Uk Senior Mathematical Challenge (Sample Questions)

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Here is a question?

1) How many squares of area 1cm squared have a total perimeter length which is equal to the perimeter of a single square of area 4cm squared?

2) A furlong is 220 yards long and a yard is 36 inches. A chain is 44 cubits long and a cubit is 54 barleycorns. There are 10 chains in a furlong. How many barleycorns are thre in one inch?

3) When n=81 what is thhe value of n^20/3^n?

4) What is the remainder when 123456789 8 987654321 is divided by 6?

5) The value of the product wxyz is 2002 and w, x,y,z are prime numbers. What is the value of w^2, x^2, y^2 and z^2.

6) For how many integer values of n does the equation x^2 +nx -16 = 0 have integer solutions?

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This is no competition, discuss the answers in this thread?

Thank You

Reply 1

SsEe

1) 2
2) 3 bc/in (ooohhhh)
3) 1/3
4) 5
5) 4, 49, 121, 169
6) 5. n=0, 6, -6, 15, -15

1) A 4x4 square has perimeter 8cm. And 2 1cm squares will also have total perimeter 8.

2) 1 chain = 44 cubits = 44*54 = 2376 barleycorns
220 yards = 1 furlong = 10 chains = 10*2376 = 23760 barleycorns
1 yard = 23760/220 = 108 barleycorns = 36 inches
1 inch = 108/36 = 3 barleycorns

3) [81^20]/[3^81] = [3^80]/[3^81] = 1/3

4) Digit sum of 1234567898987654321 is 98 which is not divisible by 3. ....4322 digit sum is 99 which is divisible by 3. It is an even multiple of 3 so must also be a multiple of 6. So ...4321 must leave a remainder of 5.

5) Prime factorization of 2002 is 2*7*11*13. So these numbers squared give 4, 49, 121 and 169

6) If we factorize x² + nx - 16 we must have brackets like (x...)(x...)
The only combinations for the rest of the brackets that multiply to give -16 are (4, -4) (-4, 4) (-8, 2) (8, -2) (16, -1) and (-16, 1). To get n we add the two numbers together. So we get n = 0, 0, -6, 6, 15 and -15. That's 5 distinct values of n.