Question

If arc PQR above is a semicircle, what is the length of diameter PR ?
(1) a = 4
(2) b = 1

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

R.E.F image

Angle in the semicircle formed by

diametric pts. is ${90}^{\circ }$

$\Delta ADC$ $\Delta ABC$

$x^2=2^2+a^2$ $x^2+B{C}^2=(a+b{)}^2$

$x^2=2^2+4^2$ $\Delta BCD$

$x=\sqrt{18}$ $B{C}^2=2^2+1^2$

$\therefore$ sufficient $BC=\sqrt{5}$

alone $\therefore x^2+B{C}^2=5^2$

$x^2=25-5$

$x=\sqrt{20}$

$\therefore$ Both together sufficient