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Playing with Numbers — Chapter Test

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Q1
The two-digit number 'ab' equals ___ ?
ab = 10a + b.
Q2
47 = 10 × 4 + ___ ?
47 = 40 + 7.
Q3
ab − ba is always divisible by ___ ?
ab − ba = 9(a − b), a multiple of 9.
Q4
ab + ba is always divisible by ___ ?
ab + ba = 11(a + b), a multiple of 11.
Q5
Write 38 in generalised form.
38 = 30 + 8.
Q6
Is 153 divisible by 9?
Digit sum 1 + 5 + 3 = 9, so yes.
Q7
Is 246 divisible by 3?
Digit sum 2 + 4 + 6 = 12, divisible by 3, so yes.
Q8
What is 72 − 27?
72 − 27 = 45 = 9 × 5.
Q9
What is 41 + 14?
41 + 14 = 55 = 11 × 5.
Q10
What is the reverse of 58?
Swapping the digits gives 85.
Q11
A number 29 is reversed to 92. What is the difference?
92 − 29 = 63 = 9 × 7.
Q12
Is 1,210 divisible by 11?
Alternating sum 1 − 2 + 1 − 0 = 0, so yes.
Q13
If ab − ba = 36, then a − b = ___ ?
9(a − b) = 36, so a − b = 4.
Q14
The sum of a two-digit number and its reverse is 88. What is a + b?
11(a + b) = 88, so a + b = 8.
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