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

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Lolaergasheva
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R is the set of positive odd integers less than 50, and S is [#permalink] New post   08 Mar 2011, 06:52
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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
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C
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gmat1220
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Re: p/s sets [#permalink] New post   08 Mar 2011, 07:12
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
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Bunuel
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Re: p/s sets [#permalink] New post   08 Mar 2011, 07:18
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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.

Answer: C.
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Re: p/s sets [#permalink] New post   21 Dec 2012, 19:38
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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.
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johnwesley
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Re: R is the set of positive odd integers less than 50, and S is [#permalink] New post   19 Mar 2013, 05:26
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

Answer: C
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Re: R is the set of positive odd integers less than 50, and S is [#permalink] New post   23 Jul 2016, 07:25
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

ANSWER IS C
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Re: R is the set of positive odd integers less than 50, and S is [#permalink] New post   20 Aug 2018, 11:41
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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.

Answer: C
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Re: R is the set of positive odd integers less than 50, and S is [#permalink] New post   12 Apr 2020, 11:32
Bunuel wrote:
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.

Answer: C.


Hi Bunuel,

I think there is the typing mistake in the square of 3
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BrentGMATPrepNow
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Re: R is the set of positive odd integers less than 50, and S is [#permalink] New post   05 Feb 2021, 08:21
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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



So, we need to count all values that satisfy both conditions
In other words, we need to count all values that are BOTH odd integers less than 50 AND are squares of integers

Let's list possible values:
1² = 1 1 is less than 50....keep]
3² = 9 [9 is less than 50....keep]
5² = 25 [25 is less than 50....keep]
7² = 49 [49 is less than 50....keep]
9² = 81 [81 is NOT less than 50.... DON'T keep]

So, the values that satisfy both conditions are: 1, 9, 25, 49
Answer: C

Cheers,
Brent
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Re: R is the set of positive odd integers less than 50, and S is [#permalink] New post   21 Dec 2023, 18:26
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Re: R is the set of positive odd integers less than 50, and S is [#permalink]
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