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Intern  Joined: 04 Feb 2011
Posts: 48
Location: US
R is the set of positive odd integers less than 50, and S is  [#permalink]

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3 00:00

Difficulty:   5% (low)

Question Stats: 86% (01:14) correct 14% (01:01) wrong based on 295 sessions

### HideShow timer Statistics 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: 704

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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 V
Joined: 02 Sep 2009
Posts: 56371

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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
Posts: 4

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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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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 V
Joined: 02 Sep 2009
Posts: 56371
Re: R is the set of positive odd integers less than 50, and S is  [#permalink]

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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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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  B
Joined: 04 Jun 2016
Posts: 562
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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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

_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2821
Re: R is the set of positive odd integers less than 50, and S is  [#permalink]

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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.

_________________

# Jeffrey Miller

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: R is the set of positive odd integers less than 50, and S is   [#permalink] 20 Aug 2018, 11:41
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# R is the set of positive odd integers less than 50, and S is  