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# R is the set of positive odd integers less than 50, and S is

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Manager
Joined: 04 Feb 2011
Posts: 52
Location: US
R is the set of positive odd integers less than 50, and S is  [#permalink]

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08 Mar 2011, 05:52
3
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:13) correct 12% (01:00) wrong based on 268 sessions

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R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

(A) None
(B) Two
(C) Four
(D) Five
(E) Seven
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 742

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08 Mar 2011, 06:12
squares < 50 {1,4,9,16,25,36,49 }
S = {1,9,25,49}
R = {1,3,.....49}
Hence C.

Lolaergasheva wrote:
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A) None
(B) Two
(C) Four
(D) Five
(E) Seven
Math Expert
Joined: 02 Sep 2009
Posts: 51099

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08 Mar 2011, 06:18
1
gmat1220 wrote:
squares < 50 {1,4,9,16,25,36,49 }
S = {1,9,25,49}
R = {1,3,.....49}
Hence C.

Lolaergasheva wrote:
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A) None
(B) Two
(C) Four
(D) Five
(E) Seven

R is the set of positive odd integers less than 50: R={1, 3, 5, ..., 49}
S is the set of the squares of the integers in R: S={1^2, 3^2, 5^2, ..., 49^2}={1, 9, 25, 49, 81, 121, ..., 2401}

The intersection of R and S contains the odd perfect squares which are less than 50: 1^2=1, 3^2=29, 5^2=25, and 7^2=49.

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Intern
Joined: 17 Dec 2012
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21 Dec 2012, 18:38
1
simple question, but let's solve it in a GMAT way - with out writing any numbers/sets down

Given,
R is set of positive ODD integers < 50
S is set of squares of integers in R

now, we know that all numbers in R are ODD. square of an ODD number is ODD. the qtn is what are the ODD and PERFECT squares < 50. 1, 3,25, and 49...i hope you got what i mean and why i solved this in this way. This is a simple question but solving this question in this way would help us solve 700+ level questions.
Manager
Joined: 24 Jan 2013
Posts: 72
R is the set of positive odd integers less than 50, and S is  [#permalink]

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19 Mar 2013, 04:21
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?

A. None
B. Two
C. Four
D. Five
E. Seven
Math Expert
Joined: 02 Sep 2009
Posts: 51099
Re: R is the set of positive odd integers less than 50, and S is  [#permalink]

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19 Mar 2013, 04:23
johnwesley wrote:
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?

A. None
B. Two
C. Four
D. Five
E. Seven

Merging similar topics. Please refer to the solutions above.
_________________
Manager
Joined: 24 Jan 2013
Posts: 72
Re: R is the set of positive odd integers less than 50, and S is  [#permalink]

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19 Mar 2013, 04:26
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?

R=1,3,5,7,9,11,13,15...

S=1,9,25,49,81...

Numbers: 1, 9, 25, and 49 are odd integers (less than 50) that are in both sets.

Solution: Four

Director
Joined: 04 Jun 2016
Posts: 572
GMAT 1: 750 Q49 V43
Re: R is the set of positive odd integers less than 50, and S is  [#permalink]

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23 Jul 2016, 06:25
Lolaergasheva wrote:
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

(A) None
(B) Two
(C) Four
(D) Five
(E) Seven

R={1,3,5,7,9,11,13,15,17,19,21,..................49}
S={1,4,9,16,25,36,49................ 2401}

Common will only be
$$1^2=1$$
$$3^2=9$$
$$5^2=25$$
$$7^2=49$$

so four elements are common in both set

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Re: R is the set of positive odd integers less than 50, and S is  [#permalink]

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20 Aug 2018, 10:41
Lolaergasheva wrote:
R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

(A) None
(B) Two
(C) Four
(D) Five
(E) Seven

Since the a number’s square grows much faster than the number itself, let’s look at the odd perfect squares in S:

1^2 = 1, 3^2 = 9, 5^2 = 25, 7^2 = 49, 9^2 = 81, etc.

We see that, of the numbers in S, 1, 9, 25 and 49 are also in R, so R and S have 4 numbers in common.

_________________

Jeffery Miller

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Re: R is the set of positive odd integers less than 50, and S is &nbs [#permalink] 20 Aug 2018, 10:41
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