QuestionDetermine the pattern connecting the pairs: (12, 9), (7, 4), (2, ?), (6, 5), (4, 5), (9, 10).
Studdy Solution
STEP 1
Assumptions1. The table contains pairs of numbers, with each pair in a separate row.
. There is a consistent rule that connects the two numbers in each row.
3. We need to find this rule and use it to determine the missing number in the third row.
STEP 2
Let's examine the first row. The numbers are12 and9. We need to find a rule that connects these two numbers.
STEP 3
Let's try subtraction. If we subtract the second number from the first, we get
STEP 4
Now let's apply the same rule to the second row. The numbers are7 and4. If we subtract the second number from the first, we get
STEP 5
It seems like the rule might be that the difference between the two numbers in each row is always3. Let's test this rule on the fourth row. The numbers are and5. If we subtract the second number from the first, we get
STEP 6
The rule does not hold for the fourth row, so our initial hypothesis was incorrect. Let's try a different rule.
STEP 7
Let's try addition. If we add3 to the second number in the first row, we get
STEP 8
Now let's apply the same rule to the second row. If we add3 to the second number, we get
STEP 9
It seems like the rule might be that if we add3 to the second number in each row, we get the first number. Let's test this rule on the fourth row. If we add3 to the second number, we get
STEP 10
The rule does not hold for the fourth row, so our second hypothesis was incorrect. Let's try a different rule.
STEP 11
Let's try to see if the second number is the result of subtracting3 from the first number. If we subtract3 from the first number in the first row, we get
STEP 12
Now let's apply the same rule to the second row. If we subtract from the first number, we get
STEP 13
It seems like the rule might be that if we subtract3 from the first number in each row, we get the second number. Let's test this rule on the fourth row. If we subtract3 from the first number, we get
STEP 14
The rule does not hold for the fourth row, so our third hypothesis was incorrect. Let's try a different rule.
STEP 15
Let's try to see if the second number is the result of adding to the first number. If we add to the first number in the first row, we get
STEP 16
The rule does not hold for the first row, so our fourth hypothesis was incorrect. Let's try a different rule.
STEP 17
Let's try to see if the second number is the result of subtracting from the first number. If we subtract from the first number in the first row, we get
STEP 18
The rule does not hold for the first row, so our fifth hypothesis was incorrect. Let's try a different rule.
STEP 19
Let's try to see if the second number is the result of subtracting the first number from21. If we subtract the first number in the first row from21, we get
STEP 20
Now let's apply the same rule to the second row. If we subtract the first number from, we get
STEP 21
The rule does not hold for the second row, so our sixth hypothesis was incorrect. Let's try a different rule.
STEP 22
Let's try to see if the second number is the result of subtracting the first number from15. If we subtract the first number in the first row from15, we get
STEP 23
Now let's apply the same rule to the second row. If we subtract the first number from15, we get
STEP 24
The rule does not hold for the second row, so our seventh hypothesis was incorrect. Let's try a different rule.
STEP 25
Let's try to see if the second number is the result of subtracting the first number from21. If we subtract the first number in the first row from21, we get
STEP 26
Now let's apply the same rule to the second row. If we subtract the first number from21, we get
STEP 27
The rule does not hold for the second row, so our eighth hypothesis was incorrect. Let's try a different rule.
STEP 28
After trying many rules, it seems that there is no consistent rule that connects the two numbers in each row. Therefore, we cannot determine the missing number in the third row.
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