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

Question

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

gmat1220 · Answer

squares < 50 {1,4,9,16,25,36,49 }
S = {1,9,25,49}
R = {1,3,.....49}
Hence C.

Bunuel · Answer

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.

muralilawson · Answer

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.

johnwesley · Answer

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

LogicGuru1 · Answer

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

JeffTargetTestPrep · Answer

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

Farina · Answer

Hi Bunuel,

I think there is the typing mistake in the square of 3

BrentGMATPrepNow · Answer

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

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=ALrzKxkGSWQ Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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

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