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In a set of first 1000 natural numbers find the number of prime numbers:

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Important Questions on Number System

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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 153
There are three different teams engaged in laying the optical fiber cable under the ground. Team A is comprised of 11 men can lay 6 km cable in a certain time and team C is comprised of 19 men can lay 11 km cable in a certain time. Team B is less efficient than team A but more efficient than team C. Each member of a particular team is equally efficient. If team B lays n km cable in a certain time, where n is a natural number, then what could be the minimum number of men in team B?
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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 154
The co-founder of a company called Lamamia thought that in the beginning it's practically impossible to take away some salary, so he devised an ingenious way to get some salary from his own company. Taking into confidence the other co-founders he decided to take Rs. n2 in the nth month, starting from the very first month up to the first five years. After working for sometime he realized total Rs. 21740 from his company as his salary. However, he didn't take a single penny in a month when he was on bed-rest after he got diagnosed of severe back problem. In which month he didn't work for his company?
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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 155

Two friends Azad and Bose are vacationing in India and they have some Indian currency in their wallets. Each one has some notes of denominations of Rs. 1000, Rs. 100, Rs. 10 and Rs. 1. The total number of notes with each one is same but the total amount with each one is distinct. None of them has 10 or more notes of any denomination.

What information is necessary to find the total amount that they could have together in their wallets, if used together with the possible amount given in the respective options?

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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 156
Ravikishan is a sales executive who has five different simcard for his mobile handset. Each simcard supports different talk-time. For each simcard the talk-time is always in integers and measured in minutes only. When he is working in the remote fields, he carries exactly five fully charged simcard with him. On ten different days he used different pairs of simcard and observed the total talk-time each day as 122, 124, 125, 126, 127, 128, 129, 130, 132, and 133 min. What is the highest talk time that a simcard supports?
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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 157

The following figure shows the three gears, which work in tandem. That means when anyone of the gears rotates, all other gears will also rotate. One gear has 36 teeth, another one has 25 teeth and the third one has 30 teeth. Though the number of teeth is not shown correctly in the given figure.

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The gears are now in starting position. If you start turning them and continue to turn them, eventually all three will end up at their starting positions. Each gear makes x, y, z complete turns in order to have all three in their starting positions. What is the value of x+y+z?

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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 158
An integer n is called square-free if does not have a divisor of the form k2 where k∈{2,3,…,n}. Find the number of square-free integers between 1 and 120:
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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 159
How many positive integral solutions exist for: ab+cd=a+b+c+d, where 1≤a≤b≤c≤d?
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Quantum CAT Also Useful for XAT>Chapter 1 - SNAP>CMAT>Q 160
Ishaan Awasthi, a dyslexic boy, has some difficulties in reading but does not suffer from dyscalculia. Once his professor Mr. Nikumbh gave him a simple multiplication problem involving two distinct numbers. The numbers were exactly two-digit numbers, and none of the four digits was the same. He asked him to multiply both the numbers and find the answer. Due to inability in reading, Ishaan interchanged the positions of tens and unit digits mutually in each of the two numbers, and then he multiplied the resultant numbers. But the answer was still the same and correct. After realizing this amazing fact, now Nikumbh sir wants to know the number of pairs of two digit-numbers, which exists in our decimal number system.