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Math Expert V
Joined: 02 Sep 2009
Posts: 58340
How many integers between 101 and 201 are equal to the square of some  [#permalink]

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Difficulty:   15% (low)

Question Stats: 79% (00:55) correct 21% (00:56) wrong based on 42 sessions

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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

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Manager  G
Joined: 05 Feb 2016
Posts: 168
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4999
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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
Intern  B
Joined: 28 Sep 2018
Posts: 29
Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4999
Location: India
Concentration: Sustainability, Marketing
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Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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 ;
Intern  B
Joined: 28 Sep 2018
Posts: 29
Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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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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.

Posted from my mobile device

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..
Intern  B
Joined: 28 Sep 2018
Posts: 29
Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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.

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Intern  B
Joined: 28 Sep 2018
Posts: 29
Re: How many integers between 101 and 201 are equal to the square of some  [#permalink]

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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.

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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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.

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

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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. Re: How many integers between 101 and 201 are equal to the square of some   [#permalink] 11 Feb 2019, 09:13
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