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

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by BTGmoderatorLU » Fri Feb 05, 2021 3:10 am
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Source: GMAT Prep

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

A. One
B. Two
C. Four
D. Five
E. Seven

The OA is C
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Re: R is the set of positive odd integers less than 50, and S is the set of squares of the integers in R. How many eleme

by Brent@GMATPrepNow » Fri Feb 05, 2021 7:21 am
BTGmoderatorLU wrote: ↑
Fri Feb 05, 2021 3:10 am
 Source: GMAT Prep

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

A. One
B. Two
C. Four
D. Five
E. Seven

The OA is C
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
Brent Hanneson - Creator of GMATPrepNow.com
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