When two numbers are added together, their sum is 25, and their product is given by 30. What is the square of their difference equal to?
Answer Choices
Correct answer marked belowSee the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Unlock the full explanation
Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.
Classic sum/product setup. Key move for me was recalling (x-y)^2 = x^2 - 2xy + y^2, and then rewriting x^2 + y^2 from the sum squared. Took me a second to see it but it's clean once you do.
Same, I almost started solving for x and y individually lol
Yeah the identity route is way faster than substitution here
Wait, I got confused because I thought I needed to actually find the two numbers. Do we ever need their individual values, or is the identity enough?
You don't need them individually. The difference squared comes straight from (x+y)^2 - 4xy
The numbers aren't even nice integers, so I respect that they made this solvable without finding them. Took me longer than it should have though.
Quick strategy note: whenever I see sum and product given and they ask for something symmetric like difference squared, I immediately write down (x+y)^2 and xy. Saved me a lot of time.
Good tip. I'm going to start looking for that pattern
What it tests
Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.
Common trap
Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.