Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?
The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples.
Consider the following statements:
1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.
2. The total cost of one orange and one mango is equal to the cost of one apple.
Which of the statements given above is/are correct?
$32^5 + 2^{27}$ is divisible by
Let $p$ and $q$ be positive integers satisfying $p < q$ and $p + q = k$. What is the smallest value of $k$ that does not determine $p$ and $q$ uniquely?
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