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# What is the positive difference between the largest and the smallest

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
What is the positive difference between the largest and the smallest  [#permalink]

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15 Jan 2019, 01:15
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Difficulty:

35% (medium)

Question Stats:

73% (02:43) correct 27% (02:22) wrong based on 75 sessions

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$$\frac{5}{9}, \ \frac{5}{12}, \ \frac{23}{48}, \ \frac{11}{24}, \ \frac{3}{7}$$.

What is the positive difference between the largest and the smallest of the fractions below.

A. 1/12

B. 5/36

C. 1/4

D. 1/3

E. 7/18

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3078
What is the positive difference between the largest and the smallest  [#permalink]

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15 Jan 2019, 06:33

Solution

Given:
• Few fractions

To find:
• The difference between the largest and the smallest of the given fractions

Approach and Working:
$$\frac{5}{9}, \frac{5}{12}, \frac{23}{48}, \frac{11}{24}, \frac{3}{7}$$
• $$\frac{5}{9} > \frac{5}{12}$$
• $$\frac{23}{48} > \frac{11}{24} = \frac{22}{48}$$

$$\frac{5}{9} = \frac{25}{45} > \frac{23}{48} > \frac{22}{48} > \frac{3}{7} = \frac{21}{49} > \frac{5}{12} = \frac{20}{48}$$

Therefore, the answer is $$\frac{5}{9} – \frac{5}{12} = \frac{5 * 3}{9 * 12} = \frac{5}{36}$$

Hence, the correct answer is Option B

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Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the positive difference between the largest and the smallest  [#permalink]

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15 Jan 2019, 06:58
2
Bunuel wrote:
$$\frac{5}{9}, \ \frac{5}{12}, \ \frac{23}{48}, \ \frac{11}{24}, \ \frac{3}{7}$$.

What is the positive difference between the largest and the smallest of the fractions below.
A. 1/12

B. 5/36

C. 1/4

D. 1/3

E. 7/18

Now lets see, so many fractions, we can approximate to know which one will be the greatest and which will be the smallest

$$\frac{5}{9}$$ will be > 1/2

$$\frac{5}{12}$$ will be 20/48

$$\ \frac{23}{48}$$

$$\ \frac{11}{24}$$ will be 22/48

$$\ \frac{3}{7}$$ will be 21/49

You may notice that only 5/9 is greater than 1/2 which means this is the largest term,rest all will be less than 0.50

Now we need to find the smallest term, so as you notice there are three values with base as 48, out of which 20/48 will be the smallest.

5/9 - 5/12 = (20 - 15)/ 36 = 5/36

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Re: What is the positive difference between the largest and the smallest  [#permalink]

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17 Jan 2019, 19:09
Bunuel wrote:
$$\frac{5}{9}, \ \frac{5}{12}, \ \frac{23}{48}, \ \frac{11}{24}, \ \frac{3}{7}$$.

What is the positive difference between the largest and the smallest of the fractions below.

A. 1/12

B. 5/36

C. 1/4

D. 1/3

E. 7/18

Looking at the given fractions, we see that 5/9 is the only fraction above 1/2; thus, 5/9 is the largest.

Getting common denominators for the 2nd, 3rd, and 4th fractions we have:

20/48, 23/48, and 22/48, so we see that 5/12 is the smallest from that group.

Getting common denominators for 5/12 and 3/7 we have:

35/84 and 36/84, so we see that 5/12 is smaller than 3/7.

So we have:

Largest - smallest = 5/9 - 5/12 = 20/36 - 15/36 = 5/36.

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Intern
Joined: 11 Oct 2018
Posts: 21
Location: Germany
What is the positive difference between the largest and the smallest  [#permalink]

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22 Jan 2019, 14:22
EgmatQuantExpert wrote:

Solution

Given:
• Few fractions

To find:
• The difference between the largest and the smallest of the given fractions

Approach and Working:
$$\frac{5}{9}, \frac{5}{12}, \frac{23}{48}, \frac{11}{24}, \frac{3}{7}$$
• $$\frac{5}{9} > \frac{5}{12}$$
• $$\frac{23}{48} > \frac{11}{24} = \frac{22}{48}$$

$$\frac{5}{9} = \frac{25}{45} > \frac{23}{48} > \frac{22}{48} > \frac{3}{7} = \frac{21}{49} > \frac{5}{12} = \frac{20}{48}$$

Therefore, the answer is $$\frac{5}{9} – \frac{5}{12} = \frac{5 * 3}{9 * 12} = \frac{5}{36}$$

Hence, the correct answer is Option B

Hi EgmatQuantExpert,

can you please elaborate the highlighted step? I don't understand how you performed a multiplication out of a subtraction. Thank You.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3078
Re: What is the positive difference between the largest and the smallest  [#permalink]

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22 Jan 2019, 23:44
1
mtambiev wrote:

Hi EgmatQuantExpert,

can you please elaborate the highlighted step? I don't understand how you performed a multiplication out of a subtraction. Thank You.

Hi,

So, we have, $$\frac{5}{9} - \frac{5}{12}$$

Now, take the common term 5 out,
$$5(\frac{1}{9} - \frac{1}{12})$$ ......... (1)

Multiply and divide $$\frac{1}{9}$$ with 12, $$\frac{12}{9*12}$$

Similarly, multiply and divide 1/12 with 9, $$\frac{9}{12*9}$$

Replacing them in equation (1), we get,
$$5(\frac{12}{9*12} - \frac{9}{9*12}) = \frac{5(12 - 9)}{9*12} = \frac{5*3}{9*12}$$

Regards,
_________________
Re: What is the positive difference between the largest and the smallest   [#permalink] 22 Jan 2019, 23:44
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