If the sum of two positive integers is 100 and their product is 2464,

Question

If the sum of two positive integers is 100 and their product is 2464, what is the value of the positive difference of the two integers ?

A. 4
B. 6
C. 8
D. 10
E. 12

JerryAtDreamScore · Accepted Answer

Breaking Down the Info:

Since the two numbers add up to 100, they must have an average of 50. We can write the two numbers as  50 + x  and  50 - x .

Then  (50 + x)(50 - x) = 2464 = 2500 - x^2 . We have  x^2 = 36  and  x = 6 , hence the difference is  2x = 12 .

Answer: E

chetan2u · Answer

The question should immediately tell you to look for the factors of 2464.

2464=8*308=8*2*154=8*2*2*77=8*2*2*7*11

Since the sum is even and is 100, the integers should be clearly less than 100 each. 
One way would be start from multiples of 11.
2464 = (11*2)*(7*16)…..No as 7*16>100
2464=11*4*7*8=44*56….Yes as 44+56=100.

Or form an equation 
So the integers will be  (7*2^x)+(11*2^{5-x})=100 
When x=3, integers are 56 and 44

Difference = 56-44 = 12

E

QuantMadeEasy · Answer

Let x and y are two positive integers
x+y = 100
x*y = 2464

Factorize the product 2464 = 2*2*2*2*2*7*11

Finding sum x+y = 100, using the factors of 2464
x = 56, y = 44

x - y = 12

E is correct

Suhasi · Answer

Let the two numbers be a and b. Then a + b = 100, and ab = 2464.

Two equations to know -
 (a+b)^2 = a^2 + b^2 + 2ab 
(a-b)^2 = a^2 + b^2 - 2ab

Equation 1: 
(a+b)^2 = a^2 + b^2 + 2ab 
(100)^2 = a^2 + b^2 + 2(2464)
 a^2 + b^2 = (10000 - 4928)

Substitute this value in  Equation 2: 
(a-b)^2 = a^2 + b^2 - 2ab
(a-b)^2 = (10000 - 4928) - 4928
(a-b)^2 = 144

Therefore, 
(a-b) = 12 (We need positive difference)

There are various ways to solve this question but if you're comfortable working with these 2 algebraic identities, this method works well.

GynCliff · Answer

The easier ways is to use the answers to complete the second equation, solve the two equations and test if the product of the answers you get is = 2464.

Assume x is bigger number and y is the smaller number.

So equation 1...
 x + y = 100

equation 2....

x - y = Either 4, 6, 8, 10, or 12

Working with 12

x + y = 100
x - y = 12

add the two equations

2x = 112

x = 56

Therefore y = 44

The product xy = 2464

Answer E

rey1009 · Answer

If the sum of two positive integers is 100 and their product is 2464, what is the value of the positive difference of the two integers ?
(x+y) =100
xy=2464
x-y ={(x+y)^2 -4xy}^1/2
x-y= (10000-4*2464)^1/2
x-y=144^1/2
x-y=12

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the sum of two positive integers is 100 and their product is 2464,

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the sum of two positive integers is 100 and their product is 2464,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards