Data Interpretation - Caselets for Competitive Exams

Data Interpretation - Caselets

Q. If 2x + 3 = 11, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

2x = 11 - 3 = 8, so x = 8/2 = 4.

Correct Answer: B — 3

Q. If a number is divisible by both 4 and 6, what is the smallest positive integer it can be?

A. 12
B. 24
C. 6
D. 8

Solution

The least common multiple of 4 and 6 is 12.

Correct Answer: A — 12

Q. If a number is divisible by both 4 and 6, what is the smallest possible value?

A. 12
B. 24
C. 36
D. 48

Solution

The least common multiple of 4 and 6 is 12.

Correct Answer: A — 12

Q. If a polynomial f(x) = x^2 - 4x + 4, what is f(2)?

A. 0
B. 1
C. 2
D. 4

Solution

f(2) = 2^2 - 4*2 + 4 = 0.

Correct Answer: A — 0

Q. If a polynomial f(x) = x^2 - 5x + 6, what are its roots?

A. 1 and 6
B. 2 and 3
C. 3 and 2
D. 5 and 1

Solution

Factoring gives (x-2)(x-3) = 0, so roots are 2 and 3.

Correct Answer: B — 2 and 3

Q. If a sequence is defined as a_n = 3n + 1, what is a_4?

A. 10
B. 11
C. 12
D. 13

Solution

a_4 = 3(4) + 1 = 12 + 1 = 13.

Correct Answer: B — 11

Q. If the sequence is defined by a_n = 3n + 1, what is a_4?

A. 10
B. 11
C. 12
D. 13

Solution

a_4 = 3(4) + 1 = 12 + 1 = 13.

Correct Answer: A — 10

Q. If x + 3 = 10, what is the value of x?

A. 5
B. 6
C. 7
D. 8

Solution

x = 10 - 3 = 7.

Correct Answer: B — 6

Q. If x is an integer such that 3x + 5 is even, what can be said about x?

A. x is even
B. x is odd
C. x can be any integer
D. x is a prime number

Solution

For 3x + 5 to be even, x must be odd.

Correct Answer: A — x is even

Q. If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?

A. 1
B. 2
C. 3
D. 4

Solution

The smallest positive integer satisfying x ≡ 3 (mod 5) is 3.

Correct Answer: C — 3

Q. What is the 10th term of the arithmetic sequence 2, 5, 8, ...?

A. 29
B. 30
C. 31
D. 32

Solution

The nth term is given by 2 + (n-1) * 3. For n=10, it is 2 + 27 = 29.

Correct Answer: A — 29

Q. What is the 5th term of the arithmetic sequence 2, 5, 8, ...?

A. 11
B. 14
C. 17
D. 20

Solution

The common difference is 3; the 5th term is 2 + 4*3 = 14.

Correct Answer: B — 14

Q. What is the 5th term of the arithmetic sequence where the first term is 2 and the common difference is 3?

A. 11
B. 14
C. 17
D. 20

Solution

The nth term is given by a_n = a_1 + (n-1)d. Here, a_5 = 2 + 4*3 = 14.

Correct Answer: B — 14

Q. What is the remainder when 45 is divided by 7?

A. 1
B. 2
C. 3
D. 4

Solution

45 divided by 7 is 6 with a remainder of 3.

Correct Answer: A — 1

Q. What is the sum of the first 10 positive integers?

A. 45
B. 50
C. 55
D. 60

Solution

The sum is 10(10 + 1)/2 = 55.

Correct Answer: A — 45

Q. What is the value of 12 mod 5?

A. 1
B. 2
C. 3
D. 4

Solution

12 divided by 5 is 2 with a remainder of 2.

Correct Answer: C — 3

Q. What is the value of 5^3?

A. 125
B. 150
C. 175
D. 200

Solution

5^3 = 125.

Correct Answer: A — 125

Q. What is the value of 7^3 mod 5?

A. 1
B. 2
C. 3
D. 4

Solution

7 mod 5 = 2, thus 2^3 mod 5 = 8 mod 5 = 3.

Correct Answer: C — 3

Q. What is the value of x in the equation 5x - 15 = 0?

A. 2
B. 3
C. 4
D. 5

Solution

5x = 15, so x = 15/5 = 3.

Correct Answer: B — 3

Q. Which of the following is true for the polynomial x^2 - 5x + 6?

A. It has no real roots
B. It has one real root
C. It has two real roots
D. It is always positive

Solution

The roots are x = 2 and x = 3, so it has two real roots.

Correct Answer: C — It has two real roots

Q. Which polynomial has a degree of 3?

A. x^2 + 2
B. 2x^3 + x
C. x + 1
D. 3

Solution

The polynomial 2x^3 + x has the highest exponent of 3.

Correct Answer: B — 2x^3 + x

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