Categories
Arithmetic Smart Math

[Smart Math] Arithmetic Problem 13

Here’s and example of a SMART MATH problem for ARITHMETIC.

Arithmetic

Problem

In one of the following sets of fractions, the values increase progressively. Which is the one?

  1. \frac{5}{7}, \frac{8}{11}, \frac{11}{15}, \frac{13}{17}, \frac{7}{9}
  2. \frac{5}{7}, \frac{7}{9}, \frac{13}{17}, \frac{11}{15}, \frac{8}{11}
  3. \frac{5}{7}, \frac{11}{15}, \frac{8}{11}, \frac{13}{17}, \frac{7}{9}
  4. \frac{5}{7}, \frac{11}{15}, \frac{8}{11}, \frac{7}{9}, \frac{13}{17}
  5. \frac{5}{7}, \frac{13}{17}, \frac{11}{15}, \frac{7}{9}, \frac{8}{11}

The Usual Method

[contentblock id=google-adsense-post]

Equate the denominators using the LCM of the denominators as follows:

LCM of 7, 11, 15, 17, and 9 = 7 x 11 x 9 x 5 x 17 = 58905

Hence, \frac{5}{7} can be written as \frac{5}{7} = \frac{42075}{58905}

\frac{8}{11} can be written as \frac{8}{11} = \frac{42840}{58905}

\frac{11}{15} can be written as \frac{11}{15} = \frac{43197}{58905}

\frac{13}{17} can be written as \frac{13}{17} = \frac{45045}{58905}

\frac{7}{9} can be written as \frac{7}{9} = \frac{45815}{58905}

As can be seen,

\frac{42075}{58905} < \frac{42840}{58905} < \frac{43197}{58905} < \frac{45045}{58905} < \frac{45815}{58905}

Hence, \frac{5}{7} < \frac{8}{11} < \frac{11}{15} < \frac{13}{17} < \frac{7}{9}

Since, option ‘1’ gives this arrangement, it is the correct answer.

(Ans: 1)

Estimated Time to arrive at the answer = 200 seconds.

Using Technique

[contentblock id=google-adsense-post]

We already know the value of the reciprocals of 7, 11, 15, 17 and 9 as:

\frac{1}{7} = 0.1482… \therefore \frac{5}{7}=5\times 0.1428\approx 0.714

\frac{1}{11} = 0.09090… \therefore \frac{8}{11}=8\times 0.0909\approx 0.7272

\frac{1}{15} = 0.0666… \therefore \frac{11}{15}=11\times 0.066\approx 0.7337

\frac{1}{17} = 0.0588… \therefore \frac{13}{17}=13\times 0.0588=0.764

\frac{1}{9} = 0.1111… \therefore \frac{7}{9}=7\times 0.1111=0.7777

From above it is clear that,

\frac{5}{7} < \frac{8}{11} < \frac{11}{15} < \frac{13}{17} < \frac{7}{9}

(Ans: 1)

Estimated Time to arrive at the answer = 60 seconds.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

Leave a Reply

Your email address will not be published. Required fields are marked *