GMAT Practice Question: Two numbers differ by 2 and sum to S...
Question
Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
- \frac{S}{2}-1
- \frac{S}{2}
- \frac{S}{2}+\frac{1}{2}
- \frac{S}{2}+1
- \frac{S}{2}+2
Topics: linear equations, word problems
Solution
Step 1
We first create unknowns for the two numbers
g = \text{greater number} s = \text{smaller number}
Step 2
We translate the statement \textbf{\text{"sum to "}} S into an equation
g + s = S
Step 3
We translate the statement \textbf{\text{"differ by "}} 2 into an equation by taking the greater minus the smaller
g - s = 2
Step 4
We add the two equations to eliminate s
g + s = S g - s = 2 2g = S + 2
Step 5
We divide both sides by 2 to isolate g and simplify
x = \frac{S + 2}{2} = \frac{S}{2} + 1
Answer
\frac{S}{2} + 1
