Quantitative Reasoning - I MCQs

Question 1:

If the sum of the first n odd integers is 225, what is the value of n?

A) 15
B) 16
C) 18
D) 25

Answer: A) 15

Explanation: The sum of the first n odd integers is given by $n^2$ . So, $n^2 = 225$ , thus $n = 15$ .

Question 2:

A car travels 60 km in the first hour, 50 km in the second hour, and 40 km in the third hour. What is the average speed of the car for the entire journey?

A) 50 km/h
B) 45 km/h
C) 40 km/h
D) 48.33 km/h

Answer: B) 45 km/h

Explanation: The total distance is $60 + 50 + 40 = 150$ km, and the total time is $1 + 1 + 1 = 3$ hours. The average speed is $1503=50\frac{150}{3} = 50$ km/h.

Question 3:

If $x$ is a positive integer and $x^2 – 4x = 0$ , what is the value of $x$ ?

A) 0
B) 2
C) 4
D) 8

Answer: B) 2

Explanation: $x^2 – 4x = 0$ can be factored as $x (x - 4) = 0$ , so $x = 0$ or $x = 4$ . Since $x$ is positive, the value of $x$ is 4.

Question 4:

The cost of 5 pens and 7 pencils is $3.50, and the cost of 4 pens and 5 pencils is $2.75. What is the cost of one pen?

A) $0.50
B) $0.75
C) $1.00
D) $1.25

Answer: B) $0.75

*Explanation: Let the cost of a pen be $p$ and the cost of a pencil be $q$ . Then, we have the system of equations:

$5 p + 7 q = 3.50$
$4 p + 5 q = 2.75$

Solving this system, we find that $p = 0.75$ .*

Question 5:

What is the value of $3 x + 5 y$ if $x = 2$ and $y = 4$ ?

A) 15
B) 20
C) 22
D) 23

Answer: C) 22

*Explanation: Substitute $x = 2$ and $y = 4$ into $3 x + 5 y$ :

$3 (2) + 5 (4) = 6 + 20 = 22$

So, the value is 22.*

Question 6:

A person invested $2,000 in a savings account with an annual interest rate of 5%, compounded annually. What will the value of the investment be after 3 years?

A) $2,350
B) $2,500
C) $2,610.25
D) $2,800

Answer: C) $2,610.25

*Explanation: The formula for compound interest is $\frac{r}{100})^t$ , where:

$P$ is the principal amount,
$r$ is the interest rate,
$t$ is the time in years.

Substitute the given values:

$\left( 1 + \frac{5}{100} \right)^3 = 2000(1.05)^3 = 2000 \times 1.157625 = 2610.25$

Thus, the value of the investment is $2,610.25.*

Question 7:

In a box, there are 10 red balls, 5 green balls, and 15 blue balls. If a ball is selected at random, what is the probability that the ball is either red or blue?

A) 0.5
B) 0.75
C) 0.85
D) 0.9

Answer: B) 0.75

*Explanation: The total number of balls is $10 + 5 + 15 = 30$ . The number of red or blue balls is $10 + 15 = 25$ . Therefore, the probability is:

$2530=56≈0.75\frac{25}{30} = \frac{5}{6} \approx 0.75$

So, the probability is 0.75.*

Question 8:

The average of five consecutive integers is 20. What is the largest of these integers?

A) 21
B) 22
C) 23
D) 24

Answer: C) 23

*Explanation: Let the integers be $x, x + 1, x + 2, x + 3, x + 4$ . The average is $x+(x+1)+(x+2)+(x+3)+(x+4)5=20\frac{x + (x+1) + (x+2) + (x+3) + (x+4)}{5} = 20$ . Simplifying:

$5x+105=20⇒5x+10=100⇒5x=90⇒x=18\frac{5x + 10}{5} = 20 \Rightarrow 5x + 10 = 100 \Rightarrow 5x = 90 \Rightarrow x = 18$

The integers are 18, 19, 20, 21, and 22. The largest is 22.*

Question 9:

If a rectangle has a length of 12 cm and a width of 5 cm, what is its area?

A) 60 cm²
B) 55 cm²
C) 40 cm²
D) 50 cm²

Answer: A) 60 cm²

Explanation: The area of a rectangle is given by $cm2\text{Area} = \text{length} \times \text{width} = 12 \times 5 = 60 \, \text{cm}^2$ .

Question 10:

What is the sum of the arithmetic sequence 3, 8, 13, …, up to the 20th term?

A) 500
B) 510
C) 505
D) 515

Answer: B) 510

*Explanation: The nth term of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$ , where $a_1 = 3$ and $d = 5$ . The 20th term is:

$a20=3+(20−1)×5=3+95=98a_{20} = 3 + (20-1) \times 5 = 3 + 95 = 98$

The sum of an arithmetic sequence is $Sn=n2(a1+an)S_n = \frac{n}{2} (a_1 + a_n)$ , where $n = 20$ , $a_1 = 3$ , and $a_n = 98$ :

$S20=202×(3+98)=10×101=510S_{20} = \frac{20}{2} \times (3 + 98) = 10 \times 101 = 510$

Thus, the sum is 510.*

Quantitative Reasoning – I MCQs