7th and 8th grade, March

    C.1185. Is there a positive whole number n such that:

    C.1186. Out of the numbers divisible by 3, we picked four consecutive numbers. To the sum of these, we added a third of the sum, and then a half of the third of the sum. We got 225. What were those four numbers?

    C.1187. Towards the end of the opening month of a new school year, two students are talking after school:

    – What is the average of your grades in Math now?

    – 4.6

    – That is impossible since the year just started. You could not possibly have that many grades.

    What was the doubting student thinking of if the possible grades teachers give out in this school are 1, 2, 3, 4, and 5; 5 being the best grade?

    C.1188. Sam and his father are talking:

    – Son, how many pages are there in the book you have to read for school?

    – Less than 1000.

    – Have you started reading it yet?

    – Yes, on Sunday I already passed page 150.

    – And how many pages did you read today?

    – Very many! The sum of the page numbers of the pages I read today is 2761.

    What pages did Sam read on the day of this conversation?

    C.1189. Is there a number that has at least 2 digits, is a square number, has all different digits, and if you change the order of its digits you always get a square number?

    C.1190. Grandma Olga is baking a cake in a 24 x 42 cm rectangular baking dish. Up until now, grandma always cut her cakes in the baking dish by 5 straight cuts parallel to the shorter side of the dish, and 3 cuts parallel to the other side of the dish to get 24 equal pieces. Her handy grandson, however, made an L shape knife for her with one 6 cm long blade and another 7 cm long blade which is perpendicular to the shorter one. She just has to push this knife into the cake from the top to make a cut. At least how many times does grandma have to push this knife into the cake to make her usual 24 equal pieces?

    C.1191. Are there eleven consecutive positive whole numbers whose sum is prime? If so, find all of them; if not, prove it!

    C.1192. In a class 85% of the students received the highest grade in English Literature, 80% in Math, 75% in History, and 30% in Chemistry. About what percent of the students could you say for sure received the highest grade in all four of these subjects?

    Please send your solutions here.

    The Sharma Kamala Educational Trust is sponsoring the participation of students from India. So, if you are a student living in India, please, send your solutions to: Group C from India

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