HCL Number System Quiz-1

Solution
a^{2} - b^{2} = (a+b)(a-b)
725^{2} - 240^{2} = (725+240)(725-240) = 468025
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Solution
Sum of first n odd numbers = n^{2} = 241^{2} =58081
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Solution

\frac{17}{21}, \frac{13}{15}, \frac{4}{7}, \frac{11}{13}

 

LCM of 21, 15, 7 and 13 

21 = 3 x 7

15 = 3 x 5

7 = 1 x 7

13 = 1 x 13

LCM = 3 x 5 x 7 x 13 = 1365

\frac{1105}{1365}, \frac{1183}{1365}, \frac{780}{1365}, \frac{1155}{1365}

So,  \frac{13}{15} is largest 

Solution
Let A purchased x chocolates
According to the question
x \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{4} = 8
x=128

Solution
Let numbers are x, x+1 , x+2
According to question
x +(x+1)+( x+2) = 3603
3x+3 = 3603
3x=3600
x=1200
x+1 = 1200+1 = 1201

Solution
8^{\frac{1}{3}} \times 256^{\frac{1}{2}} \times 3
2 \times 16 \times 3 = 96

Solution
prime numbers between 22 and 40 = {23, 29, 31, 37}
The number of prime numbers between 22 and 40 which is divisible by 7 is zero because a prime number is divisible by 1 or itself.

Solution
4+1+2+6+5+3 = 21 which is divisible by 3
So, 412653 is divisible by 3.

Solution
Let numbers are x, (x+1) , x+2
According to question

3x+5(x+1)+2(x+2) = 199
3x+5x+5+2x+4 = 199
10x+9 = 199
10x = 190
x= 19
Numbers are 19, 20, 21
Middle no = 20

Solution
Let number is x
According to question
93 + \frac{1}{3} \times x = 134
\frac{x}{3} \times = 134 - 93
x=123