Answer
d) is correct.
Work Step by Step
We have
$p_A=\frac{1}{2}m_0v_0$; its vector is directed due north.
$p_B=m_0v_0$; its vector is directed due east.
$p_C=2m_0v_0$; its vector is directed due south.
$p_D=2m_0v_0$; its vector is directed due west.
$p_E=\frac{1}{2}m_0v_0$; its vector is directed due north.
$p_F=4m_0v_0$; its vector is directed due west.
So runners A and E have identical momenta.
