How to find the missing number in a set

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GRE Quantitative Reasoning › How to find the missing number in a set

Questions 1 - 4

The product of two integers is 14. Which of the following could be the average of the two numbers?

$\dpi{100} \small -4.5$

$\dpi{100} \small -5.5$

$\dpi{100} \small 3.5$

$\dpi{100} \small -6.5$

$\dpi{100} \small 5.5$

Explanation

The two integers in this case, and their respective averages, could be:

$2\ and\ 7=4.5$

$-2\ and\ -7=-4.5$

$1\ and\ 14=7.5$

$-1\ and\ -14=-7.5$

Only $\dpi{100} \small -4.5$ is one of the answer choices.

In the set of positive, distinct integers , the median is . What is the minimum value of ?

Explanation

We know that all the numbers are positive, so they are greater than zero. We also know that the numbers are distinct, so they are all unique.

We can write this as {a + b + 8 + d + e}, so let a and b be 1 and 2 respectively, the smallest possible positive, distinct integers. Then let d and e be 9 and 10, the smallest positive, distinct integers larger than 8.

We add the set {1 + 2 + 8 + 9 + 10} to find it equals 30.

Which of these is a natural number?

None of these are natural numbers .

All of these are natural numbers.

Explanation

The natural numbers are the positive integers (whole numbers) starting with 1.

Which of the following pairs of events are mutually exclusive?

the even numbers, the numbers greater than

the positive numbers, the numbers less than

the numbers less than , the numbers greater than

for all values, the numbers greater than

the negative numbers,

Explanation

We can think of mutually exclusive in terms of a Venn diagram. We are looking for the pair of events that has nothing in common. The only sets that don't have a single number in common are the positive numbers and the numbers less than –200.

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