The stress versus strain graphs for wires of two materials A and B are as shown in the figure.  If Y_A and Y_B are the Young's moduli of the materials, then 

The Young's modulus is determined by the stress vs strain graph's slope.
The graph shows the angle that the line in the stress vs. strain graph makes in each scenario.
We are aware that slope equals $\tan \theta$.
The slope in the case of material (A) is equal to $\tan {60}^{°}$
The slope in Material (B) is $\tan {30}^{°}$.

We know that the slope is equal to Young's modulus,

${\mathrm{Y}}_{\mathrm{A}}=\tan {60}^{°}=\sqrt{3}$

${\mathrm{Y}}_{\mathrm{B}}=\tan {30}^{°}=\frac{1}{\sqrt{3}}$

$\frac{{\mathrm{Y}}_{\mathrm{A}}}{{\mathrm{Y}}_{\mathrm{B}}}=\frac{\tan {60}^{°}}{\tan {30}^{°}}=\frac{\sqrt{3}}{{\displaystyle \frac{1}{\sqrt{3}}}}=3$

$3{\mathrm{Y}}_{\mathrm{B}}={\mathrm{Y}}_{\mathrm{A}}$

Hence the correct answer is ${\mathrm{Y}}_{\mathrm{A}}=3{\mathrm{Y}}_{\mathrm{B}}.$