### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #51 : Data Analysis / Probablility

A standard deck of 52 cards is altered by adding the jacks from another deck. What are the odds against a randomly drawn card being a club?

**Possible Answers:**

**Correct answer:**

Before the addition of the jacks, the deck had 13 clubs and 39 other cards. The 4 jacks from the other deck include 1 club and 3 other cards, so the altered deck contains 14 jacks and 42 other cards. That makes the odds against drawing a club at random

- that is, 3 to 1, just as in the unaltered deck

### Example Question #51 : Data Analysis / Probablility

Which of the following ways can you alter a standard deck of 52 cards in order to *neither increase nor* *decrease *the probability that a randomly-drawn card would be a king?

**Possible Answers:**

Remove both of the black queens.

Remove the jacks.

Add the joker.

Add the clubs from another deck.

Add the aces from another deck.

**Correct answer:**

Add the clubs from another deck.

In an unaltered deck, 4 of the 52 cards, or of the cards, are kings. We are looking for an action that preserves this ratio.

We see that if the clubs from another deck are added, then there are 5 kings (the 4 original kings plus an added king) and 65 cards total (the original 53 plus the 13 added clubs). 5 of the 65 cards, or of the cards, are kings, thereby preserving the ratio.

Of the other choices, none of them change the number of kings in the deck, but all change the total number of cards. Therefore, the ratio of kings to total cards must change.

### Example Question #1681 : Ssat Upper Level Quantitative (Math)

A standard deck of 53 cards (including the joker) is altered by adding the sevens from another deck. What are the odds against a randomly drawn card being a heart?

**Possible Answers:**

**Correct answer:**

Adding the four sevens from another deck to a 53-card deck will yield a 57-card deck with 14 hearts - the original 13 hearts and the added seven of hearts - and 43 other cards. Therefore, the odds against drawing a heart will be 43 to 14.

### Example Question #52 : Data Analysis / Probablility

Which of the following ways can you alter a standard deck of 52 cards in order to *neither increase nor* *decrease *the probability that a randomly-drawn card would be a spade?

**Possible Answers:**

Add the joker.

None of the other responses gives a correct answer.

Remove the red fours and the black fives.

Add the red sevens from another deck.

Add the clubs from another deck.

**Correct answer:**

Remove the red fours and the black fives.

In an unaltered deck, 13 of the 52 cards, or of the cards, are spades. We are looking for an action that preserves this ratio.

If the red fours and the black fives, including the five of spades, are removed, then there are 12 spades left out of 48 cards, which means that of the cards are spades. This is the correct choice.

Of the other choices, none of them change the number of spades in the deck, but all change the total number of cards. Therefore, the ratio of spades to total cards must change.

### Example Question #81 : Data Analysis

Aaron, Gary, Craig, and Boone are sitting down in a row of four chairs. What is the probability that Aaron and Gary will be seated beside each other?

**Possible Answers:**

**Correct answer:**

Consider first all of the possible ways the men may be arranged, which is

Now, consider all of the ways that Aaron and Gary could be seated beside each other; it may be easier to visualize by drawing it out:

- A G _ _
- G A _ _
- _ A G _
- _ G A _
- _ _ A G
- _ _ G A

As seen, there are six possibilities.

Finally, for each of these cases, Craige and Boone could be seated in one of two ways.

So the probability that Aaron and Gary will be seated beside each other is:

### Example Question #52 : Data Analysis / Probablility

A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.

All of the tiles are placed in a large box. What is the probability that a randomly drawn tile will be a vowel?

Note: for purposes of this question, "Y" is a consonant.

**Possible Answers:**

**Correct answer:**

Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of

tiles out of 100.

This makes the probability of drawing one of these tiles

### Example Question #51 : Data Analysis / Probablility

Eight standard decks of 52 cards are shuffled together; four jokers are shuffled in as well. A card is selected at random from this new deck. What is the probability that a spade will be selected?

**Possible Answers:**

**Correct answer:**

Eight decks of 52 cards, with 4 jokers added, comprise a total of

cards. A standard deck of 52 cards has 13 spades, so the eight decks together have a total of

spades. This makes the probability of a random draw resulting in a spade

### Example Question #51 : Data Analysis / Probablility

The above set of balls is placed in a box. Give the probability that, if a ball is drawn at random, it will be a gray ball marked with an odd number.

**Possible Answers:**

**Correct answer:**

As seen in the diagram below, nine of the twenty-five balls in the box are both gray and marked with odd numbers.

This makes the probability that a random selection will yield one of these balls .

### Example Question #54 : Data Analysis / Probablility

The above set of balls is placed in a box. Give the probability that, if a ball is drawn at random, it will be a white ball marked with a prime number.

**Possible Answers:**

**Correct answer:**

Out of the whole numbers from 1 through 9, there are four prime numbers - 2, 3, 5, and 7. As seen in the diagram below, there are five out of twenty-five balls that are both white and marked with a prime number.

This makes the probability of drawing one of these balls .

### Example Question #55 : Data Analysis / Probablility

Mark is playing a board game in which spaces represent property that can be "bought" and "sold"; the above diagram represents part of the board. Mark is represented by the red triangle, and he is moving in a left-to-right direction.

Mark is about to roll a pair of fair six-sided dice. If he lands on one of the yellow spaces, he will have to pay a huge fee to his opponent, Jennifer, who "owns" the properties represented by the spaces; if this happens, he will be out of the game.

What are the odds of this happening?

**Possible Answers:**

11 to 7 against

2 to 1 against

5 to 4 against

Even odds

**Correct answer:**

11 to 7 against

The undesirable rolls are 5, 6, and 8. As can be seen in the diagram below, out of thirty-six equally probable outcomes possible with the roll of two fair six-sided dice, fourteen are undesirable, and twenty-two are desirable.

The odds against an undesirable roll are

- that is, 11 to 7.

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