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# CAT4 – Quantitative Reasoning

## What includes in the CAT4 Quantitative Reasoning?

The CAT4 Quantitative Reasoning section is composed of several subtests that assess a student’s ability to reason and solve problems using mathematical concepts and operations. The specific subtests included in the Quantitative Reasoning section may vary depending on the level of the test and the testing organization, but generally, number series and number analogies are included. These subtests, along with examples, are explained below.

## Number Series

This subtest requires students to work out the rule or recognize the pattern underlying the progression in a series of numbers and then select the next number in the series from five answer choices.

Examples of Number Series questions are below from lower-level questions to higher-level questions.

Instruction:  Look at the numbers in each row below. There is a rule that governs the order in which the numbers occur in the series. Figure out the rule and then choose the number that comes next from the answer choices below.

Example 1:
3    8    13    18    23    ___

A.  26           B. 27           C.  28           D.  29           E.  30

Answer:  C. 28 – The rule is to add 5. 3 + 5 = 8, 8 + 5 = 13, 13 + 5 = 18, 18 + 5 = 23, 23 + 5 = 28

Example 2:
150    140    130    120    110    ___

A.  100           B. 101           C.  111           D.  121           E.  123

Answer:  A. 100 – The rule is to subtract 10. 150 – 10 = 140, 140 – 10 = 130, 130 – 10 = 120, 120 – 10 = 110, 110 – 10 = 100

Example 3:
4    8    16    32    64    ___

A.  84           B. 104           C.  128           D.  138           E.  158

Answer:  C. 128 – The rule is to double the number. 4 x 2 = 8, 8 x 2 = 16, 16 x 2 = 32, 32 x 2 = 64, 64 x 2 = 128

Example 4:
143    254    365    476    587    ___

A.  600           B. 625           C.  649           D.  687           E.  698

Answer:  E. 698 – The rule is to increase each digit by 1. The number 587 becomes 5 + 1 = 6, 8 + 1 = 9, 7 + 1 = 8 or 698.

## Number Analogies

This subtest assesses a student’s ability to recognize and understand the relationship between two sets of numbers and to identify the missing number that completes an analogy.

Examples of Number Analogy questions are below from lower-level questions to higher-level questions.

Instruction:  Below you are given two pairs of numbers and then a third number without its pair.  The first two pairs of numbers are related in some way.  Figure out what the relationship is between the numbers within each of the pairs.  Choose an answer that creates a third pair of numbers that are related to each other in the same way that the first two pairs are related.

Example 1:
[4      1]   [8    5]    [12      ?]

A.  3           B.  15           C.  9           D.  1           E.  16

Answer:  C. 9 – The rule is to subtract 3 from the first number. 4 – 3 = 1, 8 – 3 = 5, 12 – 3 = 9

Example 2:
[33      3]   [77      7]    [132       ?]

A.  8           B.  10           C.  101           D.  110           E.  12

Answer:  E. 12 – The rule is to divide the first number by 11.

Example 3:
[12      48]   [8      32]    [24      ?]

A.  72           B.  96           C.  108           D.  24           E.  48

Answer:  B. 96 – The rule is to multiply the first number by 4. 12 x 4 = 48, 8 x 4 = 32, 24 x 4 = 96

Example 4:
[1      1]   [4      16]    [5      ?]

A.  5           B.  20           C.  25           D.  3           E.  35

Answer:  C. 25 – The rule is to square the first number. 1 x 1 = 1, 4 x 4 = 16, 5 x 5 = 25

Students are allowed to have paper and pen and use scratch paper to make calculations during this portion of the test.  At the higher levels, encourage your child to use scratch paper as some questions are multi-step and students must work out intermediate solutions.

Overall, the Quantitative Reasoning section of the CAT4 is designed to assess a student’s ability to reason and solve problems using mathematical concepts and operations. The questions in this section may involve recognizing patterns and relationships between numbers, performing basic mathematical calculations, reasoning and solving problems involving ratios, fractions, percentages, and other proportional relationships, and recognizing and understanding patterns in a sequence of numbers or shapes.