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ISEE Middle Level Quantitative Reasoning › Sets

Questions 1 - 10

A geometric sequence begins as follows:

Which is the greater quantity?

(a) The seventh term of the sequence

(b)

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

The common ratio of the sequence is $15 \div 5 = 3$ , so the next four terms of the sequence are:

$45 \times 3 = 135$

$135\times 3 = 405$

$405\times 3 = 1,215$

$1,215 \times 3 = 3,645$ , the seventh term, which is greater than 3,000.

A geometric sequence begins as follows:

Which is the greater quantity?

(a) The seventh term of the sequence

(b)

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

The common ratio of the sequence is $15 \div 5 = 3$ , so the next four terms of the sequence are:

$45 \times 3 = 135$

$135\times 3 = 405$

$405\times 3 = 1,215$

$1,215 \times 3 = 3,645$ , the seventh term, which is greater than 3,000.

Define $L = \left { x ; | ; x \textrm{ is a multiple of 4 }\right }$ .

Which of the following is not a subset of the set ?

$\left { 4876, 3296, 8878, 9004, 7612\right }$

None of the other responses gives a correct answer.

$\left { 9456, 9260, 7848, 6116, 8744\right }$

$\left { 8908, 5428, 9380, 7212, 7756 \right }$

$\left { 8320, 9652, 8772, 5432, 9936\right }$

Explanation

For a set to be a subset of , all of its elements must also be elements of - that is, all of its elements must be multiples of 4. An integer is a multple of 4 if and only the number formed by its last two digits is also a multiple of 4, so all we have to do is examine the last two digits of each number in all four sets.

Of all of the numbers in the four sets listed, only 8,878 has this characteristic:

$78 \div 4 = 19 \textrm{ R }2$

8,878 is not a multiple of 4, so among the sets from which to choose,

$\left { 4876, 3296, 8878, 9004, 7612\right }$

is the only set that is not a subset of .

Define $L = \left { x ; | ; x \textrm{ is a multiple of 4 }\right }$ .

Which of the following is not a subset of the set ?

$\left { 4876, 3296, 8878, 9004, 7612\right }$

None of the other responses gives a correct answer.

$\left { 9456, 9260, 7848, 6116, 8744\right }$

$\left { 8908, 5428, 9380, 7212, 7756 \right }$

$\left { 8320, 9652, 8772, 5432, 9936\right }$

Explanation

Of all of the numbers in the four sets listed, only 8,878 has this characteristic:

$78 \div 4 = 19 \textrm{ R }2$

8,878 is not a multiple of 4, so among the sets from which to choose,

$\left { 4876, 3296, 8878, 9004, 7612\right }$

is the only set that is not a subset of .

$\left { 2,3,4,5,6,7,8,9\right }$

The above set represents the numbered cards in a standard deck of cards. What value is missing?

Explanation

The numbered cards in a deck range from to .

Since is not in the above set, it is the missing NUMBER card from the deck.

King and Ace are incorrect choices as they are called face cards in a deck of cards.

$\left { 2,3,4,5,6,7,8,9\right }$

The above set represents the numbered cards in a standard deck of cards. What value is missing?

Explanation

The numbered cards in a deck range from to .

Since is not in the above set, it is the missing NUMBER card from the deck.

King and Ace are incorrect choices as they are called face cards in a deck of cards.

The Fibonacci sequence begins

with each subsequent term being the sum of the previous two.

Which is the greater quantity?

(a) The product of the eighth and tenth terms of the Fibonacci sequence

(b) The square of the ninth term of the Fibonacci sequence

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

By beginning with and taking the sum of the previous two terms to get each successive term, we can generate the Fibonacci sequence:

(a) The eighth and tenth terms are 21 and 55; their product is $21\times 55 = 1,155$

(b) The ninth term is 34; its square is $34 ^{2} = 34 \times 34 = 1,156$ .

(b) is greater

The Fibonacci sequence begins

with each subsequent term being the sum of the previous two.

Which is the greater quantity?

(a) The product of the eighth and tenth terms of the Fibonacci sequence

(b) The square of the ninth term of the Fibonacci sequence

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

By beginning with and taking the sum of the previous two terms to get each successive term, we can generate the Fibonacci sequence:

(a) The eighth and tenth terms are 21 and 55; their product is $21\times 55 = 1,155$

(b) The ninth term is 34; its square is $34 ^{2} = 34 \times 34 = 1,156$ .

(b) is greater

Assorted 2

Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?

Figure (c)

Figure (d)

Figure (a)

Figure (b)

Explanation

The square with the diagonal line alternates between the square on the left and the square on the right. Therefore, the next figure in the sequence will have its diagonal line in the rightmost square, eliminating Figures (b) and (d) and leaving Figures (a) and (c).

Also, the shaded square moves one position to the right from figure to figure, so in the next figure, the shaded square must be the one at the extreme right. Figure (c) matches that description.

Assorted 2

Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?

Figure (c)

Figure (d)

Figure (a)

Figure (b)

Explanation

Also, the shaded square moves one position to the right from figure to figure, so in the next figure, the shaded square must be the one at the extreme right. Figure (c) matches that description.

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