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Which of the following fractions is the largest?

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

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New post 10 Nov 2016, 22:42
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Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72
[Reveal] Spoiler: OA

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

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New post 11 Nov 2016, 00:14
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stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72


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.

7/30 = 1/ (30/7) = 1/4.29
13/56 = 1/ (56/13) = 1/4.3

Since 1/4.29 has the smallest denominator, the largest fraction will be 7/30.

Answer (B)
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Re: Which of the following fractions is the largest? [#permalink]

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New post 11 Nov 2016, 08:14
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stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72


Compare two fractions at a time.

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:
[Reveal] Spoiler:
B


NOTE: That was more calculating than I like to do on GMAT questions, BUT at least we were able to quickly eliminate 3 answer choices first.

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

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New post 11 Nov 2016, 12:41
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stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72


A = 4.xx %
B = 23.xx %
C = 2.xx %
D = 23.xx %
E = 1.xx %

Now, check between (B) an (D)

B = 196/840
D = 195/840

So, (D) is the largest fraction...

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

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

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New post 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

Answer: B

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

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

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New post 13 Sep 2017, 18:18
Here lets check

1/24, 1/45,1/72 So 1/24 is the greatest of three.

So betweeen 1/24 nearly 4 % is and 7/30 is nearly 22%

So 7/30 is greater of the 4 . Then between 7/30 and 13/56

we can check by cross multiplication
7 * 56 > 13*30

so 7/30 is greatest
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Re: Which of the following fractions is the largest?   [#permalink] 13 Sep 2017, 18:18
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