Integral Solutions

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# Integral Solutions

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1/X + 1/Y = 1/3....How many ordered pair (x.y) satisfy this.

20 Answers
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Swadesh threw five standard dice simultaneously. He found that the product of the numbers on the top faces was 216. which of the following could not be the sum of the numbers on the top five faces?

1. 17

2. 18

3. 19

4. 20

Difference cases are
1*1*6*6*6 sum = 20
2*1*3*6*6 sum = 18
2*2*3*3*6 sum = 16
1*4*3*3*6 sum = 17

Hence 19 cannot be the sum

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how many positive integers less than or equal to 120 are relatively prime to 120?

120 (1-1/2)(1-1/3)(1-1/5) = 32 numbers

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the value of x+y such that x square - y square =343 and x,y are positive integers is,

1. 343

2. 49

3. 7

4. a or b

(x+y)(x-y) = 343
possible solutions
343*1
49*7
Hence value of x+y is a or b

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the difference between the cubes of two consecutive positive integers is 1027. then the product of these integers is.

(a+1)^3 - a^3 = 1027
3a^2+3a+1 = 1027
3(a^2+a) = 1026
a^2 +a = 342
a(a+1) = 342

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The teacher of Confucius, the confused soul, told him: "my age a two digit number is not prime but odd and if you reverse the digits of my age and add that number to my age , you obtain a number that is a perfect square. if you reverse the digits of my age and subtract the number from my age you again have a perfect square.

the age of Confucius teacher was a number divisible by

7, 9, 13, 15

ab= 10a+b
ba = 10b+a
sum = 11a+11b = 11(a+b), since it is a perfect square, hence a+b = 11
possible values (65, 74, 83, 92)
only difference 0f 65 and 56 (reverse) is perfect square.
Hence number is 65
65 is divisible by 13.

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Agree with comment above me.

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