A farmer planned fence-posts at $6$ metre intervals along a straight side, posts at both ends. He bought posts but found he had $5$ less than needed for $6$ m spacing. However, with $8$ m spacing, he had exactly enough. What is the length of the side and how many posts did he buy?
Show Hint
- 100, 15
- 100, 16
- 120, 15
- 120, 16
The Correct Option is D
Solution and Explanation
Top Questions on Arithmetic
- The sum of series, $(-100) + (-95) + (-90) + \dots + 110 + 115 + 120$, is:
- For two positive integers $a$ and $b$, if $(a+b)^{(a+b)}$ is divisible by $500$, then the least possible value of $a\times b$ is:
- Each day on Planet M is 10 hours, each hour 60 minutes and each minute 40 seconds. The inhabitants use a 10-hour analog clock. If such a clock shows \(\,3\) hours \(42\) minutes \(20\) seconds in a {mirror, what will be the time on Planet M exactly after \(5\) minutes?}
- In an amusement park, a visitor gets to ride on three different rides (A, B and C) for free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A or B (i.e., they were outside $A \cup B$). How many visited the amusement park on that day?
- At a bookstore, 'MODERN BOOK STORE' is flashed using neon lights. The words are individually flashed at the intervals of \( \frac{1}{2} \) s, \( \frac{1}{4} \) s and \( \frac{1}{8} \) s respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is:
Questions Asked in CAT exam
The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question.
In the summer of 2022, subscribers to the US streaming service HBO MAX were alarmed to discover that dozens of the platform’s offerings – from the Covid-themed heist thriller Locked Down to the recent remake of The Witches – had been quietly removed from the service . . . The news seemed like vindication to those who had long warned that streaming was more about controlling access to the cultural commons than expanding it, as did reports (since denied by the show’s creators) that Netflix had begun editing old episodes of Stranger Things to retroactively improve their visual effects.
What’s less clear is whether the commonly prescribed cure for these cultural ills – a return to the material pleasures of physical media – is the right one. While the makers of Blu-ray discs claim they have a shelf life of 100 years, such statistics remain largely theoretical until they come to pass, and are dependent on storage conditions, not to mention the continued availability of playback equipment. The humble DVD has already proved far less resilient, with many early releases already beginning to deteriorate in quality Digital movie purchases provide even less security. Any film “bought” on iTunes could disappear if you move to another territory with a different rights agreement and try to redownload it. It’s a bold new frontier in the commodification of art: the birth of the product recall. After a man took to Twitter to bemoan losing access to Cars 2 after moving from Canada to Australia, Apple clarified that users who downloaded films to their devices would retain permanent access to those downloads, even if they relocated to a hemisphere where the [content was] subject to a different set of rights agreements. Thanks to the company’s ironclad digital rights management technology, however, such files cannot be moved or backed up, locking you into watching with your Apple account.
Anyone who does manage to acquire Digital Rights Management free (DRM-free) copies of their favourite films must nonetheless grapple with ever-changing file format standards, not to mention data decay – the gradual process by which electronic information slowly but surely corrupts. Only the regular migration of files from hard drive to hard drive can delay the inevitable, in a sisyphean battle against the ravages of digital time.
In a sense, none of this is new. Charlie Chaplin burned the negative of his 1926 film A Woman of the Sea as a tax write-off. Many more films have been lost through accident, negligence or plain indifference. During a heatwave in July 1937, a Fox film vault in New Jersey burned down, destroying a majority of the silent films produced by the studio.
Back then, at least, cinema was defined by its ephemerality: the sense that a film was as good as gone once it left your local cinema. Today, with film studios keen to stress the breadth of their back catalogues (or to put in Hollywood terms, the value of their IPs), audiences may start to wonder why those same studios seem happy to set the vault alight themselves if it’ll help next quarter’s numbers.- CAT - 2024
- Reading Comprehension
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
- CAT - 2024
- Algebra
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- If m and n are natural numbers such that n > 1, and mn = 225 × 340, then m − n equals
- CAT - 2024
- Exponents and Powers