Sets - ISEE Middle Level Quantitative Reasoning
Card 0 of 10
An arithmetic sequence begins
Which is the greater quantity?
(a) The fiftieth term of the sequence
(b) 
An arithmetic sequence begins
Which is the greater quantity?
(a) The fiftieth term of the sequence
(b)
The common difference of the sequence is 
, so the fiftieth term will be:
,
which is less than 450.
The common difference of the sequence is
which is less than 450.
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An arithmetic sequence begins:
Which is the greater quantity?
(a) 
(b) The tenth term of the sequence
An arithmetic sequence begins:
Which is the greater quantity?
(a)
(b) The tenth term of the sequence
The common difference of the sequence is 
. The tenth term of the sequence is 
.
This makes (b) greater.
The common difference of the sequence is
This makes (b) greater.
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A geometric sequence begins as follows:
Which is the greater quantity?
(a) The seventh term of the sequence
(b) 
A geometric sequence begins as follows:
Which is the greater quantity?
(a) The seventh term of the sequence
(b)
The common ratio of the sequence is 
, so the next four terms of the sequence are:
, the seventh term, which is greater than 3,000.
The common ratio of the sequence is
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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 fifth and eighth terms of the Fibonacci sequence
(b) The product of the sixth and seventh terms of the Fibonacci sequence
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 fifth and eighth terms of the Fibonacci sequence
(b) The product of the sixth and seventh terms of the Fibonacci sequence
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 fifth and eighth terms are 5 and 21; their product is 
(b) The sixth and seventh terms are 8 and 13; their product is 
(a) is greater.
By beginning with
(a) The fifth and eighth terms are 5 and 21; their product is
(b) The sixth and seventh terms are 8 and 13; their product is
(a) is greater.
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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
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
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 
(b) The ninth term is 34; its square is 
.
(b) is greater
By beginning with
(a) The eighth and tenth terms are 21 and 55; their product is
(b) The ninth term is 34; its square is
(b) is greater
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Five candidates are running for school board. A voter chooses two of the candidates.
Which is the greater quantity?
(a) The number of ways a voter can mark his or her ballot
(b) 
Five candidates are running for school board. A voter chooses two of the candidates.
Which is the greater quantity?
(a) The number of ways a voter can mark his or her ballot
(b)
This is a choice of two out of five without regard to order - that is, the number of combinations of two out of a set of five. This is
There are ten possible ways to choose, and 
.
This is a choice of two out of five without regard to order - that is, the number of combinations of two out of a set of five. This is
There are ten possible ways to choose, and
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Seven students are running for student council. A student can vote for any three. Steve wants to vote for his girlfriend Marsha.
Which is the greater quantity?
(a) The number of ways Steve can fill out his ballot so that he can vote for Marsha
(b) 
Seven students are running for student council. A student can vote for any three. Steve wants to vote for his girlfriend Marsha.
Which is the greater quantity?
(a) The number of ways Steve can fill out his ballot so that he can vote for Marsha
(b)
Since one of Steve's votes has already been decided, this is a choice of two out of the remaining six without regard to order - that is, the number of combinations of two out of a set of six. This is
Since one of Steve's votes has already been decided, this is a choice of two out of the remaining six without regard to order - that is, the number of combinations of two out of a set of six. This is
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Eight students are running for student council. A student can vote for any two. Phil only wants to vote for male candidates; Sandee only wants to vote for female candidates.
Which is the greater quantity?
(a) The number of ways Phil can fill out his ballot so that he can vote for two male candidates
(b) The number of ways Sandee can fill out her ballot so that she can vote for two female candidates
Eight students are running for student council. A student can vote for any two. Phil only wants to vote for male candidates; Sandee only wants to vote for female candidates.
Which is the greater quantity?
(a) The number of ways Phil can fill out his ballot so that he can vote for two male candidates
(b) The number of ways Sandee can fill out her ballot so that she can vote for two female candidates
This question is impossible to answer, because it is not known how many candidates are male and how many are female.
This question is impossible to answer, because it is not known how many candidates are male and how many are female.
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What is the next number in the series above?
What is the next number in the series above?
First, you must determine the pattern in the series. The pattern is adding the two preceding terms to give you the next term (ex: 
). Therefore, apply that rule to calculate 
, which gives you 13 as the next term.
First, you must determine the pattern in the series. The pattern is adding the two preceding terms to give you the next term (ex:
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Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?
Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?
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.
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.
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