Question

What is the number of children of age 9 years or less whose height does not exceed 135 cm?

• A. 48
• B. 45
• C. 3
• D. Cannot be determined
• A. 16
• B. 40
• C. 9
• D. Cannot be determined
• A. 34
• B. 52
• C. 44
• D. Cannot be determined

Answer 1

The Correct Option is B

Step 1: Understand how to read the tables
In each table the second column is a running total. For example, in Table A the row for age 9 shows 48. That means 48 children are aged 9 years or less.
In Table B the row for 135 cm shows 45. That means 45 children are 135 cm or shorter.

Step 2: Use the key assumption
An older child is always taller and heavier. So if we line up all 100 children from youngest to oldest, the same line-up also goes from shortest to tallest.
Give the children positions 1 to 100 in that line-up.

Step 3: Place the two groups in the line-up
Children aged 9 or less are positions 1 to 48.
Children with height 135 cm or less are positions 1 to 45, because they are the 45 shortest.

Step 4: Find the overlap
We want children who are in both groups. Positions 1 to 45 lie completely inside positions 1 to 48.
So the number of children aged 9 or less AND 135 cm or less is 45.

Step 5: Why the other options are wrong
Option (1) 48 would ignore the height limit. Not all 48 children are 135 cm or shorter.
Option (3) 3 is the difference 48 - 45. It counts the children aged 9 or less who are taller than 135 cm, which is the opposite group.
Option (4) is wrong because the assumption in the question makes the answer fixed.

Final Answer:
There are 45 such children, option (2). \[ \boxed{\text{Option (2): 45}} \]

Answer 2

Step 1: Understand the tables
Each table gives a running total of children up to the stated value. There are 100 children in all (the last row of every table is 100).
Because an older child is taller and heavier, we can line up the 100 children from youngest to oldest, and this is also the order from shortest to tallest and from lightest to heaviest.

Step 2: Turn each condition into a block of positions
Age more than 10 years: 60 children are aged 10 or less, so the older ones are 100 - 60 = 40 children, positions 61 to 100.
Taller than 150 cm: 75 children are 150 cm or shorter, so the taller ones are 100 - 75 = 25 children, positions 76 to 100.
Weight not more than 48 kg: 91 children weigh 48 kg or less, so these are positions 1 to 91.

Step 3: Find the overlap
Positions 76 to 100 (taller than 150 cm) are all inside positions 61 to 100 (older than 10). So the age condition adds nothing new.
Now take positions 76 to 100 and keep only those at positions 1 to 91. That leaves positions 76 to 91.
Number of children = 91 - 76 + 1 = 16.

Step 4: Why the other options are wrong
Option (2) 40 is the count of all children older than 10, with no height or weight limit.
Option (3) 9 is the number of children heavier than 48 kg (100 - 91). It is the group we remove, not the group we want.
Option (4) is wrong because the ordering rule fixes the answer.

Final Answer:
Exactly 16 children meet all three conditions, option (1). \[ \boxed{\text{Option (1): 16}} \]

Answer 3

Step 1: Understand the tables
Each table gives the number of children up to a stated value, so the last row of each table is 100. Line up all 100 children from youngest to oldest. By the given assumption this is also the order of height and weight.

Step 2: Place the age group
Children aged 6 or less: 22. Children aged 12 or less: 77.
So children older than 6 but not more than 12 are positions 23 to 77, which is 77 - 22 = 55 children.

Step 3: Place the weight group
Children who weigh 38 kg or less: 33, positions 1 to 33.
Children who weigh more than 38 kg are positions 34 to 100.

Step 4: Overlap
We need positions that are in both 23 to 77 and 34 to 100. That is positions 34 to 77.
The count is 77 - 34 + 1 = 44.

Step 5: Why the other options are wrong
Option (2) 52 is not any count that fits both limits. The age group alone is 55 and the weight group alone is 67.
Option (1) 34 is also not an overlap count of these two groups.
Option (4) is wrong because the ordering assumption gives one fixed answer.

Final Answer:
Exactly 44 children, which is option (3). \[ \boxed{\text{Option (3): 44}} \]