Quantitative Aptitude - MCQ Practice Questions

Need to find LCM of 8, 12, 16. 8 = 2³, 12 = 2² × 3, 16 = 2⁴. LCM = 2⁴ × 3 = 48 minutes.

So they ring again at 12:00 + 48 min = 12:48 PM.

Let numbers be 12a and 12b where HCF(a,b)=1. LCM = 12ab = 240, so ab = 20.

Numbers: 12a and 12b with |12a - 12b| = 12, so |a - b| = 1.

If a=4, b=5: numbers are 48 and 60.

Check: 48-60 = -12 (difference is 12).

This question tests the concept of work rate and how much work is completed in a given time period.

Step 1: Find A's work rate per day

A completes the entire work in 20 days, so the work rate is 1 part per day.

Step 2: Calculate work completed in 5 days

Multiply the daily work rate by the number of days.

Step 3: Simplify the fraction

Reduce the fraction to its simplest form by dividing both numerator and denominator by 5.

A will complete $\frac{1}{4}$ of the work in 5 days.

This question asks us to find B's daily work rate when the total job can be completed in 15 days.

Step 1: Understand work rate definition

Work rate is the fraction of total work completed per day.

Step 2: Define total work as 1 complete job

Since B completes the entire job, the total work equals 1.

Step 3: Calculate B's daily work rate

B completes the job in 15 days, so divide the work by the number of days.

B's work rate is $\frac{1}{15}$ of the job per day, which means B completes one-fifteenth of the job each day for 15 days to finish it completely.

A's rate = $\frac{1}{12}$, B's rate = $\frac{1}{18}$.

Combined rate = $\frac{1}{12}$ + $\frac{1}{18}$ = $\frac{3}{36}$ + $\frac{2}{36}$ = $\frac{5}{36}$.

Time = $\frac{36}{5}$ = 7.2 days

This question tests the concept of inverse proportionality between the number of workers and the time required to complete a fixed task.

Step 1: Calculate total work in worker-days

Work is constant regardless of the number of workers, so we multiply workers by days.

Step 2: Set up the equation with new number of workers

With 10 workers, the same 40 worker-days of work must be completed.

Step 3: Solve for the number of days

Divide total work by the number of workers to find days required.

When 10 workers work together, they will build the same wall in 4 days.

Combined rate = $\frac{1}{10}$ + $\frac{1}{15}$ + $\frac{1}{30}$ = $\frac{3}{30}$ + $\frac{2}{30}$ + $\frac{1}{30}$ = $\frac{6}{30}$ = $\frac{1}{5}$.

Time = 5 days

A completes $\frac{1}{3}$ work in 5 days, so rate = $\frac{1}{15}$ per day.

Remaining work = $\frac{2}{3}$.

Days needed = ($\frac{2}{3}$)/($\frac{1}{15}$) = ($\frac{2}{3}$) × 15 = 10 days

Combined rate = $\frac{1}{8}$, A's rate = $\frac{1}{12}$. B's rate = $\frac{1}{8}$ - $\frac{1}{12}$ = $\frac{3}{24}$ - $\frac{2}{24}$ = $\frac{1}{24}$. B takes 24 days

Let A's rate = 1/x, B's rate = 1/y.

From equations: 3/x + 2/y = $\frac{1}{4}$ and 2/x + 3/y = $\frac{1}{3}$.

Solving: x = 30 days

60% work is done in 9 days.

Rate = 0.$\frac{6}{9}$ = $\frac{1}{15}$ per day.

Total days = 1/($\frac{1}{15}$) = 15 days

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

Let numbers be 5x and 7x.

Then 5x + 7x = 120, so 12x = 120, x = 10.

Larger number = 7 × 10 = 70

Odd numbers between 10 and 30: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.

Count = 10