Source: Magoosh Rank those three in order from smallest to biggest. I. 47/150 II. 111/350 III.299/900 A. I, II, III B. I, III, II C. II, I, III D. II, III, I E. III, I, II The OA is A

BTGmoderatorLU wrote:Source: Magoosh Rank those three in order from smallest to biggest. I. 47/150 II. 111/350 III.299/900 A. I, II, III B. I, III, II C. II, I, III D. II, III, I E. III, I, II The OA is A One approach is to find the common denominator of 150, 350 and 900 and then convert all 3 fractions so that they all have the same denominator. As you can imagine this will take a while. So, a faster approach may be to covert each fraction into a DECIMAL be dividing the numerator by the denominator. HOWEVER, we probably don't need to go beyond 3 decimal places. Let's try it. I. 47/150 = 47 ÷ 150 ≈ 0.313 II. 111/350 = 111 ÷ 350 ≈ 0.317 III. 299/900 = 299 ÷ 900 ≈ 0.332 0.313 < 0.317 < 0.332 So, I < II < III Answer: A Cheers, Brent

BTGmoderatorLU wrote:Source: Magoosh Rank those three in order from smallest to biggest. I. 47/150 II. 111/350 III.299/900 A. I, II, III B. I, III, II C. II, I, III D. II, III, I E. III, I, II The OA is A I. $\frac{47}{150} = \frac{48}{150} - \frac{1}{150}$ $=0.32 - \frac{1}{150}$ II. $\frac{111}{350} = \frac{112}{350} - \frac{1}{350}$ $= 0.32 - \frac{1}{350}$ III. $\frac{299}{900} = \frac{300}{900} - \frac{1}{900}$ $= 0.33333 - \frac{1}{900}$ So we can say that I $<$ II $<$ III Therefore, __A__ is the correct option.

BTGmoderatorLU wrote:Source: Magoosh Rank those three in order from smallest to biggest. I. 47/150 II. 111/350 III.299/900 A. I, II, III B. I, III, II C. II, I, III D. II, III, I E. III, I, II The OA is A Multiplying 47/150 by 6/6, we have 47/150 x 6/6 = 282/900. So 47/150 < 299/900. Multiplying 47/150 by 7/7 and 111/350 by 3/3, we have 47/150 x 7/7 = 329/1050 and 111/350 x 3/3 = 333/1050. So 47/150 < 111/350. From the above, we see that 47/150 is the smallest of the three fractions. To compare 111/350 and 299/900, we will not make both to equivalent fractions of the same denominator. We will argue that, although both are less than 1/3, 299/900 is much closer to 1/3 than 111/350 is (observe that 1/3 = 300/900 and 1/3 = 111/333). So 299/900 must be the largest of the three. Answer: A

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