ISEE Lower Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #71 : Data Analysis

Identify the value of \(\displaystyle x\) in this set:

\(\displaystyle 243, 81, 27, x, 3\)

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 6.5\)

\(\displaystyle 12\)

\(\displaystyle 5\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 9\)

Explanation:

In this set, each term is equal to the preceding term divided by 3.

\(\displaystyle 243\div3=81\)

\(\displaystyle 81\div3=27\)

\(\displaystyle 27\div3=x\)

By dividing 27 by 3, we can find the value of \(\displaystyle x\).

\(\displaystyle 27\div3=9\)

Example Question #11 : Sets

Which of the following is the most appropriate number to complete this set?

\(\displaystyle 6, 22, 38, 54, x\)

Possible Answers:

\(\displaystyle 70\)

\(\displaystyle 68\)

\(\displaystyle 65\)

\(\displaystyle 60\)

\(\displaystyle 63\)

Correct answer:

\(\displaystyle 70\)

Explanation:

The numbers in the set increase by increments of 16.

\(\displaystyle 6+16=22\)

\(\displaystyle 22+16=38\)

\(\displaystyle 38+16=54\)

The final term in the set will be the sum of 54 and 16.

\(\displaystyle 54+16=70\)

Example Question #11 : How To Find The Missing Part Of A List

Which of the following numbers can complete this set?

\(\displaystyle 2, 4, 8, 16, x\)

Possible Answers:

\(\displaystyle 36\)

\(\displaystyle 24\)

\(\displaystyle 32\)

\(\displaystyle 40\)

\(\displaystyle 18\)

Correct answer:

\(\displaystyle 32\)

Explanation:

The pattern in this set is that each preceding number is multiplied by 2.

\(\displaystyle 2\cdot2=4\)

\(\displaystyle 4\cdot2=8\)

\(\displaystyle 2\cdot8=16\)

Given that 16 multiplied by 2 equals 32, that is the correct answer. 

\(\displaystyle 2\cdot16=32=x\)

Example Question #14 : Sets

What is the missing number from this set?

\(\displaystyle x, 5, 25, 125, 625\)

Possible Answers:

None of these

\(\displaystyle 10\)

\(\displaystyle 0\)

\(\displaystyle -5\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle 1\)

Explanation:

In the set, each subsequent number if 5 times larger than the previous term.

\(\displaystyle 5\times5=25\)

\(\displaystyle 25\times5=125\)

\(\displaystyle 125\times5=625\)

To find the value of \(\displaystyle x\), we need to divide the following term by 5. In this case, that means we will need to divide 5 by 5.

\(\displaystyle x=\frac{5}{5}=1\)

Example Question #15 : Sets

What is the value of \(\displaystyle x\) in the set below?

\(\displaystyle 8, 14, 20, 26, 32, x\)

Possible Answers:

\(\displaystyle 39\)

\(\displaystyle 37\)

\(\displaystyle 38\)

\(\displaystyle 36\)

\(\displaystyle 41\)

Correct answer:

\(\displaystyle 38\)

Explanation:

Each number in the set increases from the preceding number by a value of 6.

\(\displaystyle 8+6=14\)

\(\displaystyle 14+6=20\)

\(\displaystyle 20+6=26\)

Given that \(\displaystyle 32+6=38\), the correct answer is 38. 

Example Question #11 : Sets

What is the value of \(\displaystyle x\) in the set below?

\(\displaystyle 36, 28, 20, 12, x\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 6\)

\(\displaystyle 4\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 4\)

Explanation:

The pattern here is to subtract 8 from the previous number.

Subtract 8 from 12 to get 4 as the value of \(\displaystyle x\).

 

Example Question #172 : Data Analysis And Probability

What is the value of \(\displaystyle x\) in the list below?

\(\displaystyle 5, 15, x, 135\)

Possible Answers:

\(\displaystyle 45\)

\(\displaystyle 55\)

\(\displaystyle 60\)

None of these

\(\displaystyle 50\)

Correct answer:

\(\displaystyle 45\)

Explanation:

Given that 15 is 3 times the value of 5, \(\displaystyle x\) could be equal to 3 times the value of 15. This assumes that the pattern is that each subsequent number is triple the value of the preceding number.

\(\displaystyle 5\times3=15\)

Using this pattern, \(\displaystyle x\) would be equal to 3 times 15.

\(\displaystyle x=15\times3=45\)

We can test this answer by checking that three times \(\displaystyle x\) is equal to the next number in the list, 135.

\(\displaystyle 3x=3\times45=135\)

Our answer works out, so \(\displaystyle x\) must be equal to 45.

Example Question #12 : Sets

What is the value of \(\displaystyle x\) in the set below?

\(\displaystyle 6, 12, 18, 24, x\)

Possible Answers:

\(\displaystyle 26\)

\(\displaystyle 36\)

\(\displaystyle 31\)

\(\displaystyle 30\)

Correct answer:

\(\displaystyle 30\)

Explanation:

The pattern in the set is that each number increases by 6. The last number was 24. Therefore, since 6 plus 24 equals 30, \(\displaystyle x\) would be equal to 30. 

Example Question #13 : Sets

What number should appear next in the set below?

\(\displaystyle 108, 36, 12, 4\)

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle \frac{4}{3}\)

\(\displaystyle \frac{1}{4}\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle \frac{4}{3}\)

Explanation:

In the set, \(\displaystyle 108, 36, 12, 4\), each subsequent number is one third of the preceding number. One-third of 4 is \(\displaystyle \frac{4}{3}\), which is the correct answer. 

Example Question #14 : Sets

What is the next number in the sequence below?

\(\displaystyle 10,20,40,80\)

Possible Answers:

\(\displaystyle 100\)

\(\displaystyle 140\)

\(\displaystyle 120\)

\(\displaystyle 160\)

Correct answer:

\(\displaystyle 160\)

Explanation:

In the sequence, each subsequent number doubles in value. Therefore, the next number should be twice as large as 80, or 160. Therefore, 160 is the correct answer. 

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