What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > What is the remainder when positive integer X...

Join the Discussion on the App

What is the remainder when positive integer X is divided by 40?

(1) 3X + 30 leaves remainder 93 when divided by 120.
(2) 5X - 10 leaves remainder 15 when divided by 20.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

Correct answer is option 'A'. Can you explain this answer?

Join for Free

Join for Free

Most Upvoted Answer

What is the remainder when positive integer X is divided by 40?(1) 3X ...

Statement Analysis:

Statement 1:
3X + 30 leaves a remainder of 93 when divided by 120.
This can be represented as: 3X + 30 = 120k + 93, where k is an integer.
This can be simplified as: 3X = 120k + 63
From this equation, we can see that X leaves a remainder of 21 when divided by 40. However, this information alone is not sufficient to determine the exact remainder when X is divided by 40.

Statement 2:
5X - 10 leaves a remainder of 15 when divided by 20.
This can be represented as: 5X - 10 = 20m + 15, where m is an integer.
This can be simplified as: 5X = 20m + 25
From this equation, we can see that X leaves a remainder of 5 when divided by 4. However, this information alone is not sufficient to determine the exact remainder when X is divided by 40.

Combined Analysis:
When we combine both statements, we have the following information:
X leaves a remainder of 21 when divided by 40 (from Statement 1)
X leaves a remainder of 5 when divided by 4 (from Statement 2)
By considering both pieces of information, we can determine that X leaves a remainder of 21 when divided by 40. Therefore, both statements together are sufficient to answer the question.
Therefore, the correct answer is option 'C'.

Answered by Talent Skill Learning · View profile

Community Answer

What is the remainder when positive integer X is divided by 40?(1) 3X ...

Statement (1) alone: 3X + 30 leaves a remainder of 93 when divided by 120. This statement provides information about the remainder of a specific expression involving X. We need to determine the remainder when X is divided by 40. By simplifying the expression, we can rewrite it as (3X + 30) = 120a + 93, where a is an integer. This equation tells us that 3X + 30 is congruent to 93 modulo 120. By subtracting 30 from both sides, we get 3X ≡ 63 (mod 120). Now, to find the remainder when X is divided by 40, we need to determine the value of X modulo 40. This can be done by reducing the equation further. By dividing both sides of the equation by 3, we get X ≡ 21 (mod 40). Therefore, the remainder when X is divided by 40 is 21. Statement (1) alone is sufficient to answer the question.

Statement (2) alone: 5X - 10 leaves a remainder of 15 when divided by 20. This statement provides information about the remainder of a different expression involving X. However, it doesn't provide any direct information about the remainder when X is divided by 40. Without knowing how the remainder relates to dividing X by 40, we cannot determine the remainder using this statement alone.

Since statement (1) alone is sufficient to answer the question, but statement (2) alone is not, the answer is A: Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Share via Whatsapp

Attention GMAT Students!

To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

View all answers Start learning for free

Explore Courses for GMAT exam

Similar GMAT Doubts

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwis e), you must indicate whether -Q.When a positive integer x is divided by a divisor d, the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22

View answer

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwis e), you must indicate whether -Q.Is the positive integer X divisible by 21?1. When X is divided by 14, the remainder is 42.When X is divided by 15, the remainder is 5

View answer

NumbersAll numbers used are real numbers.FiguresA figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.All figures lie in a plane unless otherwise indicated.Q.Is the positive integer X divisible by 21?1.When X is divided by 14, the remainder is 42.When X is divided by 15, the remainder is 5

View answer

What is the remainder when the positive integer x is divided by 6?Statement 1: When x is divided by 7, the remainder is 5.Statement 2: When x is divided by 9, the remainder is 3.

View answer

Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.What is the value of positive two-digit integer x?(1) The sum of the two digits is 5.(2) x is prime.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?.

Solutions for What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.(2) 5X - 10 leaves remainder 15 when divided by 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam