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Number System: Level 1 Test - 8

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Question 1
The remainder obtained when a prime number greater than 6 is divided by 6 is
1 or 3
1 or 5
3 or 5
4 or 5
Question 1 Explanation: 
Students, please note that the best way to solve this question is the method of simulation.
You can divide various prime numbers by 6 and check the remainders.
Match these with the options given and find your answer.
7 gives a remainder of 1.
11 gives a remainder of 5.
13 gives a remainder of 1.
17 gives a remainder of 5.
19 gives a remainder of 1.
23 gives a remainder of 5.
29 gives a remainder of 5.
31 gives a remainder of 1.
You can continue this and you will see that for numbers greater than 6,
the remainder is either 1 or 5 (when prime numbers are divided by 6).
This is also a method to establish whether a number is prime or not.
Question 2
A third standard teacher gave a simple multiplication exercise to the kids. But one kid reversed the digits of both the numbers and carried out the multiplication and found that the product was exactly the same as the one expected by the teacher. Only one of the following pairs of numbers will fit in the description of the exercise. Which one is that?
14, 22
13, 62
19, 33
42, 28
Question 2 Explanation: 
This is a question type which shows your alertness
and whether you have practiced all the types sufficiently.
To solve, we have a hint in this question i.e.
last two digits and the hint is that you may not verify the entire answer but only the last digits.
For eg. the last digits obtained by multiplying the the units place digits
should be the same as that obtained by multiplying the tens place digit.
Hence we find that only option (b) is the valid answer
Question 3
A 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, then back to the index finger for 10, middle finger for 11, and so on. She counted up to 1976.Find the Finger on which she ended.
index finger
middle finger
ring finger
Question 3 Explanation: 
If you were to run two of three cycles of how she is counting, you will observe that the number
that she counts on thumb are 1, 9, 17, 25 and so on. So it forms a pattern such that all the
numbers that are 1 more than the multiples of 8 are counted on thumb. The closest multiple
of 8 near 1978 is 1976. In other words she would count 1977 on thumb. So she
would count 1978 on the index finger.
Question 4
A and B are two positive integers such that AB = 64. Which of the following cannot be the value of A + B?
Question 4 Explanation: 
If we were to express 64 as product of two positive integers,
we can get the following combinations:
(64 × 1), (32 × 2), (16 × 4), (8 × 8). Thus, we find that A + B
cannot be 35.
Question 5
A green light flashes three times per minute and a red light flashes five times in 2 min at regular Intervals. If both lights start together, then how many times do they flash together in each hour?
Question 5 Explanation: 
First light blinks after 20 s. Second light blinks after 24 s. They
blink together after LCM of 20 and 24 = 120 s = 2
min. Hence, the number of times they blink together in an hour = 30.
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