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[👉Number📚Theory MCQs]
3️⃣0️⃣Find all the solutions of quadratic congruence
x^2 ≡ 29(mod 35).
2️⃣9️⃣ If a and b are two odd numbers, then which of the following is even?
📚Explanation to Question 1️⃣3️⃣👆👆👆
📚If a number is divisible by 9, then the sum of its digits must be divisible by 9.
Let's apply this rule to the number 381A:
3 + 8 + 1 + A = 12 + A
Since 18 is the next number after 12 which is divisible by 9, A must be 6.
Therefore, for this sum to be divisible by 9, A must be equal to 6, since 12 + 6 = 18, which is divisible by 9.
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2️⃣8️⃣ If a = (0.4)^2, b = 0.04, and c = 2/5, then which of the following is the correct relationship between a, b, and c?
2️⃣8️⃣ If a = (0.4)2, b = 0.04, and c = 2/5, then which of the following is the correct relationship between a, b, and c?
2️⃣7️⃣The denominator of a fraction is 3 more than its numerator. If the denominator is decreased by 2, and the numerator is increased by 7, we will get 2. What will be the sum of the numerator and denominator of that fraction?
📚Explanation to Question 1️⃣1️⃣👆👆👆
✅Which is the largest 4-digit number that can be exactly divisible by 66?
a) 9987
b) 9912
c) 9913
d) 9966
📝Solution
👉To be exactly divisible by 66, a number must be divisible by both 6 and 11.
👉For a number to be divisible by 6, it must be even and the sum of its digits must be divisible by 3.
👉For a number to be divisible by 11, the difference between the sum of its digits in the odd places and the sum of its digits in the even places must be divisible by 11.
Let's check each option:
a) 9987: The sum of its digits is 9+9+8+7=33, which is divisible by 3. The difference between the sum of its digits in the odd places (9+8=17) and the sum of its digits in the even places (9+7=16) is 1, which is not divisible by 11. Therefore, 9987 is not divisible by 66.
b) 9912: The sum of its digits is 9+9+1+2=21, which is divisible by 3. The difference between the sum of its digits in the odd places (9+1=10) and the sum of its digits in the even places (9+2=11) is -1, which is not divisible by 11. Therefore, 9912 is not divisible by 66.
c) 9913: The sum of its digits is 9+9+1+3=22, which is not divisible by 3. Therefore, 9913 is not divisible by 66.
d) 9966: The sum of its digits is 9+9+6+6=30, which is divisible by 3. The difference between the sum of its digits in the odd places (9+6=15) and the sum of its digits in the even places (9+6=15) is 0, which is divisible by 11. Therefore, 9966 is divisible by 66.
📚Therefore, the largest 4-digit number that can be exactly divisible by 66 is 9966.
✅The answer is (d)❤️
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2️⃣6️⃣If the three-fifth of a number is equal to 70% of another number, what is the ratio between the first number and second number?
[✅Number📚 System MCQs👆👇]
2️⃣5️⃣The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers?
2️⃣4️⃣The sum of three numbers is 2, if the first number is ½ times of the 2nd number, and the third number is ¼ times of the 2nd number. What will be the second number?
📚Explanation to Question 1️⃣0️⃣👆👆👆
📝Solution:
📚The given number is divisible by 6, so it would be divisible by 2 and 3.
✅As the last digit is 2, whatever be the value of X, it would be divisible by 2.
👉Since it is also divisible by 3, the sum of its digits is also divisible by 3. That is:
7 + X + 2 = 9 + X, must be divisible by 3.
That means X can be either 3, 6 or 9.
✅So, 3 is the required digit.
Answer is choice b.
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2️⃣3️⃣Suppose x = a(b - c), y = b(c - a),
z = c(a - b), then what is the value of
(x/a)^3 + (y/b)^3 + (z/c)^3?
[✅️Number System MCQs 👇👆]
2️⃣2️⃣What will be the result of
1397 x 1397?
2️⃣1️⃣ What is the value of (a - b), if
(a^2 - b^2)/(a + b) = 25?
📚Explanation for Question9️⃣👆👆
If the two-third of three - fourth of a number is 34, what will be the 20% of that number?
a) 13.4
b) 13.6
c) 13.7
d) 14
📝📝📝📝📝📝📝📝📝📝📝
Solution:
Let the number be X. According to the question,
2/3 * 3/4 * X = 34
6/12 * X = 34
Or,
1/2 * X = 34
So, X = 68
Now, 20% of 68 is
= 68 * 20/100
= 13.6
2️⃣0️⃣ If (64)^2 - (36)^2 = 20x, then what is the value of x?
1️⃣9️⃣The sum of four consecutive even numbers is 748, then which is the smallest number among them?
1️⃣8️⃣ If the sum of two numbers is 12 and their product is 35, then what will be the sum of their reciprocals?
📚Explanation to Question 8️⃣👆👆 ✅Which of the following is completely divisible by 45?
a) 331145
b) 306990
c) 181660
d) None of the above
📝📝📝📝📝📝📝📝📝📝📝
✅Solution:
👉A number that can be divisible by 3, 5, and 9 is also divisible by 45.
👉So, we check the divisibility of given numbers by the following rules -
1)A number is divisible by 3 if the sum of its entire digits is divisible by 3.
2)The number which ends with 0 or 5 is divisible by 5.
3)A number is divisible by 9 if the sum of its entire digits is divisible by 9.
👉since the unit digit of 306990is 0 it is divisible by 5. The sum of the digits is
3+0+6+9+9+0=27 which is divisible by 3 and 9 respectively, hence
306990 is divisible by both 3 and 9.
Therefore, the number 306990 fulfills all the requirements, so the answer is 306990.
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1️⃣7️⃣Suppose there is a number 'n'. When 'n' is divided by 5, the remainder will be 2. What will be the remainder when n2 is divided by 5?
