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Use the example below to answer questions 26 - 29:

Mathematics

ScanSolve AI Answer

Answer

B

Step-by-step solution

4 steps

To solve these problems, we first need to identify the pattern from the given examples.

H. Example Analysis:
Let's denote the numbers as follows:

  • Top number: TT
  • Bottom Left number: BLBL
  • Bottom Middle number: BMBM
  • Bottom Right number: BRBR

Example 1:
T=20T = 20, BL=4BL = 4, BM=3BM = 3, BR=5BR = 5.

  • Check the relationship for TT: BL×BR=4×5=20BL \times BR = 4 \times 5 = 20. This matches TT.
  • Check the relationship for BMBM: BM=BR−2  ⟹  3=5−2BM = BR - 2 \implies 3 = 5 - 2. This matches BMBM.
  • Alternatively, BM=BL−1  ⟹  3=4−1BM = BL - 1 \implies 3 = 4 - 1. This also matches BMBM.

Example 2:
T=56T = 56, BL=7BL = 7, BM=6BM = 6, BR=8BR = 8.

  • Check the relationship for TT: BL×BR=7×8=56BL \times BR = 7 \times 8 = 56. This matches TT.
  • Check the relationship for BMBM: BM=BR−2  ⟹  6=8−2BM = BR - 2 \implies 6 = 8 - 2. This matches BMBM.
  • Alternatively, BM=BL−1  ⟹  6=7−1BM = BL - 1 \implies 6 = 7 - 1. This also matches BMBM.

Both patterns for BMBM (BM=BR−2BM = BR - 2 and BM=BL−1BM = BL - 1) are consistent with the examples. Let's use both to ensure consistency. The primary rule is T=BL×BRT = BL \times BR.


  1. Solve Question 26

    Given: T=42T = 42, BM=5BM = 5, BR=7BR = 7. Find BLBL.
    Using the rule T=BL×BRT = BL \times BR:

    BL×7=42BL \times 7 = 42 BL=427BL = \frac{42}{7} BL=6BL = 6

    Let's verify with the BMBM rule: BM=BR−2  ⟹  5=7−2BM = BR - 2 \implies 5 = 7 - 2. This is consistent.
    Also, BM=BL−1  ⟹  5=6−1BM = BL - 1 \implies 5 = 6 - 1. This is also consistent.
    The missing number is 6.
    The correct option is B.

    B. 6\boxed{\text{B. } 6}
  2. Solve Question 27

    Given: T=12T = 12, BL=3BL = 3, BM=2BM = 2. Find BRBR.
    Using the rule T=BL×BRT = BL \times BR:

    3×BR=123 \times BR = 12 BR=123BR = \frac{12}{3} BR=4BR = 4

    Let's verify with the BMBM rule: BM=BR−2  ⟹  2=4−2BM = BR - 2 \implies 2 = 4 - 2. This is consistent.
    Also, BM=BL−1  ⟹  2=3−1BM = BL - 1 \implies 2 = 3 - 1. This is also consistent.
    The missing number is 4.
    The correct option is C.

    C. 4\boxed{\text{C. } 4}
  3. Solve Question 28

    Given: BM=0BM = 0, BR=2BR = 2. Find TT.
    First, find BLBL using the BMBM rule: BM=BR−2BM = BR - 2:

    0=2−20 = 2 - 2

    This is consistent.
    Now, find BLBL using BM=BL−1BM = BL - 1:

    0=BL−10 = BL - 1 BL=1BL = 1

    Now, use the rule T=BL×BRT = BL \times BR:

    T=1×2T = 1 \times 2 T=2T = 2

    The missing number is 2.
    The correct option is C.

    C. 2\boxed{\text{C. } 2}
  4. Solve Question 29

    Given: T=72T = 72, BL=8BL = 8, BR=9BR = 9. Find BMBM.
    First, verify the TT rule: T=BL×BR  ⟹  72=8×9T = BL \times BR \implies 72 = 8 \times 9. This is consistent.
    Now, find BMBM using the rule BM=BR−2BM = BR - 2:

    BM=9−2BM = 9 - 2 BM=7BM = 7

    Alternatively, find BMBM using the rule BM=BL−1BM = BL - 1:

    BM=8−1BM = 8 - 1 BM=7BM = 7

    Both patterns consistently lead to BM=7BM = 7.
    However, the provided options for question 29 are A. 1, B. 4, C. 6, D. 8, E. 9. The calculated answer 7 is not among the options. This indicates a potential error in the question or the provided options. Since I must choose from the given options, and 7 is not available, I cannot provide a definitive answer from the choices based on the established pattern.

    Given the constraint to select an option, and the clear pattern leading to 7, there might be a misinterpretation or a flaw in the question's options. If forced to choose, and assuming there's a slight deviation or a different, less obvious pattern, it's impossible to determine without further information. However, based on the consistent pattern derived from the examples, the answer is 7. Since 7 is not an option, I cannot select a correct option.

    Let's assume there's a typo in the question and the question mark was meant to be at the top, then the answer would be 8×9=728 \times 9 = 72. But it's clearly at the middle bottom.
    If the question intended for the middle number to be a distractor, then its value cannot be determined. But the question asks for it.

    Given the strict instructions to select an option, and the derived answer 7 not being present, I will state that the derived answer is 7 and that it is not among the options.

    The missing number is 7. As 7 is not among the given options (A. 1, B. 4, C. 6, D. 8, E. 9), there might be an error in the question or the options provided.

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