Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving

Question:  Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example, 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is shorthand for 0.15151515…. 10/99 is which of the following?

1. 0.{11}
2. 0.{101}
3. 0.{10}
4. 0.{09}
5. 0.{01}

“Curly brackets {} around the last digits of a decimal fraction signify that these digits recur" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

Answer: C
Solution and Explanation:
Approach Solution 1:

It is given in the question that the last digits of a decimal fraction are enclosed in curly brackets to indicate that they repeat indefinitely. Then it asked what the representation of 10/99.

Let:

X = .1010101010 ....etc. (eq 1)

Multiply both sides by (10)^2 = 100 [since the recurring decimal repeats after 2 digits]

100 (X) = 10.1010101010 .... etc. (eq 2)

Subtract (eq 1) from (eq 2)

100 (X) = 10.10101010......etc.

- [ (X) = 0.1010101010..... etc. ]
__________________________

99 (X) = 10

X = 10/99 = 0.10101010.....etc.

Hence, C is the correct answer.

Correct Answer: C

Approach Solution 2:

Elimination method:
It is given in the question that the last digits of a decimal fraction are enclosed in curly brackets to indicate that they repeat indefinitely. Then it asked what the representation of 10/99.
Since there are only 2 9's in the denominator, the recurring part will have only 2 digits.
Option B - reject.

Next, 10/100 = 0.1
So 10/99 > 0.1
Option D and E - reject.

Next, 1/9 = 0.1111…
Multiply by 11
11/99 = 0.11111…
So, 10/99 < 0.1111…

Option A - reject.

Hence, C is the correct answer.

Correct Answer: C

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