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Indices, SM-Bank 056

Using divisibility tests, find the largest number less than 500 that is divisible by 9.   (2 marks)

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\(\text{A number is divisible by }9\ \text{if the sum of the digits is divisible by }9.\)

\(\text{Checking numbers less than } 500\)

\(499=4+9+9=22\ \Rightarrow\ \text{ not divisible by 9}\)

\(498=4+9+8=21\ \Rightarrow\ \text{ not divisible by 9}\)

\(497=4+9+7=20\ \Rightarrow\ \text{ not divisible by 9}\)

\(496=4+9+6=19\ \Rightarrow\ \text{ not divisible by 9}\)

\(495=4+9+5=18\ \Rightarrow\ \text{ divisible by 9}\ \checkmark\)

\(\therefore\ 495\ \text{is the largest number less than }500\ \text{that is divisible by }9.\)

Indices, SM-Bank 055

Using divisibility tests, find the smallest number greater than 200 that is divisible by 6.   (2 marks)

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\(\text{A number is divisible by }6\ \text{if it is divisible by both }2\ \text{and }3.\)

\(\text{A number is divisible by }2\ \text{if the last digit is  }2 , 4 , 6 , 8 , 0.\)

\(\therefore\ \text{The possible numbers are in the pattern }202 , 204 , 206 …\ \text{as they are all divisible by }2\)

\(\text{A number is divisible by }3\ \text{if the sum of the digits is divisible by }3.\)

\(2+0+2=4\ \Rightarrow\ \text{ not divisible by 3}\)

\(2+0+4=6\ \Rightarrow\ \text{ divisible by 3}\ \checkmark\)

\(\therefore\ 204\ \text{is the smallest number greater than }200\ \text{that is divisible by }6.\)

Indices, SM-Bank 054

Using divisibility tests, find the smallest number greater than 1000 that is divisible by 6.   (2 marks)

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\(\text{A number is divisible by }6\ \text{if it is divisible by both }2\ \text{and }3.\)

\(\text{A number is divisible by }2\ \text{if the last digit is  }2 , 4 , 6 , 8 , 0.\)

\(\therefore\ \text{The first possible number is }1002\ \text{as it is divisible by }2\)

\(\text{A number is divisible by }3\ \text{if the sum of the digits is divisible by }3.\)

\(1+0+0+2=3\ \Rightarrow\ \text{divisible by 3}\ \checkmark\)

\(\therefore 1002\ \text{is the smallest number greater than }1000\ \text{that is divisible by }6.\)

Indices, SM-Bank 053

A number is divisible by 12 if it is also divisible by 3 and 4.

Prove, using the divisibility tests for 3 and 4, that 756 is divisible by 12.   (2 marks)

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\(\text{A number is divisible by }3\ \text{if the sum of the digits is divisible by }3.\)

\(7+5+6=18\ \Rightarrow\ \text{divisible by 3}\ \checkmark\)

\(\text{For divisibility by }4\ \text{the last 2 digits in the number must be divisible by }4. \)

\(56\ ÷\ 4=14\ \Rightarrow\ \text{divisible by 4}\ \checkmark\)

\(\therefore 756\ \text{is divisible by }12\ \text{as it is divisible by both }3\ \text{and }4.\)

Indices, SM-Bank 052

Prove using divisibility tests that 282 is divisible by 6.   (2 marks)

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\(\text{A number is divisible by }6\ \text{if it is divisible by both }2\ \text{and }3.\)

\(\text{For divisibility by }2\ \text{the number must end in }2 , 4 , 6 , 8 , 0.\ \checkmark\)

\(\text{For divisibility by }3\ \text{the sum of the digits must be divisible by }3.\)

\(2+8+2=12\ \Rightarrow\ \text{divisible by 3}\ \checkmark\)

\(\therefore 282\ \text{is divisible by }6\)

Indices, SM-Bank 051 MC

Which of the following numbers is not divisible by \(9\)?

  1. 234
  2. 1845
  3. 506
  4. 126
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\(C\)

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\(\text{A number is divisible by }9\ \text{if the sum of the digits is divisible by }9.\)

\(\text{Option A:}\rightarrow\) \(\ 2+3+4=9\ \checkmark\)
\(\text{Option B:}\rightarrow\) \(\ 1+8+4+5=18\ \checkmark\)
\(\text{Option C:}\rightarrow\) \(\ 5+0+6=11\ -\text{not divisible by }9\)
\(\text{Option D:}\rightarrow\) \(\ 1+2+6=9\ \checkmark\)

 
\(\Rightarrow C\)

Indices, SM-Bank 050 MC

Which of the following numbers is not divisible by \(5\)?

  1. \(1800\)
  2. \(95\)
  3. \(102\)
  4. \(1\ 202\ 005\)
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\(C\)

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\(\text{A number is divisible by }5\ \text{if the last digit is a }5 \text{ or }0.\)

\(\text{Option C:}\rightarrow\) \(\ 102\ \text{does not end in }5 \text{ or }0.\)

 
\(\Rightarrow C\)

Indices, SM-Bank 049 MC

Which of the following numbers is not divisible by 2?

  1. 505
  2. 44
  3. 1258
  4. 1202
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\(A\)

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\(\text{A number is divisible by }2\ \text{if the last digit is a }2 , 4 , 6 , 8 \text{ or }0.\)

\(\text{Option A:}\rightarrow\) \(505\ \text{does not end in }2 , 4 , 6 , 8 \text{ or }0.\)

 
\(\Rightarrow A\)

Indices, SM-Bank 048 MC

Which of the following numbers is not divisible by 4?

  1. 112
  2. 32
  3. 502
  4. 608
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\(C\)

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\(\text{A number is divisible by }4\ \text{if the last 2 digits are divisible by }4.\)

\(\text{Option A:}\rightarrow\) \(\ 12\ ÷\ 4=3\ \ \checkmark\)
\(\text{Option B:}\rightarrow\) \(\ 32\ ÷\ 4=8\ \ \checkmark\)
\(\text{Option C:}\rightarrow\) \(\ 02\ \text{not divisible by 4}\)
\(\text{Option D:}\rightarrow\) \(\ 08\ ÷\ 4=2\ \ \checkmark\)

 
\(\Rightarrow C\)

Indices, SM-Bank 047 MC

Which of the following numbers is not divisible by 3?

  1. 3102
  2. 239
  3. 42
  4. 8121
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\(B\)

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\(\text{A number is divisible by }3\ \text{if the sum of its digits is divisible by }3.\)

\(\text{Option A:}\rightarrow\) \(3+1+0+2=6\ \ \checkmark\)
\(\text{Option B:}\rightarrow\) \(2+3+9=14\ \ \text{not divisible by 3}\)
\(\text{Option C:}\rightarrow\) \(4+2=6\ \ \checkmark\)
\(\text{Option D:}\rightarrow\) \(8+1+2+1=12\ \ \checkmark\)

 
\(\Rightarrow B\)