The product of two positive integers is 96. The sum of the two number

Question

The product of two positive integers is 96. The sum of the two number is 22. Which of the following could be the difference of the two integers?

A. 2
B. 5
C. 6
D. 8
E. 10

lucajava · Answer

ab = 96 = 2^5 * 3

a + b = 22

A few attempts will lead you to the right answer. In this case,  96 = 16 * 6  and  16 + 6 = 22 . Hence,  16 - 6 = 10 .

sahibr · Answer

Let the two integers be x and y.

Hence from the question we know that,

xy=96

x+y=22
Or y=22-x

Hence xy = 96
can be written as 
x(22-x)=96

=>22x-x(sq)=96

=>x(sq)-22x+96=0

=>x(sq)-16x-6x+96=0

=>x(x-16)-6(x-16)=0

=>(x-16)(x-6)=0

=>x=16 or x=6

Hence, y=16 or y=6 respectively

Difference between the two integers  gives us 16-6=10

Hence, option E.

ScottTargetTestPrep · Answer

We can create the equations in which x = one number and y = the other number:

xy = 96

and

x + y = 22

x = 22 - y

Substituting, we have:

(22 - y)y = 96

22y - y^2 = 96

y^2 - 22y + 96 = 0

(y - 16)(y - 6) = 0

So y = 16 or 6

When y = 16, x = 6, or when y = 6, x = 16.

So the difference could be 10.

Alternate Solution:

Letting x and y denote the numbers, we are given that x + y = 22 and xy = 96. Let’s find (x + y)^2:

(x + y)^2 = 484

x^2 + 2xy + y^2 = 484

Let’s subtract 4xy = 384 from each side of this equation:

x^2 + 2xy + y^2 - 4xy = 484 - 384

x^2 - 2xy + y^2 = 100

(x - y)^2 = 100

x - y = 10 or x - y = -10

Answer: E

Hasini22 · Answer

Products of 96
(1*96,2*48,3*32,4*24,6*16)
Only adding 6 and 16 gives 22.
Therefore the difference is 10

Posted from my mobile device

Phoenix19 · Answer

i solved it on the basis of logic
Stmt 1 - xy = 96 --Which means either x or y is even
Stmt 2 - x + y = 22 ---Since sum is even therefore both x and y even.

Now unit digit of 96 is 6. Therefore look for number that satisfy these conditions. You will arrive at 16,6 in a jiffy

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The product of two positive integers is 96. The sum of the two number

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The product of two positive integers is 96. The sum of the two number

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