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 ?

GMAT Panda · Accepted Answer

S/2 + 1 We first create unknowns for the two numbers g = greater number s = smaller number We translate the statement "sum to " S into an equation g + s = S We translate the statement "differ by " 2 into an equation by taking the greater minus the smaller g - s = 2 We add the two equations to eliminate s g + s = S g - s = 2 2g = S + 2 We divide both sides by 2 to isolate g and simplify x = S + 2/2 = S/2 + 1

Explanation	Calculations	Help
$We first create unknowns for the two numbers$	$g = greater number s = smaller number$
$We translate the statement "sum to " S into an equation$	$g + s = S$
$We translate the statement "differ by " 2 into an equation by taking the greater minus the smaller$	$g - s = 2$
$We add the two equations to eliminate s$	$g + s = S g - s = 2 2 g = S + 2$
$We divide both sides by 2 to isolate g and simplify$	$x = \frac{S + 2}{2} = \frac{S}{2} + 1$

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