Number Operations and Properties

First, calculate the sum on the left: 17 + 47 = 64. The equation is 64 = 7 + x. Subtracting 7 from 64 gives 57.

To solve: 33 + 18 = 51, so 29 + ? = 51. Therefore, 51 - 29 = 22. The answer is 22. This is a basic arithmetic equation requiring you to find the missing number that balances both sides.

First, calculate the sum on the left: 56 + 81 = 137. The equation is 137 = 44 + x. Subtracting 44 from 137 gives 93.

First, calculate the left side: 54 - 32 = 22. The equation becomes 22 = 25 - x. Solving for x, we get x = 25 - 22, which equals 3.

Let the number be x. According to the problem: 4x + 10 = 5x - 5. Solving: 10 + 5 = 5x - 4x, so 15 = x. Therefore the number is 15. Option A is correct.

The sequence repeats the block '6 9 + + 9 6 X X'. In the third iteration, it reaches '6 9 + + ? 6 X ?'. Comparing it to the previous blocks, the first '?' should be 9 and the second '?' should be X.

The pattern shows a + b = (a+b)², so 3+2=(5)²=25 and 3+4=(7)²=49. Therefore, 2+3=(5)²=25. The operation is addition followed by squaring the sum, not simple addition.

Dividing by 1/2 is the same as multiplying by 2. So, 30 divided by 0.5 equals 60. Adding 10 to 60 results in 70. Common errors include dividing by 2 (getting 15) or misinterpreting the fraction.

To find trailing zeros, count factors of 10 = min(factors of 2, factors of 5). Factor each number: 175 has 5², 180 has 2²·5, 12 has 2², 44 has 2², 80 has 2⁴·5, 66 has 2. Total twos = 11, total fives = 4. Min(11,4) = 4 trailing zeros.

Use Legendre's formula: exponent of prime p in n! = floor(n/p) + floor(n/p²) + floor(n/p³) + ... For 150! and p=2: floor(150/2)=75, floor(150/4)=37, floor(150/8)=18, floor(150/16)=9, floor(150/32)=4, floor(150/64)=2, floor(150/128)=1. Sum = 146.

The sum of 10 consecutive numbers starting from x is 10x + 45 (since 0+1+...+9 = 45). The sum of 11 consecutive numbers starting from y is 11y + 55 (since 0+1+...+10 = 55). Setting them equal gives 10x + 45 = 11y + 55, which simplifies to 10x - 11y = 10. This is one equation with two variables, so x - y cannot be uniquely determined - it depends on the specific values chosen.

Dividing by half is the same as multiplying by 2. 40 / 0.5 = 80. Then, 80 + 10 = 90. A common mistake is to divide by 2 (40/2=20), which would lead to 30.

Following the order of operations, 5 divided by 1/2 is equivalent to 5 multiplied by 2, which equals 10. Adding 3 to 10 results in 13. Distractors like 5.5 or 12 result from incorrect arithmetic or ignoring the reciprocal rule.

This is a logic puzzle. You can only subtract 6 from 30 once, because after you subtract it, you are subtracting from 24, then 18, and so on. The question asks how many times you can subtract it from 30 specifically.

This is a visual riddle. If you 'subtract' (remove) the top half of the digit '8', you are left with a '0' (or two zeros). Mathematically, subtracting half of 8 (4) leaves 4, but the riddle relies on the shape of the numeral.