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The integer a is greater than 1 and is not equal to the squ [#permalink]
21 Jun 2017, 13:48
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The integer a is greater than 1 and is not equal to the square of an integer. Which of the following answer choices could potentially be equal to the square of an integer? Indicate all that apply. ❑ \(\sqrt{a}\) ❑ \(a^2\) \( 1\) ❑ \(a^2\) \(+ 1\) ❑ \(a^2\) \( a\) ❑ \(a^2\) \( 2a + 1\) ❑ \(2a\)
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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
12 Oct 2017, 02:04
Carcass wrote: The integer a is greater than 1 and is not equal to the square of an integer. Which of the following answer choices could potentially be equal to the square of an integer? Indicate all that apply. ❑ \(\sqrt{a}\) ❑ \(a^2\) – 1 ❑ \(a^2\) + 1 ❑ \(a^2\) – a ❑ \(a^2\) – 2a + 1 ❑ \(2a\) What's the best strategy here? I got the right answers but I decided to stop because I did not find examples for the other choices but it is not the best way to deal with it.



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
20 Feb 2018, 10:08
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What the question ask we find is x^2 which equals x*x. A is not a square of a number;thus a is also not a quadruple power of any number;therefore, sqrt a can not be x^2. A is not correct. Only the square of 0 and square of 1 and 1 is 1 away from each other;therefore B,C are not correct. a^2a=a*(a1) doesn't match witch x*x. D is also not correct. a^22a+1=(a1)(a1)=(a1)^2 E is correct. a could equal to 2. 2*2=2^2 F is correct



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
23 Feb 2018, 22:53
I don't understand why E is the correct answer. Maybe I don't clearly understand the question, but I used the plugging in method to solve this problem. I have a=2 and found that only 2a (F) works. hugebigmac wrote: What the question ask we find is x^2 which equals x*x. A is not a square of a number;thus a is also not a quadruple power of any number;therefore, sqrt a can not be x^2. A is not correct. Only the square of 0 and square of 1 and 1 is 1 away from each other;therefore B,C are not correct. a^2a=a*(a1) doesn't match witch x*x. D is also not correct. a^22a+1=(a1)(a1)=(a1)^2 E is correct. a could equal to 2. 2*2=2^2 F is correct



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
24 Feb 2018, 02:18
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You cannot pick two because the stem says: is not equal to the square of an integer. Which means 4 is the square of two so you cannot pick four. But is also true the other way around: cannot pick two as well. 6 and 8, for instance, are good numbers to pick. Hope this helps
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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
24 Feb 2018, 02:36
I see now what you mean. This type of question can be tricky because of the wording. Thanks Carcass wrote: You cannot pick two because the stem says: is not equal to the square of an integer.
Which means 4 is the square of two so you cannot pick four. But is also true the other way around: cannot pick two as well.
6 and 8, for instance, are good numbers to pick.
Hope this helps



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
24 Feb 2018, 09:58
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gremather wrote: I don't understand why E is the correct answer. Maybe I don't clearly understand the question, but I used the plugging in method to solve this problem. I have a=2 and found that only 2a (F) works. hugebigmac wrote: What the question ask we find is x^2 which equals x*x. A is not a square of a number;thus a is also not a quadruple power of any number;therefore, sqrt a can not be x^2. A is not correct. Only the square of 0 and square of 1 and 1 is 1 away from each other;therefore B,C are not correct. a^2a=a*(a1) doesn't match witch x*x. D is also not correct. a^22a+1=(a1)(a1)=(a1)^2 E is correct. a could equal to 2. 2*2=2^2 F is correct 2*22*2+1=1 which equals 1^2 so e is correct.



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
10 Apr 2018, 03:21
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E is the identity a^2  2*a*b + b^2 = (a  b)^2 where a is a and b is 1.
for b and c options, we can just see that no two squares are consecutive numbers, hence we can rule em out



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
11 Apr 2018, 19:35
Is plugging some integers only option to solve this? If yes then how do we decide which number to select.



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
12 Apr 2018, 05:58
If you follow the stem, then it is very clear. You have to pick a number > 1 and that is not a square of an integer. I.E 2 and 4 NO because they are square: 4 is the square of 2. 9 neither, is the square of 3. As such, 3 and 9 are out.. And so forth
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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
24 May 2018, 10:26
Carcass wrote: If you follow the stem, then it is very clear.
You have to pick a number > 1 and that is not a square of an integer.
I.E 2 and 4 NO because they are square: 4 is the square of 2.
9 neither, is the square of 3. As such, 3 and 9 are out..
And so forth 2 is not square of any integer. Then why can't we take 2?? Please clarify my doubt.



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
26 May 2018, 01:14
You cannot pick two because the stem says: is not equal to the square of an integer. Which means 4 is the square of two so you cannot pick four. But is also true the other way around: cannot pick two as well. 6 and 8, for instance, are good numbers to pick.
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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
11 Dec 2018, 17:37
I misunderstood the potentially part so I totally skipped F. IS there any other logical solutions besides plugging in?



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
12 Dec 2018, 04:20
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I think no in this specific case. However, that is me. Regards
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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
30 Apr 2019, 02:59
Carcass wrote: You cannot pick two because the stem says: is not equal to the square of an integer.
Which means 4 is the square of two so you cannot pick four. But is also true the other way around: cannot pick two as well.
6 and 8, for instance, are good numbers to pick. I am really sorry, but I still cant wrap my head around why 2 cannot be used. If we follow your advice then even 6 has a square 36. So I wouldn't pick both 36 and 6, in the same way I wouldn't pick 4 and 2. OP says "is not equal to the square of an integer"  2 is the square of ~1.414, which is a non integer. "Which means 4 is the square of two so you cannot pick four. But is also true the other way around: cannot pick two as well."  this is true for any integer, because any integer will have some square (which is itself an integer). I am confused about the other way round part.



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
01 May 2019, 11:36
On the number line if you do list the numbers > 1 2,3,4,5,6,7,8,9,10,11,12,13,14,.............. 4 is the natural square of 2 However, 5 is NOT a square of any number 6 as well 7 as well 8 as well 9 yes, is the square of 3 Hope this helps
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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
13 Jun 2019, 12:19
If we pick 5 then 2a = 10 > which wont be the square of an integer. But the OA says E and F both.



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Re: The integer a is greater than 1 and is not equal to the squ [#permalink]
19 Jul 2020, 11:03
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If you can't use 2 (which I don't understand, I think you can use 2 as the stem says N>1 and not a square of a number, which would not rule out 2), you have to go all the way up to 18 to find 2a = 36, which is 6*6, therefore F is also correct




Re: The integer a is greater than 1 and is not equal to the squ
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19 Jul 2020, 11:03





