Problem Solving

Hi All,

We're told that R is the set of positive ODD integers LESS than 50, and S is the set of the SQUARES of the integers in R. We're asked for the number of elements that are in BOTH R and S. This question is built around some basic Arithmetic and note taking.

To start, I'm going to list the first several terms in Set R: 1, 3, 5, 7, 9, 11....47, 49
The corresponding values in Set S would then be: 1, 9, 25, 49, 81, 121...

As the numbers in Set R increase, the corresponding values in Set S will increase even faster (since we're SQUARING the terms in Set R), so there's really no need to any additional work beyond what's already been done (NONE of those larger values in Set S will be in Set R, since the numbers in Set R are all LESS than 50).

The numbers that appear in BOTH Sets are: 1, 9, 25 and 49 --> 4 total terms.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

swerve 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 as S contain?

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

How many elements does the intersection of R as S contain?
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 the 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

swerve 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 as 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