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Do some quick comparisons. For larger fraction, the numerator should be larger (denominators are same) and/or denominator should be smaller (numerators are same).

So comparing 1/24, 1/45 and 1/72, we ignore 1/45 and 1/72.

Compare 1/24 and 7/30: Since 7/28 = 1/4, we know that 7/30 is a little bit smaller than 1/4. So, 7/30 is definitely bigger than 1/24 (ELIMINATE A) Compare 7/30 and 1/45: Since we already we know that 7/30 is a little bit smaller than 1/4, we know that 7/30 is definitely bigger than 1/45 and 1/72 (ELIMINATE C and E) We're left with 7/30 and 13/56. These two are VERY CLOSE in size, so we may need to resort to long division. NOTE: When we do so, let's stop at 2 decimal places. Hopefully that will be enough... 7 ÷ 30 ≈ 0.23 13 ÷ 56 ≈ 0.23 Shoot, still too close to call. One more calculation gets us to.... 7 ÷ 30 ≈ 0.233 13 ÷ 56 ≈ 0.232 Answer:

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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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Which of the following fractions is the largest? [#permalink]

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23 Jul 2017, 23:28

I used the following method:

Which of the following fractions is the largest? A. 1/24 B. 7/30 C. 1/45 D. 13/56 E. 1/72

STEP-1: A. 1/24 = can be rewritten as 5/120 B. 7/30 = can be rewritten as 28/120 So B is bigger

STEP-2: B. 7/30 = can be rewritten as 21/90 C. 1/45 = can be rewritten as 2/90 So B is bigger

STEP-3: D. 13/56 = Here I paused and waited to eliminate B or E

STEP-4: E. 1/72 = can be rewritten as 5/360 B. 7/30 = can be rewritten as 84/360 So B is bigger

STEP-5: Coming back to Choices D and B D. 13/56 = can be rewritten as (13*30)/(30*56) = 390/(30*56) B. 7/30 = can be rewritten as (7*56)/(30*56) = 392/(30*56) So B is bigger

Re: Which of the following fractions is the largest? [#permalink]

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24 Jul 2017, 01:10

stonecold wrote:

Which of the following fractions is the largest?

A. 1/24 (1/24*4/4 =4/96) B. 7/30 (7/30 * 3/3 = 21/90) C. 1/45 (1/45 * 2/2 = 2/90) D. 13/56 (13/56*2/2 = 26/112) E. 1/72

(1/72)

the larger the numerator and smaller the denominator, the larger is the fraction. as one can see that A, C and E are smallest their denominators are larger and numerator are smallest among D and B, B is largest as 21 is little less than 26 but 112 is larger than 90. So its B
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