If R is the set of all numbers that, when squared, have a units digit

Question

If R is the set of all numbers that, when squared, have a units digit of 1 or 9, then which of the following must be true about set R?

I. All members of R are prime.

II. If N is a member of R, –N is a member of R.

III. If N is a member of R, N^2 is a member of R.

A. I only
B. II only
C. I and II only
D. II and III only 
E. I, II, and III

jppresa · Answer

OE

Since there are unknown values in the question stem and the question asks what “must be true,” this is a Plug In Twice problem. First, Plug In values that have a units digit of 1 or 9 when squared. Set R could contain the elements 1, 3, 7, and 9 since 12 is 1, 32 is 9, 72 is 49, and 92 is 81. Roman numeral I does not have to be true since 1 and 9 are not prime, so eliminate choices A, C, and E. Since Roman numeral II occurs in the remaining answer choices, it must be true. Now, evaluate Roman numeral III which states that if N is a member of R, then N² is a member of R. This is true for each of the numbers that were Plugged In. In fact, it must be true for all numbers that, when squared, have a units digit of 1 or 9. Any number that has a units digit of 1, when squared, will still have a units digit of 1. The square of any number with a units digit of 9, will have a units digit of 1. So, the square of any member of R will also be a member of R. The correct answer is choice D.

ramlala · Answer

Hi  jppresa

Please see the highlighted part.
There is something missing in question after comma.

ScottTargetTestPrep · Answer

Solution:

Since R is the set of all numbers that, when squared, have a units digit of 1 or 9, the numbers in R are integers whose units digit is 1, 3, 7 or 9. Now, let’s analyze the Roman numeral statements.

I.  All members of R are prime.

This is not true since 9 (at the least) is in R and 9 is not a prime. Notice that the square of 9 has a units digit of 1.

II.  If N is a member of R, –N is a member of R.

This is true since R consists of INTEGERS whose units digit is 1, 3, 7, or 9, and integers can be positive or negative. Since the squares of N and -N are equal, if N is a member of R (which means the units digit of N^2 is either 1 or 9), then -N is also a member of R (because the square of -N has the same units digit as the square of N).

III.  If N is a member of R, N^2 is a member of R.

This is true since when an integer with units digit of 1, 3, 7, or 9 is squared, the square has a units digit of 1 or 9. When that is squared again, the square of the square also has a units digit of 1 or 9.

Answer: D

samarth1222 · Answer

In the 3rd option, the rule u have described does it imply for all the numbers or just for those numbers whose squares have a unit of 1 and 9

tvarma · Answer

How are we assuming that Set R consists of only integers and not real numbers?

bumpbot · Answer

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If R is the set of all numbers that, when squared, have a units digit

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If R is the set of all numbers that, when squared, have a units digit

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