Question Detail

Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

$\begin{aligned} \frac{290}{289} \end{aligned}$
$\begin{aligned} \frac{1}{289} \end{aligned}$
$\begin{aligned} \frac{290}{90} \end{aligned}$
$\begin{aligned} \frac{290}{19} \end{aligned}$

Answer: Option A

Explanation:

If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.

$\begin{aligned} \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{1^2} + \frac{1}{17^2} \end{aligned}$

$\begin{aligned} = \frac{290}{289} \end{aligned}$

1. Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

$\begin{aligned} \frac{290}{289} \end{aligned}$
$\begin{aligned} \frac{1}{289} \end{aligned}$
$\begin{aligned} \frac{290}{90} \end{aligned}$
$\begin{aligned} \frac{290}{19} \end{aligned}$

Answer: Option A

Explanation:

If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.

$\begin{aligned} \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{1^2} + \frac{1}{17^2} \end{aligned}$

$\begin{aligned} = \frac{290}{289} \end{aligned}$

2. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is

Answer: Option C

Explanation:

Let the three integers be x, x+2 and x+4.
Then, 3x = 2(x+4)+3,
x= 11
Therefore, third integer x+4 = 15

3. find the number, difference between number and its 3/5 is 50.

Answer: Option D

Explanation:

Let the number = x,
Then, x-(3/5)x = 50,
=> (2/5)x = 50 => 2x = 50*5,
=> x = 125

4. Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is

10:3
5:9
11:9
13:9

Answer: Option C

Explanation:

$\begin{aligned} => \frac{(x+y)}{(x-y)} = \frac{40}{4} \end{aligned}$

$\begin{aligned} => (x+y)= 10(x-y) \end{aligned}$

$\begin{aligned} => 9x = 11y => \frac{x}{y} = \frac{11}{9} \end{aligned}$

5. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number

Answer: Option D

Explanation:

If the number is x,

Then, x + 17 = 60/x

x2 + 17x - 60 = 0

(x + 20)(x - 3) = 0

x = 3, -20, so x = 3 (as 3 is positive)

Question Detail

Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

1. Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

2. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is

3. find the number, difference between number and its 3/5 is 50.

4. Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is

5. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number

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Question Detail

Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

1. Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is

2. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is

3. find the number, difference between number and its 3/5 is 50.

4. Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is

5. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number

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