 42 have perfect square in them as a factor.
*******************************************

Just write down all perfect squares greater than 1 and less than 75;
4,9,16,25,36,49,64

75 = 25*3. 25 is a perfect square
42 = 7*2*3. No perfect squares here
32 = 16*2. 16 is a perfect square
25. 25 is a perfect square
12 = 4*3. 4 is a perfect square

Ans: "B"
*********************************

I guess this is also somewhere else in the forum.
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Re: 1000PS: Section 4 Question 13 [#permalink] New post 17 Mar 2011, 00:44
The answer is B, all other choices have square of an integer > 1 as a factor.
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Re: 1000PS: Section 4 Question 13 [#permalink] New post 21 Apr 2011, 16:25
Answer is B.

thats the only integer which doesnt have an integer divisor>1 and also a square of other integer.
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Re: 1000PS: Section 4 Question 13 [#permalink] New post 21 Apr 2011, 17:58
Acer86 wrote:
Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?
(A) 75
(B) 42
(C) 32
(D) 25
(E) 12



I have no clue as to how to attempt this question. Can someone help me out :(

Converting the choices does the trick. Ans. B
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Re: 1000PS: Section 4 Question 13 [#permalink] New post 22 Apr 2011, 09:31
Correct Answer B

All others have square whose integer is greater than 1
Re: 1000PS: Section 4 Question 13   [#permalink] 22 Apr 2011, 09:31
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