Aptitude Discussion

**Common Information**

A boy is roaming on the roof of his house observes that the insects are there in bunches. He found '$p$' insects on day 1. On day two, the number of insects doubled and he takes out '$q$' insects and kills them. On the third day again, the insects left is doubled and he again takes out '$q$' insects and kill them. On the fourth day also he found the same, insects left is doubled and he takes out '$q$' insects again. He is surprised to find that there are no insects left on his roof.

Q. |
The minimum number of insects that he left on day 1 is? |

✖ A. |
8 |

✔ B. |
7 |

✖ C. |
0 |

✖ D. |
6 |

**Solution:**

Option(**B**) is correct

Day (1) -> Number of insects $-> p$

Day (2) -> Number of insects $-> 2p−q$

Day (3) -> Number of insects $-> 4p−3q$

Day (4) -> Number of insects $-> 8p−7q$

Thus

\(8p-7q=0\)

\(\Rightarrow q=\dfrac{8p}{7}\)

$⇒ P$ has to multiple of 7 so that $q$ is an integer

For $p$ is to minimum $q=8$

Thus, $p =7$