GAT GENERAL TEST Sample 2 Questions Solution(Quantitative)
Solution of GAT GENERAL TEST Sample 2 Questions
1.
To solve the given expression:
26.34 + 152.312 - 92.123
We can perform the arithmetic calculations:
26.34 + 152.312 = 178.652 178.652 - 92.123 = 86.529
So, the correct answer is 86.529.
2.
To solve the given expression:
0.145 x 5.42
We can multiply the numbers:
0.145 x 5.42 = 0.7859
So, the correct answer is 0.7859.
3.
To solve the given expression:
26.8 divided by 1.52
We can divide the numbers:
26.8 / 1.52 = 17.63157894736842
Rounding this to the nearest decimal place, the estimated answer is approximately 17.6.
So, the correct answer is 17.6.
4..
To determine if 27 is a multiple of 3 and 7, we can check if it is divisible evenly by both numbers.
Divisibility by 3:
To check if a number is divisible by 3, we sum its digits and check if the resulting sum is divisible by 3. In the case of 27, the sum of its digits is 2 + 7 = 9. Since 9 is divisible by 3, we can conclude that 27 is divisible by 3.
Divisibility by 7:
To check if a number is divisible by 7, we can use a division test. Divide the number by 7 and check if the remainder is 0. When we divide 27 by 7, we get a quotient of 3 and a remainder of 6. Since the remainder is not 0, we can conclude that 27 is not divisible by 7.
Therefore, based on the above analysis, we can say that 27 is a multiple of 3 but not a multiple of 7. So the right answer is NO.
5.
To determine if 51 is a multiple of 5, we can check if it is divisible evenly by 5.
To check divisibility by 5, we need to check the unit digit of the number. If the unit digit is 0 or 5, then the number is divisible by 5.
In the case of 51, the unit digit is 1. Since the unit digit is not 0 or 5, we can conclude that 51 is not divisible by 5.
Therefore, 51 is not a multiple of 5. So the right answer is NO.
6.
To calculate the number of different ways we can arrange 50 chairs in a room, where each chair contains a different tag, we can use the concept of permutations. The formula to calculate the number of permutations of n objects taken r at a time is given by: P(n, r) = n! / (n - r)! Where n is the total number of objects and r is the number of objects taken at a time. In this case, we want to arrange 50 chairs, so n = 50. We want to arrange all 50 chairs, so r = 50. Plugging the values into the formula: P(50, 50) = 50! / (50 - 50)! Simplifying further: P(50, 50) = 50! / 0! Since 0! (0 factorial) is equal to 1, we have: P(50, 50) = 50! Calculating 50! (50 factorial) can be computationally intensive, but it is an extremely large number. In this case, the number of different ways we can arrange 50 chairs, each with a different tag, is equal to 50 factorial (50!).
7.
To calculate the number of different ways we can arrange 50 chairs in a room with 5 rows, where each chair contains a different tag, we can use the concept of permutations. Since there are 5 rows, we need to determine how many chairs will be placed in each row. Let's consider the number of chairs in each row as follows: Row 1: x1 chairs Row 2: x2 chairs Row 3: x3 chairs Row 4: x4 chairs Row 5: x5 chairs We know that the total number of chairs is 50, so we have the equation: x1 + x2 + x3 + x4 + x5 = 50 To find the number of ways to arrange the chairs, we need to calculate the number of solutions to this equation. We can use a technique called stars and bars or balls and urns to solve this. The formula for the number of solutions is: C(n + k - 1, k - 1) where n is the number of objects to distribute (50 in this case), and k is the number of boxes or groups (5 in this case). Plugging in the values: C(50 + 5 - 1, 5 - 1) = C(54, 4) Calculating C(54, 4) requires calculating binomial coefficients, which can be computationally intensive. Therefore, the number of different ways we can arrange 50 chairs in 5 rows, with each chair containing a different tag, is C(54, 4).
8.
To find the number that has 1, 2, 4, 5, and 8 as factors, we need to identify the least common multiple (LCM) of these numbers. We can start by listing the multiples of each number until we find a common multiple: Multiples of 1: 1, 2, 3, 4, 5, 6, ... Multiples of 2: 2, 4, 6, 8, 10, 12, ... Multiples of 4: 4, 8, 12, 16, 20, 24, ... Multiples of 5: 5, 10, 15, 20, 25, 30, ... Multiples of 8: 8, 16, 24, 32, 40, 48, ... From the lists above, we can see that the least common multiple (LCM) of 1, 2, 4, 5, and 8 is 40. Therefore, the number that has 1, 2, 4, 5, and 8 as factors is 40.
9.
To find the factors of 19, we need to determine the numbers that divide evenly into 19 without leaving a remainder. When we check the divisibility of 19, we find that it is only divisible by 1 and 19 itself. Therefore, the factors of 19 are 1 and 19. In summary, the factors of 19 are:1, 19
That's why 19 is a prime number.
10.
To find the 5th multiple of 7, we can simply multiply 7 by 5: 7 × 5 = 35 Therefore, the 5th multiple of 7 is 35.
11.
The number that is a factor of all numbers is 1. Every positive integer has 1 as a factor because any number divided by 1 equals itself. Additionally, 1 is the smallest positive integer and is a factor of all other numbers. In other words, for any number n, we have: n ÷ 1 = n Therefore, 1 is a factor of all numbers.
12.
To determine if 720 is divisible by 2 or 3, we can check the divisibility rules for these numbers. Divisibility by 2: A number is divisible by 2 if its last digit is even, meaning it ends in 0, 2, 4, 6, or 8. In the case of 720, the last digit is 0, which is even. Therefore, 720 is divisible by 2. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. Let's calculate the sum of the digits 720: 7 + 2 + 0 = 9 The sum of the digits, 9, is divisible by 3. Therefore, 720 is divisible by 3. In summary, 720 is divisible by both 2 and 3. So the answer is YES.
13.
If a number ends in 0, 2, 4, 6, or 8, then the number is divisible by 2.
14.
A number is divisible by 3 if the sum of its digits is divisible by 3.
15.
To determine if 14563 is divisible by 3, we need to calculate the sum of its digits and check if that sum is divisible by 3. The sum of the digits of 14563: 1 + 4 + 5 + 6 + 3 = 19 The sum of the digits, 19, is not divisible by 3. Therefore, 14563 is not divisible by 3. So the answer is NO.
16.
To determine if 34563 is divisible by 3, we need to calculate the sum of its digits and check if that sum is divisible by 3. The sum of the digits of 34563: 3 + 4 + 5 + 6 + 3 = 21 The sum of the digits, 21, is divisible by 3. Therefore, 34563 is divisible by 3. So the answer is YES.
17.
A number is divisible by 4 if its last two digits (the one's digit and tens digit) are divisible by 4.
18.
To determine if 12428 is divisible by 4, we need to check if its last two digits (the one's digit and tens digit) are divisible by 4. The last two digits of 12428 are 28. Since 28 is divisible by 4, we can conclude that 12428 is divisible by 4. So the answer is YES.
19.
To determine if 2007 is divisible by 4, we need to check if its last two digits (the one's digit and tens digit) are divisible by 4. The last two digits of 2007 are 07. Since 7 is not divisible by 4, we can conclude that 2007 is not divisible by 4. So the answer is NO.
20.
To determine if 3123 is divisible by 3, we need to calculate the sum of its digits and check if that sum is divisible by 3. Sum of the digits of 3123: 3 + 1 + 2 + 3 = 9 The sum of the digits, 9, is divisible by 3. Therefore, 3123 is divisible by 3. So the answer is YES.
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