Her birthday is December 31st. Today is January 1st so she was 7 two days ago, and turned 7 last year. Now she’s 8 and will turn 9 this year. And next year she’ll turn 10.
For example, if today is 01 Jan 2015:
30 Dec 2014 = age 7 (two days ago)
01 Jan 2015 = age 8 (today, she turned 8 on 31 Dec 2014, which was last year)
31 Dec 2015 = age 9 (her birthday this year)
31 Dec 2016 = age 10 (her birthday next year)
From a basket of mangoes when counted in twos there was one extra,
counted in threes there were two extra,
counted in fours there were three extra,
counted in fives there were four extra,
counted in sixes there were five extra,
but counted in sevens there were no extras.
At least how many mangoes were there in the basket?
119. The number has to be evenly divisible by seven for there to be no extras when counting in sevens, and it has to be odd in order for there to be one extra when counting by twos. It also can’t be evenly divisible by three through six. 119 is the first odd multiple of 7 that satisfies the requirements.
Jim and Wanda both have some apples. If Jim gives Wanda an apple, they will both have the same number of apples. However, if Wanda gives Jim an apple, Jim will have twice as many as Wanda. How many apples do Jim and Wanda each have?