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# The integer a is greater than 1 and is not equal to the squ

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Founder
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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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Question Stats:

43% (02:43) correct 56% (01:30) wrong based on 125 sessions

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.

❑ $$\sqrt{a}$$

❑ $$a^2$$ $$- 1$$

❑ $$a^2$$ $$+ 1$$

❑ $$a^2$$ $$- a$$

❑ $$a^2$$ $$- 2a + 1$$

❑ $$2a$$
[Reveal] Spoiler: OA

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Director
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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

❑ $$2a$$

[Reveal] Spoiler: OA
E,F

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^2-a=a*(a-1) doesn't match witch x*x. D is also not correct.
a^2-2a+1=(a-1)(a-1)=(a-1)^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^2-a=a*(a-1) doesn't match witch x*x. D is also not correct.
a^2-2a+1=(a-1)(a-1)=(a-1)^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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Expert's post
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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Manager
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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^2-a=a*(a-1) doesn't match witch x*x. D is also not correct.
a^2-2a+1=(a-1)(a-1)=(a-1)^2 E is correct.
a could equal to 2. 2*2=2^2 F is correct

2*2-2*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
Expert's post
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
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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.
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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
Expert's post
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   [#permalink] 19 Jul 2020, 11:03
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