Question: A young girl counted in the following way on the fingers of her left hand. She started calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index finger 8, thumb 9 and then back to the index finger for 10, middle finger for 11 and so on. She counted up 1994. She ended on her

1. thumb
2. the index finger
3. the middle finger
4. the ring finger
5. the little finger

“A young girl counted in the following way on the fingers of her left hand. She started calling the thumb 1" - 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: B

Solution and Explanation:

Approach Solution 1:

On her left hand's fingers, a young girl counted in the manner shown. The thumb was called first, followed by the index finger, middle finger, ring finger, little finger, and thumb. She then reversed the order, calling the ring finger, middle finger, index finger, thumb, and middle finger in that order. She tallied 1994.

The thumb series is 1, 9, 17, 25, 33,…
Therefore 8n+1=1994
8n=1993
remainder=1
Therefore, the thumb is for 1993, and the next one is the index.
The answer is the index finger.
B is the correct answer.

Approach Solution 2:

On her left hand's fingers, a young girl counted in the manner shown. The thumb was called first, followed by the index finger, middle finger, ring finger, little finger, and thumb. She then reversed the order, calling the ring finger, middle finger, index finger, thumb, and middle finger in that order. She tallied 1994.

From left to right, the first letters of the fingers are written as T, I, M, R, and L, with the numbering proceeding logically.

Currently, the first row contains 5 digits ranging from 1 to 5, therefore the remaining numbers are: 1994-5=1989

Now, we can see that each row contains four numbers.

Let's say that the first row starts at position 6 and is designated as the odd row, the second row starts at position 10, and so on. Now, 1989/4 provides the quotient: 497, which is the odd row and ends at the thumb finger, and the remainder: 1,
which is at the index finger, designates that answer B.

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