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Sajjad1994
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Which one of the following is the minimum value of the sum of two 27 Nov 2016, 11:32
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Question Stats:

82% (00:44) correct 18% (00:49) wrong based on 123 sessions

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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) 13
(E) 12

Source: Nova GMAT
Difficulty Level: 550
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E
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Which one of the following is the minimum value of the sum of two 01 Oct 2019, 00:06
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SajjadAhmad
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) 13
(E) 12

Source: Nova GMAT
Difficulty Level: 550

SajjadAhmad,

I think it's a flawed question. why ?

let's integers be x and y.

Their sign is not stated in the question. Thus they both can be negative or both can be positive.

xy = 36

1 x 36 = 36

2 x 18 = 36

3 x 12 = 36

4 x 9 = 36

6 x 6 = 36.

Since we don't know their sign , both x and y could be negative . Ultimate product is positive.

-1 x -36 = 36

Minimum Value : -1 + (-36) = -37.

This option is not included in the question .

Thnks.
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Which one of the following is the minimum value of the sum of two 27 Nov 2016, 13:43
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SajjadAhmad
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) 13
(E) 12

a*b = 36

If a = b = 6 ; then ab = 36

a + b = 12 ( which is among the given option )

Hence, answer will be (E) 12
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Which one of the following is the minimum value of the sum of two 27 Nov 2016, 18:36
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SajjadAhmad
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) 13
(E) 12

\((a-b)^2 \geq 0 \iff (a+b)^2 \geq 4ab \iff a+b \geq 2\sqrt{ab} \quad \forall a,b>0\)

Hence \(a+b \geq 2\sqrt{ab} =2\sqrt{36} =12 \iff a=b=6\)

The answer is E

Mathematically, AM-GM inequality is defined that: \(x+y \geq 2\sqrt{xy} \quad \forall x,y \geq 0\)
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Which one of the following is the minimum value of the sum of two 07 Oct 2019, 20:04
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SajjadAhmad
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) 13
(E) 12

Source: Nova GMAT
Difficulty Level: 550


We have the following positive integers that yield a product of 36.

1 and 36

2 and 18

3 and 12

4 and 9

6 and 6

Thus, the minimum sum is 6 + 6 = 12.

Alternate Solution:

It is a well-known fact that for a given area of a rectangle, the smallest perimeter is obtained when the shape is a square. We can use this fact, noting that xy = 36 is an area formula, where x = length and y = width. Thus, since a square has length and width equal, we see that x = y, so we can have x^2 = 36, and so x = 6. Thus, the minimum sum (half-perimeter) will be 6 + 6 = 12.

Answer: E
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