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Which of the following fractions is the largest?

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by Brent@GMATPrepNow » Fri Sep 22, 2017 6:08 am
ardz24 wrote:Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72
It doesn't take long to realize that A, C and E are not contenders, so we can eliminate them.
Then we're left with B and D

From here, one option is to convert them both to decimals (perhaps to three decimal places) by dividing the numerator by the denominator.
When we do this, we get....
B) 7/30 ≈ 0.233
D) 13/56 ≈ 0.232
Answer: B

Another option is to rewrite the two fractions with a common denominator, which is equal to the product (30)(56)
B) 7/30 = (7)(56)/(30)(56)
= 393/(30)(56) [aside: we need not evaluate the denominator]
D) 13/56 = (13)(30)/(56)(30)
= 390/(30)(56)
Answer: B


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by Jeff@TargetTestPrep » Thu Dec 07, 2017 9:31 am
ardz24 wrote:Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72
We need to determine the largest fraction. Let's weed out some obvious ones: 1/72 and 1/45 are each smaller than 13/56, and 1/24 is smaller than 7/30.

So we are left with 7/30 and 13/56 as the candidates for the largest fraction.

To compare two positive fractions, we can cross-multiply the numerator of one fraction with the denominator of the other fraction. That is, if a/b > c/d, then ad > bc (and vice versa), provided that a, b, c, and d are all positive.

Here we want to compare 7/30 and 13/56, and we have 7(56) = 392 and 13(30) = 390. Since 392 > 390, 7/30 > 13/56. Therefore, 7/30 is the largest fraction.

Answer: B

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by Matt@VeritasPrep » Thu Dec 07, 2017 5:56 pm
For D to be the largest, it'd have to be bigger than B. To compare two fractions, we could test an inequality:

7/30 > 13/56

7*56 > 13*30

392 > 390

Success! This is true, so 7/30 IS > 13/56.
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