The product of two whole numbers is 10,000,000. None of them is a
multiple of ten. What is the sum of both the numbers?
A – 20, B – 78253, C – 4264, D – 29574, E – 35233
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The product of two whole numbers is 10,000,000. None of them is a
multiple of ten. What is the sum of both the numbers?
A – 20, B – 78253, C – 4264, D – 29574, E – 35233
Just try all of the answers to see which one is correct. Here is the methodology:
xy = 1e7
x+y = c
x = c-y
(c-y)y = 1e7
cy - y2 = 1e7
y2 - cy + 1e7 = 0
Use quadratic equation to solve for y. Try the given values of c to see which one works (B – 78253). .:)
No, that's not it. B is correct, but the solution is much simpler.
10,000,000 = 107 = 27 * 57
Since neither of the numbers in question is a multiple of 10, the only solution is 128 + 78125 = 78253
since 10,000,000 is = (2*5)7
Then if the 2 unknown numbers are represented as A and B, such that
A = 2x*5y
B = 2(7-x)*5(7-y)
Then,
If A and/or B was divisible by 10 then x and y would both have to at least 1.
But since you indicate that A and B are both not divisible by 10, then
either x = 0 and y = 7, or verse visa.
Either way,
the 2 numbers that multiply to 10,000,000 where neither are divisible by 10 are 27 and 57
and their sum is 78253.
[EDIT]:thumb: LogoPhobic! :)[/EDIT]
Nice, elegant solution. But I don't understand your comment. What isn't it?Quote:
Originally Posted by Logophobic
If the solution was not given as multiple-choice, your method would be of no use:
The product of two whole numbers is 583,443. Neither number is a
multiple of 21. What is the sum of these two numbers?
In which deductive way did you come to your solution?Quote:
Originally Posted by Logophobic
True, but since the answers were given, it seems like a perfectly valid approach to me. Just using the information provided.....:)Quote:
Originally Posted by Logophobic