Quantitative Aptitude - MCQ Practice Questions

Sum of first n natural numbers = n(n+1)/2.

Here n=10, so sum = 10(11)/2 = $\frac{110}{2}$ = 55

Check: 21=3×7 (not prime), 23 is only divisible by 1 and 23 (prime), 25=5×5 (not prime), 27=3×9 (not prime).

So 23 is the smallest prime greater than 20.

Factors of 48: 1,2,3,4,6,8,12,16,24,48.

Factors of 64: 1,2,4,8,16,32,64.

Common factors: 1,2,4,8,16. HCF = 16

If a number is divisible by both 3 and 5, and 3 and 5 are coprime (HCF=1), then the number must be divisible by their product: 3×5 = 15

First five prime numbers are 2, 3, 5, 7, 11.

Product = 2 × 3 × 5 × 7 × 11 = 2310

This question asks us to identify which number is a perfect square (a number that equals an integer multiplied by itself).

Step 1: Understand Perfect Squares

A perfect square is a number that can be expressed as n × n where n is an integer.

Step 2: Check Each Option

Test each option by finding if its square root is a whole number.

Step 3: Verify the Correct Answer

Only 169 has a whole number square root.

169 is a perfect square because 13 × 13 = 169, making the correct answer (B).

Largest 3-digit number = 999, Smallest 3-digit number = 100.

Difference = 999 - 100 = 899

This question asks us to find an unknown number based on a sequence of arithmetic operations performed on it.

Step 1: Set up the equation

Let the unknown number be x. According to the problem, when x is multiplied by 8 and then 15 is subtracted, the result is 49.

Step 2: Isolate the variable term

Add 15 to both sides of the equation to move the constant to the right side.

Step 3: Solve for the number

Divide both sides by 8 to find the value of x.

The number is 8, which corresponds to answer choice (B).

This question asks us to find the average value of the numbers 1 through 15.

Step 1: Identify the first 15 natural numbers

The first 15 natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

Step 2: Calculate the sum of first 15 natural numbers

Use the formula for sum of first n natural numbers:

Step 3: Calculate the average

Average is the sum divided by the count of numbers.

The average of the first 15 natural numbers is 8.

To find the remainder when a number is divided by another, use the division algorithm: $\text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}$

Step 1: Set up the division

We need to express 527 in the form:

where $q$ is the quotient and $r$ is the remainder with $0\le r<15$.

Step 2: Divide 527 by 15

Perform the division:

The quotient is $q=35$.

Step 3: Calculate the product

Step 4: Find the remainder

Subtract the product from the dividend:

Since $0\le 2<15$, this is a valid remainder.

Verification:

To find the remainder when 527 is divided by 15:

15×35=525

Now subtract:

527−525=2

Therefore, the remainder is 2.

**Answer: The remainder is $2$ (Option A)**

Using dividend = divisor × quotient + remainder: Number = 11 × 9 + 5 = 99 + 5 = 104

51 = 3 × 17 (not prime), 53 is prime (only divisible by 1 and 53), 55 = 5 × 11 (not prime), 57 = 3 × 19 (not prime).

Therefore, 53 is the smallest prime greater than 50.

36 = 2² × 3².

Number of factors = (2+1)(2+1) = 3 × 3 = 9.

The factors are: 1, 2, 3, 4, 6, 9, 12, 18, 36.

12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.

∛512 = ∛(8³) = 8, since 8 × 8 × 8 = 512.

Odd numbers between 10 and 50: 11, 13, 15, ..., 49.

This is an AP with first term 11, last term 49, and common difference 2.

Number of terms = (49-11)/2 + 1 = 19 + 1 = 20.

Let the number be n.

Given: n = 8k + 5 for some integer k.

When divided by 4: n = 8k + 5 = 4(2k) + 4 + 1 = 4(2k + 1) + 1.

Therefore, remainder = 1.

Prime factorization of 360: 360 = 2³ × 3² × 5.

The unique prime factors are 2, 3, and 5.

Product = 2 × 3 × 5 = 30.

Find HCF of 48 and 64 using Euclidean algorithm: 64 = 48 × 1 + 16; 48 = 16 × 3 + 0. Therefore, HCF = 16.

12 = 2² × 3; 18 = 2 × 3². LCM = 2² × 3² = 4 × 9 = 36.