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GRE Quantitative Reasoning › Other Topics

Questions 1 - 10

Which of the following is a subset of the set: $\{2,3,7,11,15\}$ ?

$\{2,15\}$

$\{8,15\}$

$\{8,13\}$

$\{7,9\}$

Explanation

Step 1: Define a subset

A subset of a big set is a set that has some of the elements that are in the bigger parent set.

The answer is $\{2,15\}$ because both and are both in the bigger set.

$A=\left \{ 3, 6, 8, 9 \right \}$

$B=\left \{ 4, 5, 6, 8 \right \}$

$C=\left \{ 1, 2, 4, 8, 9 \right \}$

$D=\left \{ 4, 5, 6, 7, 8 \right \}$

Which of the following is true about the relationship between sets?

$B\subseteq D$

$D\subseteq B$

$A\subseteq C$

$D\subseteq C$

$C\subseteq B$

Explanation

The subset symbol should be read as "is a subset of" So it's the first letter is a subset of the second letter. To be a subset, all of its elements must be contained in the other set.

The only one of these relationships that is true (where the entire set on the left is in the right set) is $B\subseteq D$

The elements of B, 4, 5, 6, and 8 all appear in set D.

What is the mean of: $\{2,3,6,7,9,11\}$

$6.\overline {33}$

Explanation

Step 1: Find the sum of the numbers

Step 2: Count how numbers there are:

There are numbers..

Step 3: Divide Sum by how many numbers

$Mean=\frac {38}{6}=6.\overline {33}$

What is the mean of

Explanation

Step 1: Find the sum of the numbers

Step 2: Find how many numbers

There are numbers..

Step 3: Divide the sum by how many numbers they are...This division gives us the mean..

$Mean=\frac {20}{5}=4$

Mohammed is being treated to ice cream for his birthday, and he's allowed to build a three-scoop sundae from any of the thirty-one available flavors, with the only condition being that each of these flavors be unique. He's also allowed to pick different toppings of the available , although he's already decided well in advance that one of them is going to be peanut butter cup pieces.

Knowing these details, how many sundae combinations are available?

Explanation

Because order is not important in this problem (i.e. chocolate chip, pecan, butterscotch is no different than pecan, butterscotch, chocolate chip), it is dealing with combinations rather than permutations.

The formula for a combination is given as:

$C(n,k)=\frac{n!}{(n-k)!k!}$

where is the number of options and is the size of the combination.

For the ice cream choices, there are thirty-one options to build a three-scoop sundae. So, the number of ice cream combinations is given as:

$C(31,3)=\frac{31!}{(31-3)!3!}=4495$

Now, for the topping combinations, we are told there are ten options and that Mohammed is allowed to pick two items; however, we are also told that Mohammed has already chosen one, so this leaves nine options with one item being selected:

$C(9,1)=\frac{9!}{(9-1)!1!}=9$