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How many integers between 101 and 201 are equal to the square of some

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How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 06 Feb 2019, 23:58
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A
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:09
Bunuel wrote:
How many integers between 101 and 201 are equal to the square of some integer ?

A. Two
B. There
C. Four
D. Five
E. Six


Four integers \(11^2,12^2,13^2,14^2\)
C
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:09
Bunuel wrote:
How many integers between 101 and 201 are equal to the square of some integer ?

A. Two
B. There
C. Four
D. Five
E. Six


101 to 201
square integers =
121,144,169,196
IMO C
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:15
1
Just wanted to know... Of eight was in the option what would be the answer?

Because the square of a negative number would also give us the same value.

Eg- 11^2 = -11^2

Thus there would be 8 integer values that would give us values between 101 and 201

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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:19
Hoozan wrote:
Just wanted to know... Of eight was in the option what would be the answer?

Because the square of a negative number would also give us the same value.

Eg- 11^2 = -11^2

Thus there would be 8 integer values that would give us values between 101 and 201

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Hoozan
rang given is 101 to 201 ; which is +ve ;
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:25
How many integers between 101 and 201 are equal to the square of some integer ?


Set = (101,102..200)

Now we are asked to find integers that are square of some integer

Thus we can narrow the set to
121,144,169 and 196

Thus the question is asking us to find the integers whose square value is in the above set

I.e... 11^=-11^= 121

The question has given us a range of n^2 and not of n

Which means n could be +ve or -ve.

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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:30
1
Hoozan wrote:
How many integers between 101 and 201 are equal to the square of some integer ?


Set = (101,102..200)

Now we are asked to find integers that are square of some integer

Thus we can narrow the set to
121,144,169 and 196

Thus the question is asking us to find the integers whose square value is in the above set

I.e... 11^=-11^= 121

The question has given us a range of n^2 and not of n

Which means n could be +ve or -ve.

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Hoozan

My understanding of question is:


question has asked for " see bold"

How many integers between 101 and 201 are equal to the square of some integer ?

so those integers values are only 4 , even if the square is either -ve or +ve..
question isnt asking for the no of integers who have a square between 101 to 201... in that case 8 would be correct..
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 00:45
How many integers between 101 and 201 are equal to the "square of some integer"

Notice the word Square of SOME INTEGER

my understanding is N^2 lies in the given range and we need to find the number of values that satisfies

101<=N^2<=201

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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 02:21
Bunuel wrote:
How many integers between 101 and 201 are equal to the square of some integer ?

A. Two
B. There
C. Four
D. Five
E. Six


Look for the closest perfect square less than 101. It is 100 (which is 10^2).
The greatest perfect square more than 201 is 225 (15^2)

So 11^2 = 121, 12^2 = 144, 13^2 = 169 and 14^2 = 196 lie in the given range.

Hence, 121, 144, 169 and 196 are the four integers between 101 and 201 which are square of some integers.
Note that 121 is the square of two integers (11 and -11). Still, it will be counted once only because both squared give 121 only. Even if 121 is the square of 2 different numbers, still it can be counted only once.


Answer (C)
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 07 Feb 2019, 02:26
VeritasKarishma wrote:
Bunuel wrote:
How many integers between 101 and 201 are equal to the square of some integer ?

A. Two
B. There
C. Four
D. Five
E. Six


Look for the closest perfect square less than 101. It is 100 (which is 10^2).
The greatest perfect square more than 201 is 225 (15^2)

So 11^2 = 121, 12^2 = 144, 13^2 = 169 and 14^2 = 196 lie in the given range.

Hence, 121, 144, 169 and 196 are the four integers between 101 and 201 which are square of some integers.
Note that 121 is the square of two integers (11 and -11). Still, it will be counted once only because both squared give 121 only. Even if 121 is the square of 2 different numbers, still it can be counted only once.


Answer (C)



So if the answer choice had eight we would still go with 4?

Because though 11 and -11 give 1 value i.e 121 we have 2 different integers which give us 121

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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 10 Feb 2019, 07:50
Bunuel wrote:
How many integers between 101 and 201 are equal to the square of some integer ?

A. Two
B. There
C. Four
D. Five
E. Six


The perfect squares between 101 and 201 are 121, 144, 169, and 196, which are 11^2, 12^2, 13^2, and 14^2, respectively.

Answer: C
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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New post 11 Feb 2019, 08:13
Bunuel wrote:
How many integers between 101 and 201 are equal to the square of some integer ?

A. Two
B. There
C. Four
D. Five
E. Six



between 101 and 201

\(121 = 11^2\)

\(196 = 14^2\)

11 , 12 , 13 , 14.

4 integers.

C is the correct answer.
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Re: How many integers between 101 and 201 are equal to the square of some   [#permalink] 11 Feb 2019, 08:13
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