Question:
A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is
A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is
Updated On: Jul 29, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 60
Solution and Explanation
Let the total number of tests be \( n \) and the overall average score be \( A \). Let's break down the problem:
1. When the first 10 tests (average = 20) are not considered, the average rises by 1.
2. When the last 10 tests (average = 30) are omitted, the average falls by 1.
These conditions can be expressed with equations:
1. \((A + 1)(n - 10) = An - 200\)
2. \((A - 1)(n - 10) = An - 300\)
Let's solve for \( A \) and \( n \):
Expanding the first equation gives:
\( An - 10A + n - 10 = An - 200 \)
\( n - 10A - 10 = -200 \)
\( n - 10A = -190 \)
From the second equation:
\( An - 10A - n + 10 = An - 300 \)
\(-n - 10A + 10 = -300 \)
\( -n - 10A = -310 \)
Now we have the equations:
\( n - 10A = -190 \)
\(-n - 10A = -310 \)
Add these to eliminate \( n \):
\( (n - 10A) + (-n - 10A) = -190 + (-310) \)
\(-20A = -500\)
\( A = 25 \)
Substitute \( A = 25 \) back into \( n - 10A = -190 \):
\( n - 10(25) = -190 \)
\( n - 250 = -190 \)
\( n = 60 \)
The total number of tests taken is \( 60 \). This value falls within the expected range of 60, confirming accuracy.
Was this answer helpful?
0
0
Top Questions on Average
- A batch of 36 school children goes for an excursion trip to Nainital. When one 10-year-old child is replaced with another child, the average age of the children in the batch increases by \( 2\frac{1}{2} \) months. What is the age of the new child?
- The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?
- The average age of a group of boys and girls is 18 years. If the average age of boys is 20 years and that of girls is 15 years, then what is the percentage of boys in the group?
- Match List-I with List-II \[\begin{array}{|c|c|} \hline \textbf{Concepts} & \textbf{Formula} \\ \hline \text{(A) Weighted Mean} & \text{(I) \(\frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}\)} \\ \hline \text{(B) Grand Mean of Combined Data} & \text{(II) \(\frac{\sum_{i=1}^{n} x_i}{n}\)} \\ \hline \text{(C) Harmonic Mean} & \text{(III) \(\frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}\)} \\ \hline \text{(D) Geometric Mean} & \text{(IV) \(\left( \prod_{i=1}^{n} x_i \right)^{1/n}\)} \\ \hline \end{array}\] Choose the correct answer from the options given below:
- What is the geometric mean of 2, 4, and 8?
View More Questions
Questions Asked in CAT exam
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Certain codes may, of course, be so widely distributed in a specific language community or culture, and be learned at so early an age, that they appear not to be constructed – the effect of an articulation between sign and referent – but to be ‘naturally’ given. Simple visual signs appear to have achieved a ‘near-universality’ in this sense: though evidence remains that even apparently ‘natural’ visual codes are culture specific. However, this does not mean that no codes have intervened; rather, that the codes have been profoundly naturalized. The operation of naturalized codes reveals not the transparency and ‘naturalness’ of language but the depth, the habituation and the near-universality of the codes in use. They produce apparently ‘natural’ recognitions. This has the (ideological) effect of concealing the practices of coding which are present.- CAT - 2024
- Para Summary
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Comprehending a wide range of emotions, Renaissance music nevertheless portrayed all emotions in a balanced and moderate fashion.
Paragraph: A volume of translated Italian madrigals were published in London during the year of 1588. This sudden public interest facilitated a surge of English Madrigal writing as well as a spurt of other secular music writing and publication. ___(1)___. This music boom lasted for thirty years and was as much a golden age of music as British literature was with Shakespeare and Queen Elizabeth I. ___(2)___. The rebirth in both literature and music originated in Italy and migrated to England; the English madrigal became more humorous and lighter in England as compared to Italy. Renaissance music was mostly polyphonic in texture. ___(3)___. Extreme use of and contrasts in dynamics, rhythm, and tone colour do not occur. ___(4)___. The rhythms in Renaissance music tend to have a smooth, soft flow instead of a sharp, well-defined pulse of accents.- CAT - 2024
- Para Completion
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Science has officially crowned us superior to our early-rising brethren. Paragraph: My fellow night owls, grab a strong cup of coffee and gather around: I have great news. ___(1)___. For a long time, our kind has been unfairly maligned. Stereotyped as lazy and undisciplined. Told we ought to be morning larks. Advised to go to bed early so we can wake before 5am and run a marathon before breakfast like all high-flyers seem to do. Now, however, we are having the last laugh. ___(2)___. It may be a tad more complicated than that. A study published last week, which you may have already seen while scrolling at 1am, suggests that staying up late could be good for brain power. ___(3)___. Is this study a thinly veiled PR exercise conducted by a caffeine-pill company? Nope, it’s legit. ___(4)___. Research led by academics at Imperial College London studied data on more than 26,000 people and found that “self-declared ‘night owls’ generally tend to have higher cognitive scores”.- CAT - 2024
- Para Completion
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Understanding central Asia’s role helps developments make more sense not only across Asia but in Europe, the Americas and Africa.
Paragraph: The nations of the Silk Roads are sometimes called ‘developing countries’, but they are actually some of the world’s most highly developed countries, the very crossroads of civilization, in advanced states of disrepair. ___(1)___. These countries lie at the centre of global affairs: they have since the beginning of history. Running across the spine of Asia, they form a web of connections fanning out in every direction, routes along which pilgrims and warriors, nomads and merchants have travelled, goods and produce have been bought and sold, and ideas exchanged, adapted and refined. ___(2)___ .They have carried not only prosperity, but also death and violence, disease and disaster. ___(3)___. The Silk Roads are the world’s central nervous system, connecting otherwise far-flung peoples and places…. ___(4)___. It allows us to see patterns and links, causes and effects that remain invisible if one looks only at Europe, or North America.- CAT - 2024
- Para Completion
View More Questions