Question

1) if the sum of two prime numbers is divisible by 7 and is a perfect square, what is a possible product of these numbers?

Answer 1

1) The sum of 2 prime numbers is ALWAYS even, so if x and y are prime number,. then (x+y)/7  = z². In this case either x = 2 or y = 5 (or vice vera). This is the only possibility to be divisible by 7 . Then (5+2)/7 = 1² = 1

2) 5 pipes → 2 hours → 2 pools
then 1 pipe takes (5x2) 10 hours to fill 2 pools
or  1 pipe takes (10/2) 5 hours to fill 1 pool

3) It's 6/30 = 0.2 or 20%

4) 35% represent 7 Students, 100% of the class represent x students:
35%/7 = 100%/x
0.35/7 = 1/x (Cross multiplication) →0.35x = 7 and x = 7/0.35 → x = 20 students

5) Let K be the age of Katie and B her brother's
K + 2 = B  OR K  = x - 2 (Today)

In 12 years (B+12), B will be twice K  (remember K = B-2) →
B+12 = 2(K) OR B+12 = 2(B-2)
B+12 = 2(B-2) →
B+12 = 2B - 4→
12 + 4 = B and B = 16. If the brother is 16, then Kate is 14
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