Number System
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Q.

Which one of the following is the minimum value of the sum of two integers whose product is 36?

 A.

37

 B.

20

 C.

15

 D.

12

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Solution:
Option(D) is correct

List all possible factors $x$ and $y$ whose product is 36, and calculate the corresponding sum $x + y$:

$x$ $y$ $x \times y$ $x+y$
1 36 36 37
2 18 36 20
3 12 36 15
4 9 36 13
5 6 36 12

From the table, the minimum sum is 12


(3) Comment(s)


Mrigendra Pratap Singh
 ()

last row, 6 x 6=36.



Arghya Chakraborty
 ()

You should say "positive" integers.

Else :

(-6)*(-6)=36

But -6-6=-12<12



Apoorv
 ()

use AM $\geq$GM formula.

let two numbers be x and y.

product $=xy=36$ (given)

sum $= x+y$

AM $\geq$ GM

$\dfrac{x+y}{2} $\geq$ square root of xy

$\dfrac{x+y}{2} \geq \sqrt{36} $

$x+y \geq 6 \times 2$

$x+y \geq 12$