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Rank those three in order from smallest to biggest.

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by Brent@GMATPrepNow » Thu Aug 22, 2019 12:49 pm
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

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Brent
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by swerve » Thu Aug 22, 2019 2:36 pm
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.
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by Scott@TargetTestPrep » Sat Aug 24, 2019 4:20 am
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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