## Quant Question Of The Day: 266

## Numbers

**If x, y are natural numbers such that 2013 + x ^{2} = y^{2}, then the minimum possible value of xy is**

A. 671

B. 668

C. 658

D. 645

Categories:
Quant question of the day, Question of the day

**If x, y are natural numbers such that 2013 + x ^{2} = y^{2}, then the minimum possible value of xy is**

A. 671

B. 668

C. 658

D. 645

**2013 = y ^{2} – x^{2}**

(y – x) (x + y) = 201

(y – x) (y + x) = 33 × 61 [2013 = 3 × 11 × 61]

y – x = 33

y + x = 61

2y = 94

y = 47

2x = 28

x = 14

(xy)min = 47 × 14 = 658

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C-658

658 (c)

C

C. 658

C – 658

Y^2-X^2=2023=61×11×3=61×33

Y+X=61

Y-X=33

X=47

Y=14

XY=658

c)