Cognizant Aptitude Screening 1 — Questions and Answers

Question 1: If the sum of two numbers is 12 and their product is 35, what is the sum of their squares?

60
74 (Correct answer)
84
90

Correct answer: 74

Let the two numbers be x and y. We are given x + y = 12 and xy = 35. To find the sum of their squares (x² + y²), we can use the algebraic identity (x + y)² = x² + 2xy + y². Rearranging this, we get x² + y² = (x + y)² - 2xy. Substituting the given values, x² + y² = (12)² - 2(35) = 144 - 70 = 74.

Question 2: A train travels 60 miles in 1.5 hours. What is its average speed?

40 mph (Correct answer)
45 mph
50 mph
55 mph

Correct answer: 40 mph

Average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the train travels 60 miles in 1.5 hours. Therefore, the average speed is 60 miles / 1.5 hours = 40 miles per hour (mph).

Question 3: If the ratio of the ages of two people is 3:5, and the sum of their ages is 40, what is the age of the older person?

15 years
20 years
25 years (Correct answer)
30 years

Correct answer: 25 years

Let the ages of the two people be 3x and 5x, according to the given ratio. The sum of their ages is 3x + 5x = 8x. Since the sum of their ages is 40, we have 8x = 40, which means x = 5. The ages are then 3 * 5 = 15 years and 5 * 5 = 25 years. The older person's age is 25 years.

Question 4: What is the next number in the sequence: 2, 6, 12, 20, ...?

26
28
30 (Correct answer)
32

Correct answer: 30

To find the next number in the sequence, we look for a pattern in the differences between consecutive terms. The differences are: 6-2=4, 12-6=6, 20-12=8. This shows that the differences are increasing by 2 each time (4, 6, 8). Therefore, the next difference should be 10, making the next number in the sequence 20 + 10 = 30.

Question 5: A person invests $1,000 at an annual simple interest rate of 5%. How much will the investment be worth after 3 years?

$1,100
$1,150 (Correct answer)
$1,200
$1,250

Correct answer: $1,150

Simple interest is calculated using the formula I = P * R * T, where I is the interest, P is the principal, R is the annual interest rate, and T is the time in years. Here, P = $1,000, R = 0.05 (5%), and T = 3 years. So, the interest earned is 1000 * 0.05 * 3 = $150. The total value of the investment after 3 years will be the principal plus the interest: $1,000 + $150 = $1,150.

Question 6: What is the value of x in the equation 3x - 7 = 11?

4
5
6 (Correct answer)
7

Correct answer: 6

To solve the equation 3x - 7 = 11, we first isolate the term with x. Add 7 to both sides of the equation: 3x - 7 + 7 = 11 + 7, which simplifies to 3x = 18. Then, divide both sides by 3 to solve for x: 3x / 3 = 18 / 3, resulting in x = 6.

Cognizant Aptitude Screening 1

If the sum of two numbers is 12 and their product is 35, what is the sum of their squares?