Two numbers are such that their sum is 54 and product is 629. What is

Question

Two numbers are such that their sum is 54 and product is 629. What is the positive difference of the numbers?

A. 20
B. 25
C. 40
D. 46
E. 48

imeanup · Answer

17*37=629

17+37=54

Positive difference  = 37-17=20

Ans A

NJ997 · Answer

Let a and b be our 2 numbers.
And we know that
 (a+b)^2 = a^2 + b^2 + 2*a*b 
 (a-b)^2 = a^2 + b^2 - 2*a*b

Hence, we can write  (a-b)^2 = (a+b)^2 - 2*a*b - 2*a*b =(a+b)^2 - 4*a*b

Substituting (a+b)=54 and (a*b) = 629,

(a-b)^2 = 54^2 - 4*629 = 400 
 (a-b) = \sqrt{400} = \pm 20 
We'll only consider 20 since we are asked the positive difference

So I think the answer is A

John1234Gmat · Answer

Is there a quicker way to figure out 629 is not prime? I got the answer A but it took me a minute to figure out 629 was divisible by 17

Vetrick · Answer

Do Prime Factorisation of 629 :
Sum of 6+2+9 is not divisible by 3. So, it is not divisible by 3 or 9
when we try dividing 629 by 7, we find that it is not divisible by 7
6+9 is not equal to 2, so 629 is not divisible by 11
when we try dividing 629 by 13, we find that it is not divisible by 13
Now we try dividing 629 by 17, we find that it is divisible by 17 and the factors of 629 are 17 and 37.

(Since 37 is a prime number, the factors are only 17 and 37)

we find that the condition a+b = 54 also is satisfied -> 17+37 = 54

So 37-17 = 20

Therefore the answer choice is A

GynCliff · Answer

Like I always say GMAT will punish you if you are too much of a stricter of methods and formulas and worse if you don't remember them.

In my case I use the answers to complete the second difference equation and the resolve.

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

Equation 1

x + y = 54 
x - y = either 20, 25, 40, 46 or 48

Remember to put in mind that all this will have a solution BUT you are looking for a solution whose product will give you 629...it's a very important factor remember.

- Another thing is that the the two number must be 2 digit numbers, so we eliminate 46 and 48. 
 
- Now working with x - y = 20

x + y = 54 
x - y = 20 
__________add the two equations

2x = 74

x = 37

Therefore y = 17

Test if the product is = 629

17 time 37 = 629

Answer A.

Abhishek009 · Answer

a + b = 54  ,  ab = 629

(a - b)^2 = (a + b)^2 - 4ab

Or,  (a - b) = \sqrt{(a + b)^2 - 4ab}

Or,  (a - b) = \sqrt{(54)^2 - 4*629}

Or,  (a - b) = \sqrt{400}

Or,  (a - b) = 20 , Answer must be (A)

Two numbers are such that their sum is 54 and product is 629. What is

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Two numbers are such that their sum is 54 and product is 629. What is

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