SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #2 : Lines

The coordinates of and are and . Find the length of the diagonal of the following rectangle:

 

 

R1

Possible Answers:

Correct answer:

Explanation:

A rectangle has two diagonals with the same length. So we should find the length of . We can use the distance formula:

 

Example Question #1 : Lines

If a circle has a radius of 12 inches, the biggest line that would be drawn within the circle is:

Possible Answers:

Correct answer:

Explanation:

The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches. 

Example Question #11 : Lines

The diameter of a circle is  centimeters. What is one-fourth of the circle's radius?

Possible Answers:

 

Correct answer:

 

Explanation:

By definition, the radius  and diameter  of a circle are related by the following equation:

Plugging in  as stated in the question, we find that .

Since the question is asking us for the value of :

.

Example Question #411 : Ssat Middle Level Quantitative (Math)

A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 3?

Possible Answers:

Correct answer:

Explanation:

There are four possible multiples of 3 that can come out: 3,6,9, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 3:

These are 12 outcomes out of 36, making the probability 

Example Question #412 : Ssat Middle Level Quantitative (Math)

A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 4?

Possible Answers:

Correct answer:

Explanation:

There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:

These are 9 outcomes out of 36, making the probability 

Example Question #1 : Outcomes

Some balls are placed in a hat - ten red, four blue, six yellow. What is the probability that a randomly drawn ball will not be blue?

Possible Answers:

Correct answer:

Explanation:

There are 20 balls in the hat. All but four - that is, sixteen - are blue, so the probability of a draw resulting in a non-blue ball is 

Example Question #3 : Probability

The red jacks are removed from a standard deck of fifty-two cards. What is the probability that a card randomly drawn from that modified deck will be black?

Possible Answers:

Correct answer:

Explanation:

The removal of two red jacks - and no black cards - results in there being fifty cards, twenty-six of them black. Therefore, the probability of a randomly drawn card being black is .

Example Question #1 : Outcomes

A standard deck of cards is modified by adding the red threes from another deck. What is the probability that a card randomly drawn from that modified deck will be a red card?

Possible Answers:

Correct answer:

Explanation:

The addition of two red threes from another deck results in the deck comprising fifty-four cards, twenty-eight of which are red. Therefore, the probability of a randomly drawn card being red is 

Example Question #4 : Probability

A standard deck of cards is modified by adding the red queens from another deck. What is the probability that a card randomly drawn from that modified deck will be a face card (jack, queen, king)?

Possible Answers:

Correct answer:

Explanation:

There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two more face cards - two red queens - have been introduced, so now there are fourteen face cards out of fifty-four. This makes the probability of a randomly drawn card being a face card

Example Question #413 : Ssat Middle Level Quantitative (Math)

In a bag of marbles, there are  blue marbles,  red marbles, and  green marbles. What is the probability of drawing two blue marbles in a row?

Possible Answers:

3

Correct answer:

Explanation:

The probability of drawing a blue marble on the first try is , since there are  blue marbles out of a total of  marbles. The probability of drawing a second blue marble is , since now there are  blue marbles remaining out of a total of  remaining marbles. The probability of drawing two blue marbles in a row is the product of the individual probabilities: .

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