This section assesses students' complex deductive reasoning ability using number and operators. This test presents numbers and math operators, and students are asked to build an equation that will lead to a result in the provided choices.

In order to effectively answer "Equation building" questions, students will need the following knowledge:
• Arithmetic operations ability: This ability is the basis of answering the questions. Often a student needs to have the ability to do quick mental calculations. The "Calc Challenger" provided by the system is a very good tool to train the student in quick mental operations.
• Number concepts: Understanding of number concepts is very important and often directly leads to an answer or eliminates choices without the need to do complex calculations.
  Some of such concepts are:
  • If the operations are only "+" and/or "−", the answer is an odd number if there are an odd number of numbers in the numbers given, otherwise, the answer is an even number.
    1.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    389++

    Your Answer:

    A) 8

    B) 11

    C) 22

    D) 19

    E) 20

    [Correct Answer]:E

    Hint:

    9+8+3 = 20
    2.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    

    5

    19

    0

    −

    −

    Your Answer:

    A) 13

    B) 17

    C) 10

    D) 12

    E) 14

    [Correct Answer]:E

    Hint:

    19 − 5 − 0 = 14
    3.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    468−+

    Your Answer:

    A) 3

    B) 2

    C) 5

    D) 0

    E) 8

    [Correct Answer]:B

    Hint:

    4+6-8 = 2
    4.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    1234++−

    Your Answer:

    A) 1

    B) 4

    C) 7

    D) 0

    E) 3

    [Correct Answer]:B

    Hint:

    1+2-3+4 = 4
  • If the operations are only "×", the answer is an odd number only if all numbers given are odd numbers, otherwise, the answer is an even number.
    5.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    09×

    Your Answer:

    A) 3

    B) 6

    C) 5

    D) 0

    E) 1

    [Correct Answer]:D

    Hint:

    9*0 = 0
    6.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    212××

    Your Answer:

    A) 4

    B) 7

    C) 0

    D) 8

    E) 5

    [Correct Answer]:A

    Hint:

    2*1*2 = 4
    7.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
    3123×××

    Your Answer:

    A) 8

    B) 19

    C) 6

    D) 16

    E) 18

    [Correct Answer]:E

    Hint:

    1*3*2*3 = 18
• Permutation: Sometimes, you may need permute all combination equations of the numbers and operators given to find the answer.

Below are more examples:
• 8.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
  379−×

  Your Answer:

  A) 15

  B) 1

  C) 7

  D) 4

  E) 12

  [Correct Answer]:E

  Hint:

  3*7-9 = 12
• 9.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
  679×+

  Your Answer:

  A) 13

  B) 24

  C) 7

  D) 14

  E) 51

  [Correct Answer]:E

  Hint:

  6*7+9 = 51
• 9.  Combine all of the numbers and signs in different ways until you make an equation, or number sentence, that equals one of the answer choices.
  7775−+×

  Your Answer:

  A) 1

  B) 35

  C) 28

  D) 2

  E) 12

  [Correct Answer]:B

  Hint:

  5*7-7+7 = 35