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# (CMBH 2015) - Question Medium of Math

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Operations with Whole Numbers
Source: CMBH
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Question 1:

Medium

João is helping his mother organize a birthday party. They want to make packages with candies to give as souvenirs to the guests. If they have 120 chocolates, 200 candies, and 80 lollipops, and they want to divide them equally among 20 packages, how many candies of each type will there be in each package? Remember that they must use all the candies without any leftovers. Note that you will have to use all four basic operations to answer this question.
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Question 2:

Hard

In an inexact division of natural numbers, the divisor is three times five. If we add one unit to the dividend and do not change the divisor, the remainder of this new division becomes as large as possible. If we add one more unit to the new dividend and still keep the initial divisor, the quotient becomes fourteen. The sum of the digits of the initial dividend is:
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Question 3:

Easy

A person bought a car for cash, obtaining a 10% discount. He paid with 37,620 fifty-cent coins. The price of the car, without the discount, was:
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Question 4:

Medium

In an archery competition, the target is a circle with a radius of 10 cm and center O. One of the competitors hits an arrow at point A on the edge of the target and another arrow at point B, which also touches the edge of the target. Both arrows start from the same point P, which is 26 cm away from the center of the target. Knowing that the line PA is 24 cm and the line PB is 18 cm, calculate the power of point P in relation to the target. Then, determine the distance from point P to point C, if C is a point on the edge of the target that is hit by a third arrow, so that PC intersects PA at D and PB at E, and PD = 15 cm and PE = 9 cm.
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