GMAT Quantitative Reasoning - DSQ: Understanding arithmetic sets

1

Number_sets

Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.

If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?

Statement 1: If $m = n \div 7$ , then would be placed in Region IV.

Statement 2: If $p = n \cdot 7$ , then would be placed in Region IV.

2

If , what is ?

(1)

(2) $S\bigcup B= [{1 , 3 , 4 , 6 , 7 , 10}]$

3

Number_sets

Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.

If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?

Statement 1: If , then would be placed in Region I.

Statement 2: If , then would be placed in Region I.

4

Number_sets

Examine the above Venn diagram, which represents the sets of real numbers.

If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?

Statement 1: is negative.

Statement 2: If $m= n \div 9$ , then would be placed in Region III.

5

Number_sets

Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.

If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?

Statement 1: If $k = n^{2}$ , then would be in Region I.

Statement 2: If $h = n^{3}$ , then would be in Region III.

6

Define sets as follows:

$A = \left { 2,4,6,8,10\right }$

$B = \left { 1,3,6,9,10\right }$

What is $\overline{A\cup B}$ ?

Statement 1: $U = \left { 1,2,3,4,5,6,7,8,9,10\right }$

Statement 2: comprises ten elements, all of which are positive integers.

7

Two courses open to students in their senior year at Johnson High School are calculus and physics; students may take either or both. Of the 524 seniors enrolled at JHS, are more of them taking calculus or physics?

Statement 1: 139 students are taking neither course.

Statement 2: One-third of the students enrolled in calculus are also enrolled in physics.

8

Let be the set of all of the multiples of 3 between 29 and 50. How many subsets of can be formed?

9

Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?

10

The senior class of Watson High School has 613 students. An election was held for Senior Class President between three candidates, Martindale, Nance, and Osgood.

If every student voted for one of these three, and the student with the most votes was declared the winner, who won the election?

Statement 1: Martindale got 240 votes.

Statement 2: Nance got 244 votes.

DSQ: Understanding arithmetic sets

Practice Questions