GRE Sample Test 3 Quantitative Reasoning 1

Since the fractions we’re comparing have the same numerator, the fraction with the smaller denominator will be larger.The comparison is thus: $\sqrt{1+\sqrt{\frac{1}{3}}}$ vs $\sqrt{1+\sqrt{\frac{1}{4}}}$ To simplify the comparison, square both quantities to arrive at: 1 + $\sqrt{\frac{1}{3}}$ vs 1 + $\sqrt{\frac{1}{4}}$ Simplify further by subtracting 1 from both quantities: $\sqrt{\frac{1}{3}}$ vs $\sqrt{\frac{1}{4}}$ Simplify further by squaring both quantities: $\frac{1}{3}$ vs $\frac{1}{4}$ Since $\frac{1}{3}$ > $\frac{1}{4}$ , the denominator in Quantity A is greater, which means the fraction in Quantity A is smaller.