Which of the Following Fractions is the Largest? GMAT Problem Solving

Question: Which of the following fractions is the largest?

1. 1/24
2. 7/30
3. 1/45
4. 13/56
5. 1/72

“Which of the following fractions is the largest?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
For larger fractions, the numerator should be larger (denominators are the same) and/or denominators should be smaller (numerators are the 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.

Correct Answer: B

Approach Solution 2:
The largest fraction needs to be determined first. 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.

Correct Answer: B

Approach Solution 3:
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

Correct Answer: B

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