Aptitude Discussion

Q. |
Let $n$ be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of $n$? |

✖ A. |
144 |

✖ B. |
168 |

✔ C. |
192 |

✖ D. |
None of these |

**Solution:**

Option(**C**) is correct

Test of divisibility by 4 is that the last two digits should be divisible by 4.

**Case 1** : When the last 2 digits are 12, i.e., _ _ _$12 = 4 × 3 × 2 = 24$ numbers

**Case 2** : When the last 2 digits are 16, there are 24 numbers

**Case 3** : When the last 2 digits are 24 there are 24 numbers

**Case 4** : When the last 2 digits are 32 there are 24numbers

**Case 5 **: When last 2 digits are 36 there are 24 numbers

**Case 6 **: When last 2 digits are 52 there are 24 numbers

**Case 7** : When last 2 digits are 56 there are 24 numbers

**Case 8 **: When last 2 digits are 64 there are 24 numbers

Total $= 8 × 24 =$ **192**

**Arun**

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**Divyansh**

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why 32,52,56,64 is considered as they r not divisible by3, then how 24 came

It is clearly mentioned the number should be divisible by number 4

**Deepak Kumar Dubey**

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why last two digit 44 not consider here plz explain.....

Because the question says, 'no digit being repeated in the numbers' thats why :)

Why option B is incorrect?