GMAT Exam  >  GMAT Tests  >  Practice Questions for GMAT  >  Test: Functions and Custom Characters - GMAT MCQ

Test: Functions and Custom Characters - GMAT MCQ


Test Description

10 Questions MCQ Test Practice Questions for GMAT - Test: Functions and Custom Characters

Test: Functions and Custom Characters for GMAT 2024 is part of Practice Questions for GMAT preparation. The Test: Functions and Custom Characters questions and answers have been prepared according to the GMAT exam syllabus.The Test: Functions and Custom Characters MCQs are made for GMAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Functions and Custom Characters below.
Solutions of Test: Functions and Custom Characters questions in English are available as part of our Practice Questions for GMAT for GMAT & Test: Functions and Custom Characters solutions in Hindi for Practice Questions for GMAT course. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free. Attempt Test: Functions and Custom Characters | 10 questions in 20 minutes | Mock test for GMAT preparation | Free important questions MCQ to study Practice Questions for GMAT for GMAT Exam | Download free PDF with solutions
Test: Functions and Custom Characters - Question 1

If [x] denotes the greatest integer less than or equal to x then is [x] = 0?

(1) [2x] = 0
(2) [3x] = 0

Detailed Solution for Test: Functions and Custom Characters - Question 1

Statement (1): [2x] = 0

In this case, [2x] will be 0 if and only if 2x is between 0 and 1 (exclusive), since [2x] represents the greatest integer less than or equal to 2x. Therefore, for [2x] to be 0, x must be between 0 and 0.5 (exclusive). Hence, statement (1) alone is sufficient to conclude that [x] = 0.

Statement (2): [3x] = 0

Similarly, [3x] will be 0 if and only if 3x is between 0 and 1 (exclusive). This means x must be between 0 and 1/3 (exclusive) for [3x] to be 0. Consequently, statement (2) alone is sufficient to conclude that [x] = 0.

Since both statements (1) and (2) independently lead to the conclusion that [x] = 0, each statement alone is sufficient to answer the question. Therefore, the correct answer is D: EACH statement ALONE is sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 2

If n is an integer and f(n) = f(n – 1) – n, what is the value of f (4)?

(1) f(3) = 14
(2) f(6) = -1

Detailed Solution for Test: Functions and Custom Characters - Question 2

To find the value of f(4), let's use the given recursive equation:

f(n) = f(n - 1) - n

We can start by finding f(3) using the equation.

Statement (1): f(3) = 14

Using the recursive equation, we have:

f(3) = f(2) - 3
f(2) = f(1) - 2
f(1) = f(0) - 1

Substituting f(1) and f(2) into the equation for f(3), we get:

f(3) = (f(0) - 1) - 2 - 3
f(3) = f(0) - 6

We know that f(3) = 14 from Statement (1), so we can solve for f(0):

14 = f(0) - 6
f(0) = 20

Now, we can use the recursive equation to find f(4):

f(4) = f(3) - 4
f(4) = 14 - 4
f(4) = 10

Therefore, from Statement (1) alone, we can determine that f(4) is equal to 10.

Statement (2): f(6) = -1

Using the same process as above, we can find f(4) if we know f(6), but Statement (2) does not provide any information about f(4). Therefore, Statement (2) alone is not sufficient to determine the value of f(4).

Since Statement (1) alone is sufficient and Statement (2) alone is not sufficient, the answer is D: EACH statement ALONE is sufficient to answer the question asked.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Functions and Custom Characters - Question 3

Max (x,y) is defined as the maximum of x and y, and Min(x,y) is defined as the minimum of x and y. What is the average of Max(x,60) and Min(40,x)?

(1) Min(x, 60) = x
(2) Max(40, x) = x

Detailed Solution for Test: Functions and Custom Characters - Question 3

Statement (1): Min(x, 60) = x

If Min(x, 60) = x, it means x is the smaller value between x and 60. Therefore, the expression Max(x, 60) will always be equal to x. We can write the expression as follows: (Max(x, 60) + Min(40, x)) / 2 = (x + Min(40, x)) / 2.

Since Max(x, 60) is always equal to x, we can simplify the expression: (x + Min(40, x)) / 2 = (x + x) / 2 = 2x / 2 = x.

Therefore, from Statement (1) alone, we can conclude that the average of Max(x, 60) and Min(40, x) is x.

Statement (2): Max(40, x) = x

If Max(40, x) = x, it means x is the greater value between x and 40. However, we cannot determine the value of Min(40, x) based on this information alone. The value of x can be greater than or equal to 40, in which case Min(40, x) would be 40. Or, x could be less than 40, in which case Min(40, x) would be x. Therefore, we cannot determine the average of Max(x, 60) and Min(40, x) solely from Statement (2).

Since Statement (1) alone is sufficient to determine the average as x, but Statement (2) alone is not sufficient, the answer is C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Test: Functions and Custom Characters - Question 4

If f(x) = 3x−5 for all x, then what is the value of x?

(1) f(x) = 22
(2) f(x2) = 22

Detailed Solution for Test: Functions and Custom Characters - Question 4

To find the value of x in the equation f(x) = 3x - 5, we can evaluate each statement separately:

Statement (1): f(x) = 22

Substituting 22 for f(x) in the equation, we have:

22 = 3x - 5

Solving for x:

3x = 27
x = 9

Therefore, from Statement (1) alone, we can determine that the value of x is 9.

Statement (2): f(x2) = 22

Substituting x2 for x in the equation, we have:

f(x2) = 3(x2) - 5

This statement does not provide a specific value for f(x2), and we cannot solve for x based on this equation alone. Therefore, Statement (2) alone is not sufficient to determine the value of x.

Since Statement (1) alone is sufficient to determine the value of x as 9, but Statement (2) alone is not sufficient, the answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 5

The function f is defined by f(x) = px, where x is an integer and p is a constant. What is the value of f(1)?

(1) f(2) = 81
(2) f(3) = -729

Detailed Solution for Test: Functions and Custom Characters - Question 5

Statement (1): f(2) = 81

Substituting 2 for x in the function, we have:

f(2) = p * 2 = 81

This equation alone does not provide enough information to determine the value of p or f(1). Therefore, Statement (1) alone is not sufficient to answer the question.

Statement (2): f(3) = -729

Substituting 3 for x in the function, we have:

f(3) = p * 3 = -729

This equation alone provides the information to determine the value of p. Dividing both sides of the equation by 3, we find:

p = -729 / 3 = -243

Now we can find the value of f(1) by substituting 1 for x in the function:

f(1) = p * 1 = -243 * 1 = -243

Therefore, from Statement (2) alone, we can determine that the value of f(1) is -243.

Since Statement (2) alone is sufficient to determine the value of f(1), but Statement (1) alone is not sufficient, the answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 6

If the symbol ∗ denotes either multiplication or division, what is the value of 6 ∗ 2?

(I) (5 ∗ 5) - (12 ∗ 2) = 1
(II) (9 ∗ 3) - (5 ∗ 5) = 2

Detailed Solution for Test: Functions and Custom Characters - Question 6

To determine the value of 6 ∗ 2, we need to identify whether the symbol ∗ represents multiplication or division. Let's evaluate each statement separately:

Statement (I): (5 ∗ 5) - (12 ∗ 2) = 1

This equation indicates that the result of (5 ∗ 5) minus (12 ∗ 2) is equal to 1. However, this equation alone does not provide enough information to determine the specific operation represented by ∗. Therefore, Statement (I) alone is not sufficient to answer the question.

Statement (II): (9 ∗ 3) - (5 ∗ 5) = 2

This equation indicates that the result of (9 ∗ 3) minus (5 ∗ 5) is equal to 2. Similarly to Statement (I), this equation alone does not provide enough information to determine the specific operation represented by ∗. Therefore, Statement (II) alone is not sufficient to answer the question.

When we consider both statements together, we have:

(5 ∗ 5) - (12 ∗ 2) = 1
(9 ∗ 3) - (5 ∗ 5) = 2

Although the specific operation represented by ∗ is unknown, we can see that both equations involve the same operands (5, 12, 2, 9, and 3) and the same result (1 and 2). This suggests that the operation ∗ might be division, as multiplication would yield different results. By assuming that ∗ represents division, we can check if the equations hold true:

(5 ÷ 5) - (12 ÷ 2) = 1 → 1 - 6 = 1 → False
(9 ÷ 3) - (5 ÷ 5) = 2 → 3 - 1 = 2 → False

Since the equations do not hold true when assuming ∗ represents division, we can conclude that ∗ represents multiplication. Therefore, 6 ∗ 2 denotes 6 multiplied by 2, resulting in 12.

Since Statement (I) alone is not sufficient to determine the operation ∗, but it provides additional information about the equation, it is sufficient to answer the question. Therefore, the answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 7

For all integers n, the function f is defined by f(n) = an, where a is a constant. What is the value of f(1)?

(1) f(2) = 100
(2) f(3) = -1,000

Detailed Solution for Test: Functions and Custom Characters - Question 7

To find the value of f(1), we need to determine the value of the constant a in the function f(n) = an. Let's evaluate each statement separately:

Statement (1): f(2) = 100

Substituting 2 for n in the function, we have:

f(2) = a * 2 = 100

This equation alone does not provide enough information to determine the value of a or f(1). Therefore, Statement (1) alone is not sufficient to answer the question.

Statement (2): f(3) = -1,000

Substituting 3 for n in the function, we have:

f(3) = a * 3 = -1,000

This equation alone provides the information to determine the value of a. Dividing both sides of the equation by 3, we find:

a = -1,000 / 3 = -333.33...

Now we can find the value of f(1) by substituting 1 for n in the function:

f(1) = a * 1 = -333.33... * 1 = -333.33...

Therefore, from Statement (2) alone, we can determine that the value of f(1) is approximately -333.33....

Since Statement (2) alone is sufficient to determine the value of f(1), but Statement (1) alone is not sufficient, the answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 8

If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?

(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.

Detailed Solution for Test: Functions and Custom Characters - Question 8

Statement (1): If r = s, then r θ s = 0.

From this statement, we know that if r is equal to s, then the result of the operation θ between r and s is 0. However, this statement does not provide specific information about the operation θ. We cannot determine which operation (+, −, ×, or ÷) corresponds to θ based solely on this statement.

Statement (2): If r ≠ s, then r θ s ≠ s θ r.

From this statement, we know that if r is not equal to s, then the result of the operation θ between r and s is not equal to the result of the operation θ between s and r. This statement provides a rule about the commutativity of the operation θ, indicating that the operation θ is not commutative. However, we still do not know the specific operation θ.

When we consider both statements together, we know that if r = s, then r θ s = 0, and if r ≠ s, then r θ s ≠ s θ r. These statements do not provide enough information to determine the exact operation θ. We only know that the operation θ must satisfy these conditions.

Therefore, Statement (1) alone is sufficient to establish a rule about the result of the operation θ, but we cannot determine the specific operation θ. The correct answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 9

If x&y = x2 − 2y, what is the value of a&2?

(1) 3&a = 13
(2) The value of a is either 2 or −2.

Detailed Solution for Test: Functions and Custom Characters - Question 9

Statement (1): 3&a = 13

Substituting 13 for 3&a in the equation, we have:

13 = a2 - 2(3)
13 = a2 - 6
a2 = 19
a = ±√19

From Statement (1) alone, we can determine the possible values of a as ±√19. However, this information is not sufficient to determine the value of a&2.

Statement (2): The value of a is either 2 or −2.

From this statement alone, we know that the value of a can be either 2 or −2. However, this information alone is not sufficient to determine the value of a&2.

When we consider both statements together, we know that a can be either ±√19 and that the value of a can be either 2 or −2. However, the value of a&2 is not affected by the possible values of a being ±√19. Since a&2 only depends on the arithmetic operation defined by the equation x&y = x− 2y, we can determine that a&2 will have a unique value regardless of the specific values of a.

Therefore, each statement alone is sufficient to determine the value of a&2. The correct answer is D: EACH statement ALONE is sufficient to answer the question asked.

Test: Functions and Custom Characters - Question 10

[x] is the greatest integer less than or equal to x, eg, [1.5] = 1. [m] = ?

(1) m > 2
(2) m < 3

Detailed Solution for Test: Functions and Custom Characters - Question 10

Statement (1): m > 2

From this statement, we know that m is greater than 2. However, we do not have any specific information about the decimal part of m or its relationship to the integer part. Therefore, we cannot determine the value of [m] based solely on this statement.

Statement (2): m < 3

From this statement, we know that m is less than 3. Similar to Statement (1), we do not have any specific information about the decimal part of m or its relationship to the integer part. Hence, we cannot determine the value of [m] based solely on this statement.

When we consider both statements together, we know that m is greater than 2 and less than 3. Since there are no integers between 2 and 3, we can conclude that the only possible value for [m] is 2.

Therefore, both statements together are sufficient to determine that [m] is equal to 2. The correct answer is C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

18 docs|139 tests
Information about Test: Functions and Custom Characters Page
In this test you can find the Exam questions for Test: Functions and Custom Characters solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Functions and Custom Characters, EduRev gives you an ample number of Online tests for practice

Top Courses for GMAT

Download as PDF

Top Courses for GMAT